Index
actuation, microscale, 3, 4, 407. See also pumpadvection, chaotic
aggregation. See bubble, aggregation; particle,aggregation; particle, concentration(or trapping); protein, aggregation
assemblyby entropic or excluded volume effects, 45particle. See also particle, aggregation
erasure though AC electro-osmotic flowreversal, 264, 335–336
using AC electro-osmotic flow, 263self or directed molecular assembly, 3
asymmetric (or antisymmetric) solution, 56, 57,62
asymptotic matching, 210–212dipole analysis of infinite prolate spheroids, 174double layer solution to Ohmic bulk solution,
83–85, 204, 206, 258, 259intermediate asymptote, 216–217, 218atmospheric breakdown. See corona discharge;
dielectric breakdownatomic dipole. See dipole, microscopicaveraging, 34, 57
coarse graining, 4, 11, 34charge density and electric force, 11, 14, 30dipole description, 16regularizing integration to remove
singularity, 376. See also singularitycross-sectional, 4, 69, 106ion transport and charge conservation
equations, 241time, 34, 73
electric force, 251–252, 257electro-osmotic slip velocity, 256–257hydrodynamic equations, 261–262product of two harmonic functions, 286
transverse, convection–diffusion equation,118–120
bacteria, 7–8. See also pathogenassembly, 176detection. See detection
differentiation, 401–402discrepancy in classical dielectrophoretic
theory, 288metabolism and growth detection, 180–183.
See also detectionband broadening, 147, 150. See also dispersion,
hydrodynamicbandgap illumination, 174biased reptation, 144, 147. See also
electrophoresisbifurcation
in electrospray data with voltage changes, 358of symmetric and nonsymmetric solutions,
60–62of vortex structures, 338
biharmonic equation. See stream functionbinding interaction, 162biosensor. See detectionbirefringence, 176Bjerrum length, 57–58, 139, 303“blob” theory, 154Bode plot, 163–165. See also Nyquist plotBohr atom, 160Boltzmann distribution, 38, 68. See also
Boltzmann factor; transformation,Boltzmann
azimuthal, 135–137, 138global stability, hydrostatic, 38, 40–41, 72–73in double layer, 76. See also Debye double
layerinappropriate for nonequilibrium
electrokinetics, 156. See electrokinetics,nonequilibrium
no analytical solution for charged particle ofarbitrary geometry, 45
nonuniform, due to electromigration, 137.See also polarization, field-induced doublelayer polarization
Boltzmann factor, 68, 80. See also Boltzmanndistribution; transformation, Boltzmann
boundary condition“bulk-scale,” 83–85
475
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476 Index
constant (or zero) potential, 48constant field, 72, 124, 142
boundary condition (cont.)effective external field condition, 216, 259,
266effective slip, 257far field, 39, 142, 170, 204, 206, 219
elimination of zeroth harmonic mode in DCTaylor cones, 404
impenetrable or ideally polarizable surface.See boundary condition, no-flux
insulated, 207, 271–272, 279. See also surface,insulating
due to double layer screening, 97. See alsoscreening
interfacial, 16, 170between gas and liquid phases, 297, 357electric field or displacement continuity and
jump conditions, 16, 18, 168, 190, 194, 381,425
normal stress jump, 28, 352, 377, 424potential continuity, 194, 195, 353tangential stress balance, 424
kinematic, 28, 382, 425mixed Stern layer, 42, 43, 45no-flux
flow, 97ion, 83, 113, 124, 142, 194, 259solute concentration, 119–120
no-slip, 124, 206, 424suppression of centrifugal force, 399
Robin, 60, 195slip, 88, 97, 113. See also electro-osmosis,
electro-osmotic slipStern layer condition, 56–60, 303–304surface, 48symmetry, 68, 70, 88no-penetration. See boundary condition,
no-fluxboundary layer, 62
Ekman, 399Bretherton equation, 430Brownian dynamics, 154Brownian motion, 401bubble
absence of double layer charging, 295aggregation, 90conducting, due to plasma generation, 295.
See also ion, plasmadisruption of electrospray stability, 351dynamics, endowed by AC induced dipoles,
338field-induced double layer polarization effects,
284. See also polarization, field-induceddouble layer polarization
frequency-dependent attraction (coalescence)and repulsion, 299–300. See alsodielectrophoresis, bubble
generation
circumvented with the use of monoliths, 151,270. See also reaction, electrolytic;reaction, Faradaic
due to increased current or electric inelectrolyte, 93
in DC electrokinetics, 6, 7, 155. See alsoreaction, electrolytic; reaction, Faradaic
suppression through high-frequency ACfields. See electric field, AC
multiphase microchannel flow, 99, 344. See alsobubble, transport in capillaries
spacers, 96train (or slugs), 99, 439–440translation speed. See capillary numbertransport in capillaries, 438–441. See also
bubble, multiphase microchannel flowtrapping, 6
buffer solutionaddition to regulate solution pH and osmotic
pressure, 6, 67–68, 129, 156. See also pHeffect of viscosity on dielectrophoretic mobility,
322–324
capacitorcurrent, 163double layer. See Debye double layer, as
capacitorrelaxation frequency, 446Stern layer, saturation at low frequencies, 304
capillary. See channelcapillary number, 428, 439, 441capillary ridge, 426–428, 429, 431capillary tube bundle, 76, 91–92, 96. See also
channelcell
blood cellage discrimination via dielectrophoresis,
311–321. See also dielectrophoresis,cellular
charge relaxation time, 311–312, 314separation, 399. See also separationshell model, 312, 313–315transport, 99–102
culture, 1dielectric properties, measured by
electrorotation, 327. See alsoelectrorotation
dispersive behavior, 177–178. See alsodielectric, dispersion
electrophoresis. See electrophoresis, cellularencapsulation, 387ion-channel, 177lysis
due to DC penetration current and electricfield, 6. See also protein, denaturing
prevented through use of high frequency ACelectric fields, 7, 251, 402
manipulation. See particle, manipulationmembrane. See membrane, lipid bilayer
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Index 477
orientation control, using electrorotation, 327.See also electrorotation
separation, 146, 333. See also separationthin double layers, 129
centrifugation, driven by ionic wind, 394–402channel
bicontinuous pore morphology, 90, 91. See alsochannel, geometry
charged, due to double layer overlap, 66–67.See also Debye double layer, overlap
closed microchannel system, 411. See alsodigital microfluidics; open microfluidicsystem
contracting–expanding, 123–127corner. See singularitycritical size to suppress electrokinetic fingering
instability, 116curved, dispersion effects, 122. See also
dispersion, hydrodynamic entrance effects,71,86,123
exit effects, 123geometry
dispersion effects, 121–122. See alsodispersion, hydrodynamic
effect on electro-osmotic slip, 79, 81. See alsoelectro-osmosis, electro-osmotic slip
load, 90–92microchannel, dimension comparable to Debye
length, 88. See also Debye double layer,overlap
nanochannel or nanopore, 5conductivity gradient, 236critical voltage for flow, 96. See also electric
field, critical (or threshold) fieldcurrent–voltage (I–V) characteristics,
239–250. See also current–voltage (I–V)characteristics
dimension comparable to Debye length,79–81. See also Debye length
electro-osmosis, 86–88. See electro-osmosis,in nanochannels or nanopores
extended polarization. See surface, extendedpolarization
ion depletion and enrichment, 202, 214, 215.See also surface, extended polarization;iondepletion (or diffusion) region; ion,enrichment region
large hydrodynamic resistance, 90. See alsohydrodynamic resistance
overall zero net charge, 87overlapping double layers. See Debye
double layer, overlappermselective, limiting resistance region, 239,
242, 245, 248–250. See also current–voltage(I–V) characteristics; current density,limiting
permselective, Ohmic region, 239, 245, 248.See also current–voltage (I–V)characteristics; Ohmic system (or region)
permselective, overlimiting region. Seeoverlimiting region; current–voltage (I–V)characteristics
optimum size, 90, 93streaming current, 80
packing, 89–90, 130, 150. See also packingfraction
porosity, 93, 94pressure-driven bubble transport, 439–440.
See also bubble, transport in capillaries;flow, pressure-driven
profiling, 122pump, 88, 90–94small channel limit, overlapping double layers,
65–71. See also Debye double layer,overlap
surface charging, 35. See also charge, surfaceT-junction, 197tortuosity, 91typical dimension, 3
charge, 8accumulation. See also charge, buildup
at contact line, 415. See also charge, trappingat critical point, 226, 233at electrode, 256at electrospray meniscus tip, 346, 364, 368,
376at ion-selective granule surface, 201, 220.
See also charge, buildupbalance with conduction current, 260due to conductivity gradient, 295due to electrothermal effect, 281, 283.
See also electrothermal effectdue to interfacial conductivity jump,
239in collapsed layer, 56. See also collapsed
diffuse double layerin diffuse double layer, 302. See also charge,
buildupin double layer. See Debye double layer,
chargingin nanochannels or nanopores, 226, 239in Stern layer, 303, 304. See also ion,
adsorptioninsufficient time in high frequency AC
electrosprays, 370outside double layer with AC fields,
280over several period cycles in nonsymmetric
electrolytes, 170zero in electroneutral Ohmic region, 33
advection, 74. See also current; ion, convectionbasis for electrophoretic separation, 144.
