Proc. Nat. Acad. Si. USAVol. 70, No. 1, pp. 124-128, January 1973

Thermal Motion and Forced Migration of Colloidal Particles GenerateHydrostatic Pressure in Solvent

(osmotic pressure/ferrofluid)

H. T. HAMMEL AND P. F. SCHOLANDER

Physiological Research Laboratory, Scripps Institution of Oceanography, University of California, San Diego, La Jolla, Calif. 92037

Contributed by P. F. Sholander, October 30, 1972

ABSTRACT A colloidal solution of ferrite particles inan osmometer has been used to demonstrate that the prop-erty that propels water across the semipermeable mem-brane is the decrease in hydrostatic pressure in the waterof the solution. A magnetic field gradient directed so as toforce the ferrite particles away from the semipermeablemembrane of the osmometer and toward the free surfaceof the solution enhanced the colloidal osmotic pressure.The enhancement ofthis pressure was always exactly equalto the augmentation of the pressure as measured by theoutward force of the particles against the area of the freesurface. Contrariwise, directing the magnetic field gradientso as to force the ferrite particles away from the free surfaceand toward the semipermeable membrane diminished thecolloidal osmotic pressure ofthe solution. For a sufficientlyforceful field gradient, the initial colloidal osmotic pres-sure could be negative, followed by an equilibrium pres-sure approaching zero regardless of the force of the par-ticles against the membkrane. Thus, the osmotic pressureof a solution is to be attributed to the pressure in the sol-vent generated in opposition to the pressure of the soluteparticles caused by their interaction with the free surface(Brownian motion and/or an external field force), or bytheir viscous shear when they migrate through the sol-vent, or both.

Recently, Scholander (1) has emphasized the view that thelowering of the chemical potential of water caused by addingmicrosolutes or colloidal particles to the water or by placingthe water in a matrix is a direct and exclusive result of lower-ing the internal hydrostatic pressure in the water. Colloidalparticles in Brownian motion in water disperse throughout thevolume and exert an outward pressure on all boundaries. Thecolloidal pressure develops an internal hydrostatic tension inthe water if there is an unrestrained surface. The magnitude ofthe colloidal particle pressure and the opposing internal neg-ative hydrostatic pressure in the water may be ascertained byseparation of the suspension from pure water by a membranepermeable only by the water. The magnitude of that negativehydrostatic pressure in the pure water sufficient to preventwater from passing through the membrane to the suspension,designated as the colloidal osmotic pressure (COP), is exactlyequal to the internal negative hydrostatic pressure in thewater of the suspension. Thus, the COP is a consequence of,and is equal to, the internal negative hydrostatic pressuregenerated in the water of the suspension by the thermalpressure of the colloidal particles against the free boundary ofthe suspension.By using a colloidal suspension of magnetic particles in

water, Scholander and Perez (2) have experimentally verifiedthat the pressure exerted by the colloidal particles at the freesurface generates the colloidal osmotic pressure of the suspen-

sion. By applying a magnetic field so as to attract the magneticparticles toward the free surface and away from the semi-permeable membrane, they showed that the COP increaseddirectly as the attractive force between the particles and themagnet increased. Contrariwise, by applying the magneticfield so as to attract the magnetic particles away from the freesurface and toward the semipermeable membrane, they foundthat the COP decreased. However, they supposed they weremeasuring the equilibrium COP, and did not recognize thetransient effects induced by the migrating magnetic particles.The purpose of this report is to describe an experiment thatdemonstrates a transient COP caused by migration or dis-persal of particles toward or away from the free surface. Sinceosmotic equilibrium often does not exist in biological systems,osmotic effects induced by migrating solutes are a principalconcern.

PROCEDURESFig. 1A illustrates how the colloidal suspension of colloidalmagnetic particles* was retained in an osmometer, and how aheterogenous magnetic field was applied to the colloidal sus-pension. The strength of the vertical component of the attrac-tive force between the suspension and the magnet was mea-sured by a calibrated Statham gauge supported above theosmometer coupled to it. COP of the suspension was measuredbefore, during, and after application of a magnetic field to thesuspension. Experiments were done with the vertical attractiveforce ranging from 0 to 35 g by variation of the separationbetween the magnet and the colloidal suspension. Since thecross-sectional area of the suspension in the osmometer was4.89 cm2, the vertical attraction pressure ranged from 0 to 7.0X 103 dyne. cm-2The osmometer (3) was assembled by stretching a wet

dialyzing membrane over a convex plastic disc that was 28 mmin diameter. A 28-cm length of 0.3-mm inner diameterpolyethylene tubing was passed through a hole at the center ofthe disc (Fig. 1B). Between the disc and the membrane wasplaced a 25-mm disc of 0.1-mm thick lens paper, which servedas a spacer. The lens-tissue disc was soaked in distilled waterovernight to cleanse it of osmotically active substances. The

* The colloidal magnetic particles of the ferrofluid used in this ex-periment were ferrite, and were about 100 A in diameter. In themanufacture of the ferrofluid, molecules of oleic acid were boundto the finely ground magnetic particles so as to prevent any closeapproach on collision that would flocculate the particles. Themagnetization of the ferrofluid was 100 G and its concentrationwas on the order of 1017 per cm8. The ferrofluid was obtained fromFerrofluidics Corp., Burlington, Mass., and is more fully describedby Rosensweig (4).

124

Abbreviations; COP, colloidal osmotic pressure.

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Hydrostatic Pressure in Solvent 125

A

V

B

0- ring

FIG. 1. (A) Apparatus for measurement of colloidal osmotic pressure of ferrofluid, F, and for measurement of change in force by mag-netic particles when they are forced to migrate toward the semipermeable membrane by the field gradient of magnet M. Transducer Pmeasures the change in force. Spring S and adjustable vise V support the weight of the osmometer and exert an additional force on P.(B) Procedure for mounting membrane and attaching capillary. (C) Details of osmometer.

dialyzing membrane was stretched by placement of the disc ona post and retention of the membrane with a stretched rubberO-ring. By pulling on the free edges of the membrane, takingcare to eliminate all creases over the edge of the disc, onecaused the membrane to stretch and compress the tissuespacer. A thread of dental floss was tied around the stretchedmembrane. A razor blade was used to cut the excess of mem-brane between the disc and the assembly post. The apparatusmust be assembled with gas-extracted distilled water in thesyringe, rubber coupling, tubing, spacer, and dialyzing mem-brane-as shown in Fig. 1B-and care must be taken to avoidtrapping bubbles below the membrane. The disc and mem-brane were pressed tightly against an 0-ring in the osmometerby a larger plastic disc, as shown in Fig. 1C, and held by threeflat-head brass screws (not shown in Fig. 1C). Approximately10 ml of ferrofluid was placed in the osmometer through a holein the cover. In the middle of the upper surface of the cover wasmounted a brass pin for exerting a force against the Stathamtransducer (model UC3). A flat spring was attached to thecover and was clamped in a vise, which could be rotated suchthat the weight of the osmometer was supported by the spring,and an additional force of about 40 g was pressed against thetransducer. As one pole of a magnetron magnet was raisedtoward the ferrofluid in the osmometer, the ferrite was drawndownward exerting a force against the membrane. Thismagnetic force diminished the force against the transducer.The magnetic field had no direct effect on the transducer. Theoutput of