See also electrophoresis
bound, 40, 169. See also charge density, boundcharge
along interface, 359, 434in Stern layer, 50, 54. See also Stern layerlocal orientation under electric field, 156
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478 Index
number density balances charges in doublelayer, 155
polarization in dielectric materials, 156.See also dielectric; polarization
polarization time scale, 161. See alsodielectric, relaxation time
charge (cont.)buildup
in extended polarization layer, 214. See alsocharge, accumulation
at corner geometries, 7. See also singularityat interfaces of ion-selective membranes, 5,
71boundary effects, giving rise to streaming
potential, 123due to transient charging, 201, 202. See also
charge, accumulationpolar, 308. See also charging, polar
bulkrelaxation to interface, 345, 360, 362, 363,
368, 376stabilization of capillary instabilities at high
frequency, 368conduction. See conduction, ionconservation, 10, 32. See also Gauss’ Law;
transport, convective-diffusive equationalong cell surface, 135
convection. See convection, iondrainage
due to drop ejection at contact line,447
due to tangential conduction, 304. See alsodiffuse double layer, tangential conduction
entrainmentin electrospray meniscus, 368–369, 372, 374,
378. See also electrospray; meniscustime scale, 73. See also RC time scale
equilibriation, 21. See also equilibrium,Poisson–Boltzmann
excessdue to tangential convection or surface
reaction at high Péclet numbers, 220in double layer, 47, 54, 73, 76in extended polarization layer, 205. See also
surface, extended polarizationsteric effects in double layer, 268
free, 169. See also charge, mobileabsent in perfect dielectrics, 156. See also
dielectricin field-induced double layer polarization,
156. See also polarization, field-induceddouble layer polarization
immobile, 56, 71induced, 16, 175, 184
atomic surface charge, 315flow generation in thick polarization layer
limit, 215. See also polarization layersaturation, 186, 442injection, 415. See also charge, accumulation;
dielectric, dielectric layer (or coating)
interfacial, 368, 436. See also charge, surface;polarization, interfacial
arising due to permittivity jump, 168conservation, 169, 358. See also charge,
conservationevolution equation, 434in electrospinning, 386. See also charge
density, interfacialinduced, 377. See also charge, inducedresponsible for jump in normal field, 16.
See also boundary condition, interfacialinversion. See charge, reversalleakage into atmosphere, 415line, constant field, 271mobile, 81. See also charge, space; ion,
mobilityassociated with Faradaic polarization, 161.
See also charging, Faradaicin collapsed and diffuse double layers, 50, 53,
55, 56in double layer, 137necessity in dielectric liquid pumps, 20–25
moiety, 136net charge giving rise to momentum transfer in
double layer, 76. See also Debye doublelayer
net charge on dipole, 170. See also dipolepoint, 9, 10, 13, 130redistribution
along contact line, 418along interface, 434
relaxation, 23, 167–168, 177characteristic relaxation frequency. See
frequency, characteristicdue to tangential conduction, 225
relaxation time, 162, 233, 345. See alsodielectric, relaxation time; dipole,relaxation time; diffusion layer, relaxationtime; Debye double layer, relaxation time;polarization, relaxation time
repulsion. See electrostatic, repulsionreversal
due to anticorrelated fluctuations betweencounterions and surface charges, 57–58
due to counterion condensation on colloids,138–139, 325
due to pH reduction, 101. See also pHduring AC electro-osmosis, 254. See also
electro-osmosis, ACnot possible through polyvalent counterion
condensation or adsorption, 63separation, 57, 137, 346. See also charge,
relaxationspace
exact differential, 44generation due to ion injection, 27in double layer, 35. See also charge, mobileresponsible for electric body force, 17, 18, 20,
39. See also charge, mobile; forceelectric
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Index 479
role in electrospray conical menisci,354–356
storage, 252. See also Debye double layer, ascapacitor; diffuse double layer, capacitance;double layer, capacitance; ion, adsorption
surfaceacquisition, 35–36, 73balances charge in nanochannel, 66. See also
channel, nanochannel or nanopore; Debyedouble layer, overlap
excess, eliminated by superimposing AC fieldon DC voltage, 361
jet, 347natural, principle behind equilibrium
electrokinetics, 7. See also electrokinetics,equilibrium
near cancellation with counterion charge incollapsed layer, 52. See also collapseddiffuse double layer
nonuniform, due to tangential surfacecurrents, 98, 137. See also ion, tangentialconduction
produces normal surface field in double layer,77
reversal. See charge, reversalrole in double layer charging, 252. See also
Debye double layer, chargingspecifies nanochannel conductance, 247–248.
See also channel, nanochannel ornanopore
total residence charge in electrospray meniscuscone, 375
transfer across interface in extendedpolarization layers, 287. See also extendedpolarization layer
transport. See ion, transporttrapping
in insulating dielectric layer, 415–416. Seealso charge, accumulation; dielectric,dielectric layer (or coating)
in thick double layers. See charge, storageresponsible for contact line pinning,
444charge density
accumulated charge, 280bound charge, 159, 169. See also charge, bound;
charge density, surface polarizationfree, 159, 169. See also charge, spacein electrospray aerosol drops, 347interfacial, 382–383
reduction due to charge trapping and partialscreening, 415. See also charge,accumulation; dielectric, dielectric layer(or coating)
line charge, 11, 359surface charge, 11
at electrospray orifice, 383balances charge in double layer to maintain
electroneutrality, 39. See alsoelectroneutrality
balances volume charge in nanopore, 68. Seealso channel, nanochannel or nanopore;Debye double layer, overlap
compensated by counter-ions in collapsedlayer, 53, 141. See also collapsed diffusedouble layer
dependence on particle size, 290determined from I–V characteristics in
Ohmic region, 247–248difference gives rise to electrophoretic
separation, 130. See also electrophoresisdistribution in electrospray meniscus,
374–375, 377does not affect membrane properties, 311.
See also membraneeffect on apparent viscosity, 126. See also
viscosity, apparentfunction of the particle potential, 56–68imbalance with counterion density in
nonequilibrium cases, 98. See alsoelectrokinetics, nonequilibrium
in Stern layer, 54–55, 303induced, 169. See also charge, inducedrelationship with ζ potential, 102. See also
potential, zeta (or ζ ) potentialtotal, comprising of free and induced charge
densities, 169surface polarization, 158. See also charge
density, bound chargetemperature induced space charge, 281volume charge, 11, 13
around particle, 302as exact differential, 38, 40balances surface charge density in diffuse
double layer, 55bulk distribution in nanopore balances
surface charge, 68convective–diffusive equation, 258. See also
transport, convective–diffusive equationgives rise to electric force, 30imbalance with surface charge density in
nonequilibrium cases, 98in polarized region, 80negligible in diffuse double layer, 304of bulk charges discharging in electrospray
meniscus, 368–369of mobile counterions in diffuse double layer,
74, 77scaling, 281total over all ionic species, 38total, comprising free and bound charge
densities, 159
vanishes in electroneutral Ohmic region, 29.See also electroneutrality
charge residue model, 348charged surface
concentration polarization, 36. See also charge,surface
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480 Index
role in the generation of equilibriumelectrokinetic phenomena, 74. See alsocharge, surface
chargingAC, 73, 251–253. See also Debye double layer,
chargingdependence on frequency, 256. See also
frequency, AC fieldin electrowetting, 441–442, 443
charging (cont.)modified model to account for double layer
steric effects, 268. See also steric effectasymmetric, around ion-specific granule, 233capacitive, 184, 217–220, 221, 265. See also
electrode, polarizationdriven by normal diffusion, 293, 295–300. See
also ion, adsorption; charging, normalfield
in dielectrophoresis, 285, 292, 300. See alsopolarization, field-induced dielectricpolarization
mechanism for AC electro-osmotic flow.See electro-osmosis, AC
transient, at low Péclet numbers, 220conductive
in dielectrophoresis, 285, 313. See alsodielectrophoresis; current, conduction;polarization, conductive
convection enhancement, 226DC, 252–253double layer. See Debye double layer, chargingdynamic. See charging, transientFaradaic, 161, 264. See also reaction, Faradaicfield-induced. See polarization, field-inducedincomplete at high frequencies. See screening,
incomplete, at high frequenciesinterfacial. See polarization, interfacialmechanisms for dielectrophoresis, 307. See also
dielectrophoresisnonuniform. See polarization, nonuniformnormal field, 7. See also Debye double layer,
normal chargingpolar
electroneutral sublayer, 227, 231. See alsoion, dynamic superconcentration
in double layer, 231, 305–311. See also ion,dynamic super-concentration
surfaceat poles. See charging, polarrole in field-induced double layer
polarization of nonconducting particles,284. See also polarization, field-induceddouble layer polarization
time, 87transient
due to external DC field, 201–203, 217suppression due to external field screening,
201. See also screeningtermination due to tangential convection,
217, 220–221. See also ion, tangentialconvection
chemical potential. See potential, chemicalchromatography
high-performance liquid chromatography(HPLC), 89, 148, 150, 378
mobile phase, 149, 150stationary phase, 148, 150
Clausius–Mossotti factor, 172, 287, 329, 333modified to account for diffuse double layer
tangential conduction, 302–303, 304–305.See also ion, tangential conduction
modified to account for normal capacitivecharging, 298. See also dielectrophoresis,bubble
particle-size dependent, 299co-ion
exclusion from ion-selective granule, 201exclusion from nanochannel, 248. See also
channel, nanochannel or nanoporecollapsed diffuse double layer, 50
conductance, 53, 140–141conduction, 139–140. See also ion, tangential
conductioncontains Stern layer, 53–54convection, 140current flux contribution in nanochannel
electro-osmotic flow, 87. See alsoelectro-osmosis, nanochannel or nanopore
disappearance at large medium conductivities,284
field line penetration, 284–285. See also electricfield, penetration
low-conductivity correction to crossoverfrequency, 288–294. See alsodielectrophoresis
screening due to trapping of large biomolecules,323
screening in weak electrolyte system, 52thickness, 48, 50, 51–52, 53
collision length, 32. See also mean free pathcolloid. See also particle
ability for nanocolloids to store ions and toform dipoles, 294
aggregation, in double layer, 322–324. See alsoaggregation
challenges in microfluidic systems involvingnanocolloids, 3
concentration (or trapping). See particle,concentration (or trapping)
counter-ion condensation on surface, 138–139.See also ion, condensation
crystal morphology. See dielectrophoresis,molecular
differential mobility analyzer, 406difficulty of manipulation with
dielectrophoresis, 174. See alsodielectrophoresis
disordering effects, 325
electrospray ring deposition patterns, 404–406.See also electrospray
nanocolloid manipulation, 2, 5
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Index 481
selection of multiple discrete harmonics in DCelectrospraying, 404–406
self-assembly, 294surface functionalization, 325suspension viscosity, 398
colloidal docking. See dockingcolloidal interaction. See particle-particle
interactioncompressibility effects. See electrostrictionconcentration gradient, in diffusion layer,
233concentration polarization. See polarization,
concentrationconducting layer, 50, 136–137conducting liquid. See electrolyteconformal mapping, 192, 419, 426conservation equations, 14, 15, 203.
See also transport, convective–diffusiveequation
contact angle, 409. See also wettingadvancing. See contact angle, hysteresisdynamic condition, 429–431frequency dependence, 443hysteresis, 412–414, 442macroscopic (or apparent), 421
dynamic, 431. See also contact angle,dynamic condition
static (or equilibrium), 421. See alsoelectrowetting, static
microscopic, voltage independent in localcontact line region, 421
receding. See contact angle, hysteresisstatic or equilibrium, 411
contact linedynamic, 409equilibrium (or static)
force balance, 409–410intermolecular interactions, 431, 446. See also
precursor filmmolecular slip, 418. See also slippinning, 412, 443–444pitting of electrode surface. See contact line,
pinningsaturation, 414–417, 422, 442–447
analogy with paramagnetism,417
critical field, 442critical radius, 442
singularity. See singularity, contact linecontinuum mechanics, validity, 4, 14convection layer, 209convection
charge or ion. See ion, convectionhydrodynamic
concentration homogenization, 334in multiscale particle trapping, 270responsible for distortion and instability of
diffusion layer, 233responsible for particle migration and vortex
formation around corners, 190solute, 117–119, 224
time scale, 117corona discharge, 20, 369–370, 394–395. See also
dielectric breakdowncorona wind. See ionic windCoulomb force. See force, electric (or
electrostatic)Coulomb’s Law, 9–10, 13, 359
coarse grained, 11, 20Coulombic fission, 346, 347, 348, 365
absence in AC electrospraying andelectrospinning, 370, 386
counterionequilibriation in double layer, 252in interfacial polarization (double) layer,
346saturation assumption in ion-selective granule,
221critical field. See electric field, critical fieldcritical point gate, 225–226crystal lattice site, 36current, 29–30. See also ion, transport
AC, 7insufficient time to penetrate biological cells,
251balance. See transport, convective–diffusive
equationcapacitive charging, 7, 170, 271. See also
charging, capacitivenormal, in thick diffuse double layers, 291,
293, 300–301, 308charging, 168, 273. See also charging, transientconduction, 167, 170. See also current,
displacement; ion, conductionarising from streaming current, 74assumption of dominance over convection
current in AC electro-osmosis, 257in double layer, 53. See also Debye double
layerinterfacial, 358penetration into ion-selective granule,
221tangential assumption breaks down for large
diffuse double layers, 300convective, 218, 358. See also ion, convectionDC, penetration damages biological cells, 6diffusion, coupling with flow velocity,
125displacement, 167electrospinning jet, 382–383. See also current,
electrosprayelectrospray, 356, 358. See also current,
electrospinning jetenhancement due to gas-phase ionization
effects, 358Faradaic charging, 7. See also reaction,
Faradaic; charging, Faradaic
flux, 30, 87, 155nanochannel or nanopore, controlled by
intrachannel and polarization layerresistances, 245
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482 Index
limiting, 215, 243–245. See also current density,limiting
breakdown of electroneutral assumption,245. See also electroneutrality
minimization through electrolyte inelectro-osmotic pump, 93. See alsoelectro-osmosis,
electro-osmotic pumpOhmic. See current, conductionoverlimiting, 235, 236, 249. See also
overlimiting regionpenetration. See electric field, penetration
current (cont.)penetration depth
small for high frequencies, 387. See also RCtime scale, limitation of field-penetrationdepth
enhancement due to tangential convection,219, 221. See also ion, tangentialconvection
into ion-selective granule due to incompletescreening, 201, 203
into membrane to sustain electrolyticreaction, 90. See also reaction, electrolytic
scaling in nanopore, 66–67. See also channel,nanochannel or nanopore; Debye doublelayer, overlap
streaming, 74, 79–81, 96. See also streamingpotential
surface, 95–96, 98. See also current, tangentialtangential. See also current, surface
low conductivity correction to crossoverfrequency, 288. See also dielectrophoresis
negligible for small double layers, 255total, continuous across interface, 169. See also
boundary condition, interfacialcurrent density, 29, 32–33, 168
limiting, 209, 218, 242, 245, 249. See alsocurrent, limiting
thick polarization layer (high field) theory, 215.See also polarization layer
current–voltage (I–V) characteristics, 210–213.See also nanochannel, current–voltage(I–V) characteristics
I–V curves, 193–249pump, 96. See also pump
current–voltage (I–V) scaling, 356
Deborah number, 383, 385Debye double layer, 35, 36
as capacitor, 155, 162, 180, 252, 255–256, 260,293, 361, 443. See also Debye double layer,
chargingas equivalent series RC circuit, 180, 256, 260as surface conducting layer, 177balance with surface charges, 39, 54, 155.
See also electroneutrality
bipolar, around cylinder, 278capacitance, 256, 280, 443
decrease due to Debye double layer stericeffects, 268
dependence on ζ potential, 186, 310enhancement with zwitterion buffer, 281.
See also zwitterionlinear for small potential drop, 264negligible in electrowetting, 411. See also
electrowettingcharge balance, 255charge leakage arrested by Stern layer
adsorption, 309charge storage mechanism through Stern layer
adsorption. See charge, accumulationcharging, 47, 87, 177. See also Debye double
layer, formation and relaxation dynamics;polarization, Maxwell–Wagner
breakdown in classical Maxwell–Wagnertheory, 172. See also dielectrophoresis;polarization, Maxwell–Wagner
by conducting current, 260capacitive, in AC electro-osmosis.
See electro-osmosis, ACconditions, 251–253flux density, 306governing mechanism in AC electrowetting,
441–442, 443, 447charging time, 277. See also Debye double
layer, relaxation timeconcentration around particle, 307conductance, 52. See also collapsed diffuse
double layer, conductance; diffuse doublelayer, conductance; Stern layer,conductance
convective polar charging. See charging, polardiffuse double layer theory. See diffuse double
layerdistortion, 130, 132–133dynamic, 47. See also polarization,
field-induced double layer polarizationeffect on bubble transport, 440–441electric field, 184equilibrium, 47, 76
absence of flow, 39equilibriation time. See Debye double layer,
relaxation timefully developed flow, 252in steady-state ion-specific granule, 207
extended. See surface, extended polarizationformation and relaxation dynamics, 72–73. See
also Debye double layer, relaxation timegas phase, 295, 297governing mechanism in electrokinetic
phenomena, 73–74in concentration polarization layer, 241increased thickness at poles of ion-specific
granule, 231, 345, 363. See also ion,dynamic superconcentration
interfacial. See also polarization layer,interfacial
large shear and viscous dissipation, 6, 78
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Index 483
linear theory (Debye-Hückel approximation),45–47. See also Debye-Hückelapproximation
localization of AC current within, 7near-equilibrium, 204nonequilibrium, 184nonlinear effects, 52, 58. See also polarization,
field-induced double layer polarizationnonlinear theory, 47–53normal charging, 277overlap, 65–72, 86, 90, 93, 236. See also
electro-osmosis, in nanochannels ornanopores
allowed for by symmetry boundary condition,124. See also boundary condition,symmetry
counterion concentration, 248in annular films, 441overlap: nanochannel, loss of permselectivity,
239polarization. See polarization, field-induced
double layer polarizationpossible mechanism for dielectric dispersion,
177potential drop across. See potential, zeta
(or ζ ) potentialquasi-steady equilibrium assumption, 263,
295relaxation time, 47. See also dielectric,
relaxation time; dipole, relaxation timecharacteristic time for double layer
formation, 73, 167, 291, 292. See alsoDebye double layer, formation andrelaxation dynamics; RC time scale
diffusion in gas bubble, 295electrospray charging dynamics, 363. See also
RC time scalereturn to symmetry after double layer
distortion, 132role in electrotation, 329. See also
electrorotationrole in nonequilibrium electrokinetics, 8. See
also electrokinetics, nonequilibrium;polarization, field-induced double layerpolarization
screening. See screeningscreening length. See Debye lengthslip plane, 55, 74, 76, 78tangential conduction. See ion, tangential
conductionthermal gradients in large double layers, 281,
283. See also thermal gradientthickness. See Debye lengthtypical dimension, 76
Debye length, 46. See also screeningaround ion-selective granule surface, 227at corner geometries, 200effect on electroviscous effect, 125–126, 132. See
also electroviscous effectindependent of surface charge, 47
optimum channel dimension forelectro-osmotic flow, 67, 79–81. See alsoelectro-osmosis
pertinent length scale in AC electrowetting. Seelength scale, characteristic
role in extended polarization layer generation,202, 204, 214
weak logarithmic dependence on ζ potential,49. See also potential, zeta (or ζ ) potential
Debye–Hückel approximation, 46, 49. See alsoDebye–Hückel equation; linearization
limitations, 46, 47–48, 65. See alsoDebye–Hückel limit
Debye–Hückel equation, 46. See alsoDebye–Hückel approximation
Debye–Hückel limit, 47–48, 138. See alsoDebye–Hückel approximation
Debye–Hückel theory. See Debye–Hückelapproximation
DEP. See dielectrophoresisdepolarizing factor. See particle, polarizability
(ellipsoid or prolate spheroid)Derjaguin approximation, 57. See also DLVO
theorydetection, 3, 411–412
biological, 1–3, 268, 326integrated dielectrophoretic chip, 329–331.
See also dielectrophoresisvia ionic wind driven microcentrifugation,
398, 399detection threshold, 2, 268explosives, 1optical, 3, 5sample, 145
diagnostic (or genetic) bead, 2–3, 5, 7, 321–327diagnostics, 2–3dielectric
dielectric layer (or coating), 7, 410. See alsoelectrical insulator
minimum thickness, 415nonuniform thickness, 432thickness, 421
dispersion, 162, 166. See also time scale, chargedispersion
dissipation factor. See dielectric, loss tangentdouble layer charging on dielectric surfaces,
253heterogeneous, 17. See also dielectric, mediumideal, 16, 17, 159. See also dielectric, mediuminhomogeneous, 168interface, 156. See also interfaceleaky. See dielectric, Maxwell–Wagnerlinear. See dielectric, idealliquid. See also dielectric, medium
absence of electrospray Taylor cone, 354.See also electrospray; meniscus, conical
cancellation between electric andhydrodynamic pressures, 19
electrokinetic flow, 18, 20–29, 35loss tangent, 167
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484 Index
lossy. See dielectric, Maxwell–WagnerMaxwell–Wagner, 165–177, 311, 328medium, 156, 158. See also dielectric, liquid
additional forces due to induced charges, 9storage of capacitive energy, 166
nonideal. See dielectric, Maxwell–Wagnerperfect, 156. See also electrical insulatorpermittivity. See permittivitypolarization. See polarization, field-induced
dielectric polarizationrelaxation mechanism, 177–180relaxation time, 167, 172, 177–180. See also
dipole, relaxation timedielectric (cont.)
solid, 20, 45. See also dielectric, mediumspectroscopy, 177surface, 50, 98
dielectric breakdown, 369, 407, 415dielectric constant, 159. See also permittivity,
relativemembrane, effect on crossover frequency, 318
dielectric polarization. See polarization,field-induced dielectric polarization
dielectrophoresis, 285–311AC electro-osmotic flow enhanced trapping,
334–336advantage of using AC fields, 287bubble, 295–300
double crossover frequency due to normaldiffusive charging, 295–297, 299
cellular, 312double crossover frequency due to internal
fluid conductivity, 311–312, 313, 314,318–321. See also cell, blood cell
effect of membrane permittivity andcytoplasm conductivity on crossoverfrequency, 314, 315–317
conducting Stern and collapsed diffuse doublelayer correction, 288–294
crossover frequency, 172, 280, 287, 335anomalous drop at high medium
conductivity, 305corresponding to distinct relaxation times,
292–294dependence on medium conductivity, 291,
292, 309dependence on particle size, 290–291, 293,
297field dependence, 293, 308increase at intermediate medium
conductivity, 300–305independent of medium conductivity,
289–290, 308, 310low-conductivity correction through
conducting Stern and collapsed doublelayers, 289–290, 310
maximum, 311modification through DNA hybridization,
326. See also DNA, hybridization
DC, inability to generate particle aggregationand vortices around corners, 189–190
dielectric polarization mechanism, 287dielectrophoretic mobility, 174, 176, 294
cells, 311polyelectrolytes, 325
dielectrophoretic velocity, 175–176, 294, 335force, 174, 273, 286–287, 294
localization at stagnation point for trapping,335
relation to electrocapillarity, 423scaling with particle size, 331time-averaged, 286traveling-wave dielectrophoresis, 333
gate, 331integrated chip for bioparticle sorting and
detection, 329–331. See also particle,sorting
mechanism for drawing particles into surfacevortices, 397–398
molecular, 321–327associated time scales, 325colloidal crystal morphology, 324dependence of crossover on DNA
concentration and conformation, 325–326.See also DNA; polyelectrolyte
vanishing dielectrophoretic mobility at lowfrequencies, 322–324
negative, 287positive, 287protein crystal migration, 342. See also protein,
crystallizationthree-dimensional continuous flow, 329–331trap, 176traveling wave, 332–334separation, 176
diffuse double layer, 53–56. See also Debyedouble layer
capacitance, 256, 310dependence on ζ potential, 186when tangential conduction is significant, 309
collapsed. See collapsed diffuse double layerconductance, 52, 140. See also diffuse double
layer, conductanceconduction, 81, 140convection, 140electro-osmotic slip, 73–74, 76. See also
electro-osmosisfield line penetration, 284–285. See also electric
field, penetrationin polarization produced by conductivity
gradients, 287–288relationship to Debye length, 47. See also
Debye lengthrelationship to Maxwell–Wagner dielectrics,
170. See also dielectric, Maxwell–Wagnerrole of space charge in screening external field
around thick layers, 303, 308space charge distribution, 302
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tangential conduction, 301, 303, 307–309. Seealso ion, tangential conduction
tangential diffusion, 307–308thickness, to allow for tangential conduction,
303. See also ion, tangential conductiondiffusion
diffusion coefficient. See diffusivityion
balance with electromigration underequilibrium conditions, 130, 134. See alsoion, electromigration; equilibrium,Poisson–Boltzmann
limitation to pore transport, 71relationship with ion mobility, 31–32. See also
ion, mobilitylength scale, 106, 110, 136, 215. See also length
scalemolecular, 7, 114, 117normal, 260plasma, 396relaxation time, role in electrorotation,
329solute, 105, 117–122, 147tangential, 141. See also diffuse double layer,
tangential diffusionthermal, 58, 133, 404. See also thermal
fluctuationtime scale, 117, 178, 223, 256, 263
diffusion front, 104, 107–109, 114diffusion layer, 204, 215, 218, 241, 245. See also
polarization layercharging dynamics, 236, 237–238compression/dilation due to convection,
234concentration profile, 243–245electroneutral, 206, 219, 233, 235relaxation time, 239
tangential diffusion, 292, 293thickness, 216, 218
correspondence to convection layer length,209
growth induced through AC forcing, 236independence of field strength and
frequency, 236limited through tangential convection, 219,
221scaling with Péclet number, 217selection of vortex dimension, 233, 236,
239diffusivity
absence in Dukhin scaling, 202, 206. See alsoDukhin (low Péclet number) theory
dependence in electrophoretic velocity in highPéclet number theory, 219
enhancement due to mixing, 223ion, 32
assumption of equal co-ion and counter-iondiffusivities, 105
effective, 32relationship to ion mobility, 30, 31
lysozyme, 339plasma, 295solute, effective, 105, 117–120, 122. See also
diffusivity, ionsurface, 135
digital microfluidics, 5, 411digitated platforms. See digital microfluidicsdilute system, 32, 37dipole, 177, 180
aggregation, 294alignment, 158, 170. See also dipole, orientation
during orientational polarization, 161.See also polarization, orientational
giving rise to torque, 158, 327–328. See alsodipole, torque
in dielectrophoresis, 285, 287, 332. See alsodielectrophoresis
sufficient time with low AC frequencies, 162,167
complex polarizability, 285. See also dipole,polarizability
displacement, 162force, 157, 286induced, 157–158. See also polarization,
field-induced dielectric polarizationdue to rotating electric field. See
electrorotationdue to tangential ion migration in double
layer, 301electrostatic potential, 302giving rise to dielectrophoresis, 335–336, 338.
See also dielectrophoresisjump across interface produces surface
charge, 168. See also charge, interfacialof polyelectrolyte molecule. See
polyelectrolyteparallel or antiparallel, 299–300, 328
microscopic, 16orientation, 161, 167, 339
along polyelectrolyte molecule, 339. See alsopolyelectrolyte
during dielectrophoresis, 338. See alsodielectrophoresis
orientation vector, 157permanent, 158, 160, 325, 338polarizability, 16, 158, 160, 171polarization vector, 158–159, 173, 328potential, 157potential energy, 157relaxation time, 162, 312. See also dielectric,
relaxation time; Debye double layer,relaxation time
reversal, 308. See also charge, reversal;polarization, reversal
rotation, 158, 332. See also polarization,orientational
torque, 158, 161, 327. See also particle, torquedipole moment, 157–158, 160–161, 172,
173effective, 170, 171, 174, 285
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486 Index
discrete axisymmetric harmonics. See expansion;meniscus, conical
dispersiondispersion coefficient. See diffusivitydispersivity function, 121–122hydrodynamic, 116–122. See also band
broadeningin curved channels, 122minimization using field-effect ζ -potential
variation, 187minimization with electro-osmotic flow, 76,
89, 131. See also electro-osmosissignificant in composite channels, 131
sample or solutal, 88. See also dispersion,hydrodynamic
dispersion relationshipelectrospray jet instability, 347. See also jetfilm destabilization due to Maxwell pressure, 28instability due to conductivity gradients, 114Rayleigh–Lamb, 361, 363, 364, 402
disturbance. See also fluctuationgrowth rate, 28, 110, 114, 115in viscoelastic filaments, amplified by inertial
effects, 385interfacial. See interface, deformationlinear perturbation, 28, 108, 113, 115long wavelengthmechanical, 351to extended polarization layer thickness,
234wave number, 28, 108, 114, 348. See also
instability, wavelength; fluctuationDLVO theory, 20, 46, 56, 189DNA, 7–8
condensation, 57, 139, 325. See also ion,condensation
dielectrophoretic trapping. Seedielectrophoresis, molecular
diffusion coefficient, 148, 322–324. See alsodiffusivity
encapsulation, 387field-induced polarization due to association or
dissociation, 161. See also polarization,field-induced dielectric polarization
free-draining, 152hybridization, 2, 326identification, 2immobilization and stretching using AC
electro-osmotic converging-stagnationflow, 274–275, 276
ionization and mass spectrometry, 151, 344.See also mass spectrometry, electrosprayionization (ESI-MS)
separation, 147, 152–154. See alsoelectrophoresis, polyelectrolyte
sequencing, 1, 152stretching, 294
through converging flow at stagnation point,274–275
target sequence, 2, 325
trapping concentration, 322Donnan equilibrium relationship, 248. See also
potential, DonnanDorn effect. See sedimentation potentialdouble layer. See Debye double layerdrop, 99, 344–345. See also digital microfluidics
aerosolejection mechanism, 363, 370nanodrops, 348negative charge on drops ejected by AC
electrosprays, 369size, 347, 360
charged during electrospraying orelectrowetting, 347, 348, 446, 447
charging, 446curvature, 439, 446deformation and instability. See instability,
interfacial; interface, deformationdisintegration. See Coulombic fissionejection at electrowetting contact lines, 414,
446–447equilibrium shape, 418merging (or recombination), 438nanodrop formation with electrowetting films,
431–432splitting, 412, 436–438translation, 435. See also drop, transporttransport, 407–408, 411
Dukhin (low Péclet number) theory, 71, 215–217breakdown in Dukhin scaling due to tangential
convection, 220critical electric field limit, 202, 208, 217, 221. See
also Dukhin (low Péclet number) theoryDukhin scaling (thin polarization layer limit),
202–203, 206, 208, 214Dukhin number, 53, 81, 140–141
efficiencymixing, 7
enhancement through fingering instabilities,112
enhancement through superpositioning ofsecondary field, 222, 223
power. See power, efficiencypump, 89, 94–95
electrodeconstant potential, at high frequencies,
257electrical capacitance, 163electric displacement, 16, 158–159, 168electric field, 10, 11–14
electric fieldAC
advantages over DC fields in electrokinetics,5, 7–8
effect on polarized layer thickness, 201penetration of electrolyte to polarize double
layer, 251use for electrophoretic rattling, 223
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Index 487
use to suppress bubble generation andelectrolytic reaction, 224, 287
voltage-frequency characteristic, 340–343,370, 396
asymmetric (e.g., traveling wave), 254characteristic field strength, 208critical (or threshold) field
for electrokinetic flow of dielectric liquids,22, 25
for flow in a nanopore, 69–71, 96, 123, 215.See also electro-osmosis, nanochannel ornanopore
linear scaling with ζ potential, 71. See alsopotential, zeta (ζ ) potential
polyelectrolyte chain unfolding, 154. See alsopolyelectrolyte
transition from linear to nonlinearelectrophoresis. See Dukhin (low Pécletnumber) theory, critical electric field limit
DCability to generate nonequilibrium
electrokinetic phenomena, 184. See alsoelectrokinetics, nonequilibrium
disadvantages of use in electrokinetics, 6–7disadvantages of use in electrospraying.
See electrospray, DCdisadvantages of use in protein
crystallization, 339, 343enhancement due to particle concentration, 337existence of singular tangential field at corner,
194. See also singularityfield lines
along electrospray cone, 404attraction to granule surface due to high
conductivity, 200–201, 221attraction to nonconducting surfaces due to
conducting Stern or collapsed layers, 284.See also polarization, field-induced doublelayer polarization
coinciding with streamlines, 6, 97–99, 129. Seealso similarity, field-streamline
dipole, 157during double layer charging, 254, 277in nanowires, 174penetration in thick double layers, 252penetration into curved surface, 86
flux, 12–13focusing
geometric focusing effect in nanochannels,241, 242–243, 245. See also channel,nanochannel or nanopore
to produce thermal gradients, 281. See alsothermal gradient
fringe, at contact line, 415. See also singularity,electric field
induced, 174–175
irrotationality, 12, 22leakage. See electric field, penetration
local enhancement at electrospray meniscus tipdue to plasma polarization, 372. See alsopolarization, gas phase
nonuniform, 285–286, 329normal, in gas phase, 371, 373penetration, 155, 156
across dielectric film, 443at corners or sharp geometries, 184enhancement due to tangential convection,
219, 221. See also ion, tangentialconvection
inability for normal field to penetrate intothin double layers, 252
insufficient time at high frequencies, 304into cytoplasm at high frequency, 313, 315into double layer, 184–185, 201, 277, 284, 291,
292. See also Debye double layerinto ion-selective granule, 203minimization of penetration into liquid with
conducting liquids, 402normal field leakage through corner, 195normal, giving rise to normal capacitive
charging, 294. See also charging, normalfield
slip length condition, 216, 218suppressed by large normal surface field, 292
penetration depth, 7rotating. See electrorotationsingularity. See singularitysurface, 39
balance with normal field at critical point,226
constant, inability to produce nonequilibriumelectrokinetics, 206, 207
enhanced due to thin double layer, 305–306irrelevance in normal AC charging, 252large, implicit assumption in equilibrium
electrokinetics, 155. See alsoelectrokinetics, equilibrium
normal, at conducting gas interface, 295reversal in direction, 272
tangentialinterfacial field of electrowetting film, 426in electrospray jet, 360
electric Rayleigh number, 114electric susceptibility, 16, 160electrical admittance, 166electrical capacitance
bulk, 180–183decrease due to dielectric layer, 411dielectric layer, 411, 417membrane, 312, 318. See also electrical
capacitance, surfacesurface, 303. See also diffuse double layer,
capacitance; Debye double layer,capacitance; Stern layer, capacitance
electrical conductance, 31. See also electricalconductivity
bulk, 53, 81
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488 Index
determined from I–V characteristics in Ohmicregion, 247–248. See also electricalconductance, nanochannel or nanopore
in Ohmic region, 248, 249membrane, 312nanochannel or nanopore, 66–67, 247Stern layer. See Stern layer, conductancesurface, 52, 81, 140–141. See also collapsed
diffuse double layer, conductance; diffusedouble layer, conductance; Debye doublelayer, conductance; Stern layer,conductance relationship with Stern layerconductance, 289
electrical conductivity, 30–31, 65–66, 95. See alsoelectrical conductance
bulk, 50, 180. See also ion, conductivity;electrical conductivity, medium
critical, balance between particle and mediumconductivities
electrical conductivity (cont.)cytoplasm, 312, 314, 315–317, 318–321drives electrothermal flow, 253, 280, 283.
See also electrothermal effectelectrothermal scaling, 282. See also
electrothermal effectgradient
instabilities, 103–116introduced by surface curvature, 82produces polarization, 22, 287
medium or solution, 53, 81, 106, 172, 280.See also electrical conductivity, bulk
effect on field-induced double layerpolarization, 284–285. See alsopolarization, field-induced double layerpolarization
membrane, 311alteration through crosslinking, 312, 314.
See also reaction, cell fixationnanowire or nanotube, 174particle, 140, 172, 280, 311. See also particle,
effective conductivityplasma, 295. See also ion, plasmareduced locally by normal diffusion, 295
electrical conductor, 156–157. See also electrolyteelectrical field-streamline similarity. See
similarity, field-streamlineelectrical impedance, 162–163
AC, 7equivalent RC circuit, 180, 256–266. See also
equivalent circuit, RCparallel RC circuit, 165. See also equivalent
circuit, RCpure ideal capacitor, 163, 178pure resistor, 163sensing, 3, 180
series RC circuit, 164–165. See also equivalentcircuit, RC
spectroscopy, 162–168, 292electrospray, 366
electrical insulator, 99, 156. See also dielectric,perfect
electrical reactance, 163, 180–183frequency response, 181–183
electrical resistance, 31, 66, 156, 163. See alsoelectrical resistivity
bulk, 182–183differential, 245, 249–250in concentration polarization layer, 245, 248intrachannel or intraslot, 240, 242, 245Ohmic, 240, 245–247
tangential, dominant in thick diffuse doublelayers, 301
electrical resistivity, 30. See also electricalresistance
electrocapillarity, 408, 409, 411, 423. See alsoelectrowetting
electrodearray, 281, 317, 326, 330, 332, 340
successive activation, 411–412asymmetric, 254, 268, 281coil or spiral, 7, 275, 295, 333, 401corona, 395dielectric layer. See dielectric layer (or
coating). See also dielectricembedded, 5, 7, 187functionalization, 3. See also surface,
functionalizationgate electrode in field-effect transistors,
186housing, 6. See also membrane, Nafion R©insulated, due to double layer screening at low
frequencies, 257line, in electrowetting, 423–432orthogonal, 254, 275pin-plate, 25plate, in electrowetting, 432–438polarization, 7, 8. See also surface, polarization;
polarizationquadrupole. See electrode, arrayreaction. See reaction, electrochemical;
reaction, electrolyticrotating, 380serpentine. See electrode, coilshielding electrode for field-effect manipulation
of electro-osmotic flow, 186–187, 432wire, 7, 23, 275, 432
electrohydrodynamic atomization.See electrospray
electrokinetic force. See force, electric(or electrostatic)
electrokinetic phenomena of the second kind, 185,200–208
electrokinetic potential. See potential, zeta(or ζ ) potential
electrokinetic slip. See electro-osmosis,electro-osmotic slip; slip
electrokinetics, 2, 4–8, 40AC. See electrokinetics, nonequilibriumequilibrium, 8, 31, 35, 73–74, 141, 155–156
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Index 489
interfacial, 7, 344–345. See also interfacenonequilibrium, 8, 156, 251
DC, 184, 201requirement for field-penetration, 207
nonlinear. See electrokinetics, nonequilibriumpreferred method of microfluidic transport, 5
electrolysis, 30, 410electrolyte
concentrationabsence in Dukhin scaling, 202, 206. See also
Dukhin (low Péclet number) theorydependence in electrophoretic velocity in
high Péclet number theory, 219scaling with channel or pore dimension,
66–70. See also channel, nanochannel ornanopore
force on, 18–19, 20internal phase within particle (e.g., cytoplasm),
311polarization, 29. See also polarizationrepresented by a resistor in double layer
equivalent RC circuit, 256, 309requirement for the formation of electrospray
Taylor cones, 354. See also electrospray;meniscus, conical
strong, 47, 67, 134symmetric binary, 31, 32, 36weak, 47, 55–56
electrometer, 408electromigration. See ion, electromigrationelectron cloud, 160electron–hole pair, 161electron
as charge carrier in Stern layer, 304. See alsoStern layer
avalanche, 347, 415mobility, 347, 369. See also ion, mobility
electroneutrality, 33, 54. See also Laplaceequation
global, 39, 66, 79in nanochannels or nanopores wherein double
layers overlap, 86–87, 93local. See electroneutrality, role in the
generation of depletion regionsOhmic region, 206polarized layer asymptote, 215role in the generation of depletion regions, 71,
201–202, 204. See also ion, intermediatediffusion layer
zero net force on liquid, 29, 41electro-osmosis, 74–75, 76–77
AC, 251capacitive charging mechanism, 253–257converging-stagnation flow. See flow,
converging-stagnation; flow, stagnationpoint
enhancement of dielectrophoretic trapping.See dielectrophoresis
flow reversal, 101, 264–268limitation, 280
maximum slip, 275, 335normal double layer charging on ideally
polarizable surfaces, 277slip velocity, 254, 256–263slip velocity, combined electrothermal and
electro-osmotic effects, 281–283. See alsoelectrothermal effect; flow, electrothermal
slip velocity, time-averaged, 262, 263advantages, 89, 116–117around a 90◦ microchannel bend, 190–200conductance enhancement in nanochannel or
nanopore, 248DC
electro-osmotic pump, 6, 79, 88, 89–96.See also pump
flow rate, 88–89velocity profile, 87. See also flow, plug;
velocity profileelectro-osmotic mobility, 131, 135–136,
144electro-osmotic slip, 76–77
independent of channel size, 89electro-osmotic velocity, quadratic scaling with
voltage, 253field-effect flow manipulation, 186flow rate, independent of capillary
cross-section, 440in ion-selective granule pores, 221. See also
electro-osmosis, nanochannel or nanoporeion convection in double layers, 53. See also
ion, tangential convectionnanochannel or nanopore, 65–72, 86–88.
See also electro-osmosis, in ion-selectivegranule pores; ion, transport
flow rate, 87of annular film around bubble, 440of buffer solution in electrophoresis, 129–131,
144. See also electrophoresissecond kind, 94. See also electrokinetic
phenomena of the second kindslip velocity, 74, 76–80
in cylindrical capillaries, 80–81in diffusion layer, 217, 219inverse relation with capillary cross-section,
440nonlinear, 251nonlinear, dependence on overpotential, 221nonlinear, due to field leakage, 196nonlinear, over conducting cylinder, 279–280nonlinear, over ion-selective granule, 206,
208, 218, 219reversal across corner geometry, 194, 195,
196, 199singular, 198typical value, 94variation across channel due to field effect,
187variation with longitudinal ζ -potential
gradients, 100–103, 137–138electrophoresis, 74–75, 128–154
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apparent mobility (or velocity), 131, 144capillary, 143–154capillary electrochromatography (CEC), 6, 150,
152capillary isoelectric focusing, 149–150capillary isotachophoresis, 149capillary zone, 146–147cellular, 99–102, 133–137DC, 6differential mobility, 144, 147, 149, 150differential partitioning, 148, 150electrophoretic mobility, 128–131, 216. See also
electrophoresis, electrophoretic velocitycellular, 135–136. See also electrophoresis,
cellularDNA, 144. See also DNA, separationend-labeled free solution (ELFSE), 152negative, due to charge reversal, 138
electrophoretic velocity, 128–131. See alsoelectrophoresis, electrophoretic mobility
electrophoresis (cont.)cellular, 134–136. See also electrophoresis,
cellularelectrophoresis of the second kind, 206. See
also Dukhin (low Péclet number) theoryin presence of surface charge migration,
137–138nonlinear field dependence, 185, 206, 219nonlinear, maximum, 206, 207–208, 216–217,
218, 221. See also Dukhin (low Pécletnumber) theory
nonlinear, thick polarization layer theory,215
nonlinear, reduction due to tangentialconvection, 217, 218, 219, 221
elution time, 131, 148, 152end-labeled free solution (ELFSE), 144,
152–154entanglement effect. See electrophoresis, gelforce, 268free-solution mobility, 152gel, 130, 144, 147–148micellar affinity, 149micellar electrokinetic chromatography,
148–149microelectrophoresis, 145particle trapping, 268–270. See also particle,
concentration (or trapping)point charge theory, 128, 130, 138polyelectrolyte, 144, 152. See also
polyelectrolyteread length, 148, 152, 154regulating function, 146–147, 149retards dielectrophoretic motion, 287separation, 129, 130, 131, 143–154. See also
separation, flow or particleenhancement using field effects, 186–187resolution, 148shape independence, 130
size effects, 130, 139, 141, 144, 147
zone, 146–147, 149electrorheological fluid, 4electrorotation, 172, 327–329
velocity, 329electrospinning, 380
AC, 386–392interconnected multistrand fiber networks,
386, 390–391, 392DC, 380–386
axial and radial charge relaxation-time scales,383
encapsulation, 387–389non-Newtonian jets. See jet, non-Newtonianpolymer concentration, 387
electrospray, 345AC, 360–378
AC field superimposed on DC voltage, 361effect of liquid conductivity, 366–368, 369,
370–371, 378low frequency, 363–366spray modes, 366–368, 370charge relaxation time, 345, 360, 362, 368,
372. See also Debye double layer,relaxation time
gas phase, 373liquid phase, 373–374
cone-jet mode. See electrospray, spraymodes
continuous flow. See electrospray, spraymodes
DC, 351spray modes, 348–351
ionization, 348. See also mass spectrometry,electrospray ionization (ESI-MS)
jet. See jetlateral whipping or bending. See jet, instabilitymode (positive or negative), 347oscillating cone-jet mode, 361. See also
electrospray, modesperfect conducting limit, 353, 355pulsating flow. See electrospray, spray modesstability, 351, 354, 366
electrostatic, 8–14attraction, 8. See also force, interaction; force,
van der Waalsbetween particle and wall, 42
between two particles, 45due to negative osmotic pressure gradient,
41, 42. See also pressure, osmoticleading to film collapse, 441like-charge, 56
decoupling from hydrodynamic problem, 257electrostatic interaction, 152, 375, 411
arising from concentration polarization, 36between two charges, 8–10. See also
Coulomb’s Lawbetween particle and wall in confined
geometries, 41, 42force. See force, electric (or electrostatic)repulsion, 8, 44. See also force, interaction
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at electrospray meniscus tip, 346at electrospray orifice, 383at electrowetting contact lines, 414between particle and wall, 44, 45between trapped particles, 401between two particles, 41, 42capillary pressure compensation, 374–378due to steric effects, 39during ion adsorption, 36. See also ion,
adsorptionoffset by osmotic pressure gradient, 41.
See also pressure, osmoticelectrostriction, 17. See also force, electrostrictiveelectrothermal effect, 14, 253, 280–283
electrothermal velocity, 253electroviscous effect, 88, 122, 132–133
dilute suspension theory, 132electrowetting, 408–438
AC, 441–447advantages over DC, 407force, 443
continuous, 411DC, force, 413, 421. See also force,
electrocapillary; force, electric (orelectrostatic)
departure from perfect conducting limit, 417.See also charge, accumulation; dielectric,dielectric layer (or coating)
distinct to electrocapillarity, 409electrolytes. See electrowetting, ACequilibrium. See electrowetting, staticfilm, 423–432force, unpinning of the contact line, 445on dielectric (EWOD), 411. See also
electrowetting, staticon insulator coated electrodes (EICE), 411.
See also electrowetting, staticperfect conducting assumption, 419spontaneous, 423–438static, 409–410, 411–422
change in macroscopic contact angle, 421drop velocity, 421–422
energy balance, 14, 253, 280energy barrier, associated with contact line
pinning, 444–445. See also contact line,pinning
energy minimizationfree surface, 348Onsager’s principle of minimum energy
dissipation, 40energy
electrical (or electrostatic), 58, 139free
due to Coulombic interactions, 418excess at contact line, 418mixing, 65
kinetic, ion, 354–356potential, 37thermal, 32, 37, 47, 58, 139viscous dissipation, 418
entropic effects, 45, 139equilibrium, 38
adsorption. See isothermdouble layer. See Debye double layer,
equilibriumelectric and capillary stress balance across
interface. See stress balance,electrocapillary
electrochemical, 71electrowetting. See electrowetting, staticforce or flow, 19–20, 40–41, 42ion or charge, 36, 37, 40, 57normal and tangential force balance in
electrospray menisci, 376Poisson–Boltzmann, 19–20, 38. See also
Poisson–Boltzmann equationbetween overlapping double layers, 67–68between two oppositely charged surfaces,
57–60in double layer, 76, 77, 84modified to account for steric effects at high
frequency, 268. See also steric effectosmotic pressure effects, 39–41. See also
pressure, osmoticstability, 233violated by external field penetration, 98, 185,
203, 207static Taylor cone. See meniscus, conicalStern layer. See boundary condition, Stern
layer conditionthermodynamic, 15, 191–193
equivalent circuitcapacitors in series to model dielectric and
double layers, 443capacitors in series to model Stern and diffuse
double layers, 186–249, 256–266, 303RC
capacitive charging, 256Faradaic charging, 266parallel RC circuit, 180, 287, 363series RC circuit. See Debye double layer, as
equivalent series RC circuitRC time constant. See RC time scale
expansion, 83–85. See also linearizationof potential in spherical harmonics, 194, 352,
355, 373, 403extended space charge region, 241, 245. See also
polarization layerextensional thinning and thickening, 383–384extensional viscosity, 383–384
Faradaic dissociation. See ion, dissociationFaraday charging. See reaction, Faradaicferromagnetic liquid, 381fiber
alignment, 381, 391bead suppression due to larger extensional
stress, 391beading, 384–385, 391. See also electrospinning,
non-Newtonian jets
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composite (core-shell), 389effect of voltage and frequency on thread
characteristics, 391–392elastic recoil, 385. See also fiber, beadingembedded, 388nanoporous surface morphology, 385–386repulsive force due to charge on fiber, 392segments, oppositely charged due to dynamic
charging, 389–390, 392stabilization, 391synthesis. See electrospinning
field-effect transistor analogy, 186field-induced polarization. See polarization,
field-inducedfield-penetration. See electric field, penetrationfilm
annular, 438–439, 441dewetting, 28, 431, 436. See also wettingevolution equation, 28rupture, 28, 431, 435, 436
filtration, 2, 147, 330, 406fixed point
attractor, 268–270, 273hyperbolic. See critical point gate
flow rateelectrokinetic flow around bubble, 440electro-osmotic pumps, scaling with channel
dimension, 89–96. See also electro-osmosislongitudinal variation due to pH gradients, 100.
See also pH, gradientlow in electrokinetic pumps, 6mixed or frustrated flow, 89
flowback flow
due to field leakage around corner, 190, 194,195
imposed by pressure gradients, 91–92,222–223. See pressure, pressure gradient;pressure, pressure-driven
induced by conductivity gradients, 104. Seealso electrical conductivity, gradient
induced by pH gradients, 6, 82–100, 101, 156,222. See also pH, gradient
Batchelor, 398bulk, absent in static electrowetting, 420,
421capillary-driven, 89circulation, 25. See also vortex
AC electro-osmosis, 254due to back-pressure, 88. See also flow, back
flow; pressure, backdue to interfacial shear over cylindrical
microchamber, 395–399due to pH gradients, 6, 99–103. See also pH,
gradienteddy generation due to electroviscous effects,
133. See also electroviscous effect
in nanopores, 69. See also channel,nanochannel or nanopore
continuity (or conservation). See massconservation
converging-stagnationdue to field-penetration at corner, 185for long-range particle trapping, 270, 273,
275–276, 335–336. See also particle,concentration (or trapping)
converging, at corner geometries, 195, 199converging, helical (or spiral), 399Couette, 114, 120diverging, through AC electro-osmotic flow
reversal. See electro-osmosis, ACejection at corner, 185, 195, 199electrohydrodynamically driven air flow.
See ionic windelectrothermal, 281. See also electrothermal
effectextensional or elongational, 384. See also
stress, extensionalfrustrated, 88–89, 92, 99–103, 116imbalance, 98–99inviscid air flow due to ionic wind, 395.
See ionic windirrotational, 6, 98, 155
violation in ion-selective granule, 221mixed. See flow, frustratedpath length, 122plug
advantages, 89, 122contribution in mixed (or frustrated) flow, 89.
See also flow, frustratedflat velocity profile in electro-osmotic flow,
81, 100. See also electro-osmosisPoiseuille
contribution in mixed (or frustrated) flow, 89due to pressure-driven flow, 92, 101. See also
flow, pressure-drivenin electrowetting drop, 421solutal dispersion effects, 76, 117, 120.
See also dispersion, hydrodynamicpotential, 6, 97–98, 99, 155pressure-driven. See also flow, Poiseuille;
pressure, pressure gradientback flow. See flow, back flowdue to pH gradients, 6, 93–100, 101. See also
pH, gradientin mixed (or frustrated flow). See flow,
frustratedlarge pressures required for bubble transport,
439net streaming current, 79, 80. See also
streaming potentialsolutal dispersion effects, 76, 120, 122
quadrupolar, 279radial. See flow, quadrupolarregulation, 3reversal, 99, 101–102
AC electro-osmotic flow. Seeelectro-osmosis, AC
rotation. See also flow, circulation; vortex
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saddle point, conversion to fixed point, 270, 335separation. See separation, flow or particleshear, 117, 120, 133, 384sheath, 151, 388–389spontaneous (or dynamic), 423
absent in static electrowetting, 421stagnation point
converging AC electro-osmotic flow, 264in converging spiral flow, 399on ion-selective granule surface, 220particle trapping, 270, 272–274, 335. See also
particle, concentration (or trapping)Stokes, reciprocal theorem (boundary integral
formulation), 206, 208, 219streaming around conducting cylinder, 279stretching, 122viscous, 133
fluctuation. See also disturbance; instabilitycontact line, 446correlated, 56–59flow, due to vortex interactions, 223ion concentration, at ejecting pole of
ion-specific granule, 227–228particle aggregate concentration, 337proton, 325thermal, random, 39, 47, 53, 139
fluctuation theory, 56–63. See also couplingtheory; fluctuation
fluctuation-dissipation theorem, 32, 47force
buoyancy, 268, 273capillary, 364–365
dominant stress in polymer molecules, 385electrowetting drop, 442inverse scaling with characteristic dimension,
407stabilizing, 28, 346
centrifugalsuppression in Ekman boundary layer, 399use to generate sedimentation potential, 74used to provide local stagnation force, 268
Coulomb. See force, electric (or electrostatic)dissipative. See viscous dissipationDLVO. See DLVO theoryelectric (or electrostatic), 5, 8, 16, 17–19. See
also stress, Maxwellarising due to space or induced charges, 20,
39. See also charge, induced; charge, space
as body force term in hydrodynamicequation, 77–79. See also conservationequations
AC, 7at boundary, 40coarse graining to produce force density, 20,
30. See also averaging, coarse grainingcontribution to electrothermal effects, 253,
281. See also electrothermal effectDNA, scales with number of bases, 144.
See also DNA
due to charge accumulation at contact line,415, 417, 446. See also charge,accumulation; electrowetting, force
equal to osmotic pressure gradient, 68.See also pressure, osmotic
in double layer, 155, 446. See also Debyedouble layer
in electrophoresis, 128–129. See alsoelectrophoresis
in electrowetting, 442. See alsoelectrowetting, force
net point force at contact line, 420. See alsoelectrowetting, force
on dielectric particle, 303. See also particle,force
on electrospray meniscus, 346. See alsoelectrospray
singular. See singularitytime-averaged, 254, 372. See also averaging,
timeelectrocapillary, 409. See also electrowetting,
forceelectrostrictive, 20. See also electrostrictioninteraction (short-range repulsion or long-range
attraction), 42, 57, 58, 433. See alsoDLVO theory; electrostatic, attraction;
electrostatic, repulsion; force, van derWaals
Kelvin polarization force density, 17. See alsoforce, electric (or electrostatic)
Korteweg–Helmholtz force density, 17, 20Lorentz. See force, electric (or electrostatic)Maxwell. See force, electric (or electrostatic)particle. See particle, forceponderomotive, 17, 284, 424surface, dominance over body forces at small
scales, 344van der Waals, 39, 57, 398, 431, 435. See also
DLVO theory; force, interactionviscous (or drag)
at contact line, 436dominance over body forces at small scales,
344dominance over inertia, 252due to local electro-osmotic flow in double
layer around particle, 132. See alsoelectro-osmosis
in electrowetting drop, 421–422. See alsoelectrowetting
interfacial, 440. See also interfaceon liquid due to charge migration, 20, 128on particle, 268, 294role in jet ejection, 373
free-molecular-flow limit, 4. See also Knudsennumber
free solution, 144, 148, 152–154. See alsoelectrophoresis, end-labeled free solution(ELFSE)
free surface. See interface
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frequency spectrum: interfacial waves, 348.See also disturbance
frequencyAC field. See time scale, AC forcing
ability to selectively tune fiber morphologiesin AC electrospinning, 385, 391–392.See also electrospinning
advantages of high-frequency operation, 251control of diffusion layer thickness, 209.
See also diffusion layercritical frequency for quasi-steady electrospray
Taylor cone, 362, 366. See alsoelectrospray; meniscus, conical
double layer steric effects at high frequencies,268. See also Debye double layer; stericeffect
existence of threshold for moleculardielectrophoresis, 322–325
in electrospraying, 360–361. See alsoelectrospray
independence of, for AC electro-osmosis dueto Faradaic charging, 265. See alsoelectro-osmosis; reaction, Faradaic
frequency (cont.)operation window, 251–252, 253, 256, 257,
263optimum for electrorotation, 328. See also
electrorotationoptimum for high-frequency AC
electrospraying, 371. See also electrospray,AC
optimum for maximum electro-osmotic slip,252, 255, 256, 260, 275, 335. See alsoelectro-osmosis, slip velocity
optimum for maximum plasma generation,372, 373. See also ion, plasma
optimum for microcentrifugation, 396.optimum for mixing, 224. See also mixingoptimum for protein crystallization, 340–342.
See also protein, crystallizationrelevant time scale in AC electrosprays, 369,
384. See also electrospray, ACuse to control diffusion layer thickness, 238,
239. See also diffusion layeruse to control electrophoretic rattling, 223
characteristiccapacitive charging, 274charge relaxation, 167, 177, 283
crossover. See dielectrophoresis, crossoverfrequency
natural, 363pulsation, in oscillating menisci, 350resonant, 363, 366vibration, 366
frit. See monolith
Gauss Divergence Theorem, 13, 17, 159
Gauss’ Law, 12–14, 33, 159Guoy–Chapman theory, 45
Hamaker constant, 431. See also pressure,disjoining
Hartmann number, 133heat or mass transfer enhancement, 3, 122heating
Joulearising due to ion mobility in double layer, 95due to DC current, 6due to viscous friction on bound charges, 166generation of electrothermal effects, 14, 282,
283. See also electrothermal effectlimitation in capillary
electrochromatography, 151. See alsoelectrophoresis, capillaryelectrochromatography (CEC)
suppression with use of high frequency ACfields, 7, 402
Ohmic, 253, 280Helmholtz plane, 55high Péclet number theory, 208, 217–221. See also
near-equilibrium (low Péclet number)theory
limitations, 221Hückel equation, 129, 130, 134, 136, 138, 143hydrated phase. See ion, hydrationhydration cage, 58, 303, 339–341. See also ion,
hydrationhydrodynamic interaction, 41, 45, 152, 325hydrodynamic resistance. See also pressure,
pressure dropgeneration of electroviscous effect, 123. See also
electroviscous effectsuppression of vortex instability, 235
hydrodynamic shear. See stress, shear
I–V characteristics. See current–voltage (I–V)characteristics
ideal-gas law, 15image effect,induced-charge electrokinetic phenomena, 184.
See also electrokinetics, nonequilibriuminstability
absolute, 114–115, 116capillary. See instability, interfacialconductivity gradient driven, 103–116contact line, 414convective, 115, 116Coulombic, 347. See also Coulombic fissionextended polarization layer. See instability,
vortexfeedback mechanism, 115fingering, 104–105, 107, 111–112, 116hydrodynamic. See instability, interfacialinterfacial, 347, 380–381, 385. See also jet,
instabilityeliminated by superimposing AC fields on
DC voltage, 361kink. See jet, instabilitylong wave, 110, 383. See also lubrication
approximation
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meniscus, due to Coulombic fission, 346natural frequency of fastest growing
disturbance, 361particle clusters, 336–337Rayleigh. See instability, interfacialspiral (axisymmetric or three-dimensional),
399thermodynamic, 386varicose. See instability, interfacialvortex
analogy to Rayleigh–Bénard instability, 233suppression of diffusion layer growth, 235.
See also diffusion layersurface vortices driven by ionic wind, 396.
See also vortexwavelength, 105, 347. See also disturbance,
wave numberinterface, 344. See also dielectric, interface;
electrokinetics, interfacial; stress, interfacedeformation, 347, 395. See also meniscus,
capillary waveinduced charge, 16–17, 22–23. See also
boundary conditions, interfacialmicroscopic–nanoscopic, 5, 236, 242. See also
asymptotic matchinglarge pressure gradient, 67
net Maxwell stress, 18. See also stress, Maxwellpermittivity jump due to dielectric polarization,
17. See also polarization, interfacialshear, 395, 434, 436. See also stress, shear
interfacial destabilization, 27interfacial phenomena. See interfaceinterfacial polarization. See polarization,
interfacialinterfacial tension. See surface tensionintermediate electroneutral layer. See diffusion
layerion. See also charge
accumulation. See charge, accumulationadsorption
asymmetric, producing oppositely chargedsurfaces, 57
collapsed diffuse layer, 81. See also ion,desorption
due to solvation or hydration effects, 47.See also ion, hydration; ion, solvation
nonspecific, 402, 411responsible for surface charging, 8, 36reversible, 56–64Stern layer, 39. See also Stern layer
accounted for in thick double layertheory, 300
charge storage mechanism, 252gives rise to surface conductance, 140Helmholtz plane, 55–56prevented by charge leakage, 309time scales, 57, 304suppressed with polymer or gel, 147
association, 378equilibrium constant, 59
field induced, 325giving rise to depletion regions, 202giving rise to polarization at ends of
molecules, 161. See also polarization, fieldinduced dielectric polarization
time scale, 57bridging, 58cloud, 129, 178, 201co-ion exclusion. See ion, selectivityconcentration
beyond close packing limit, 268conservation law, 33. See also conservation
equationscritical cutoff, 268critical, for bubble motion, 441enhancement factor, 232. See also ion,
dynamic super-concentrationin Poisson–Boltzmann equilibrium, 46. See
also equilibrium, Poisson–Boltzmannscaling with pore dimension, in double layer,
79. See also Debye double layerconcentration enrichment. See ion, dynamic
superconcentrationcondensation, 138–139, 303
driving like charge attraction, 56reduces current in Stern layer, 54
conduction. See also conducting layer; ion,tangential conduction
flux, electro-osmotic flow in nanochannel, 87.See also electro-osmosis, nanochannel ornanopore
in collapsed diffuse layer, 54. See alsocollapsed diffuse layer
mechanism for charge relaxation inMaxwell–Wagner model, 177. See alsopolarization, Maxwell–Wagner
normal, 288conductivity. See electrical conductivityconservation. See charge, conservationcontamination, due to electrode reactions, 6, 7,
155, 339, 351. See also ion, generation;reaction, electrochemical; reaction,
electrolyticconvection
breakdown in Ohm’s Law, 30, 32. See alsoOhm’s Law
breakdown of thick polarization layer (highfield) theory, 215. See also polarizationlayer, thick polarization layer (high field)theory
contribution to tangential migration aroundion-specific granule, 230
enhancement of field singularities, 200flux, electro-osmotic flow in nanochannel, 87.
See also electro-osmosis, nanochannel ornanopore
gas-phase. See ionic wind
streaming currents in pressure driven flow.See current, streaming
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depletion (or diffusion) region. See depletedco-ion layer
desolvated gas phase ion, 348desorption, time scale, 57, 303diffusion–electromigration balance, 191, 200,
204–205, 208, 231. See also Péclet number,ratio of tangential electromigration todiffusion
diffusion, breakdown in Ohm’s Law, 30, 32.See also diffusion; Ohm’s Law
disordering effects, 53dissociation
due to large electric fields, 372field induced, 325giving rise to polarization at ends of
molecules, 161. See also polarization, fieldinduced dielectric polarization
kinetics, 354of surface groups, 8, 35partial, effect on charge, 129space charge generation, 21, 354. See also
Onsager’s theorydoping, 354drift velocity. See ion, mobility
ion (cont.)dynamic superconcentration, 225–233ejection at critical point, 226, 231electromigration, 302. See also current, flux;
diffusion, charge (or ion)along cell membrane, 133–137. See also cellbalance with diffusion at isoelectric point,
150dominance of tangential conduction at high
fields, 231enhancement of field singularities, 200flux or flux density, 30, 31–32, 306in diffuse layer, 56. See also diffuse double
layerin electrophoresis, 74, 128–130, 150. See also
electrophoresisin interfacial polarization layer, 169, 346mechanism for AC charging of electrode
surfaces, 7, 8. See also charging, ACnormal flux into double layer, 83, 277, 281,
300. See also charging, normal field; Debyedouble layer
enrichment region, 202, 241. See alsopolarization, concentration
filt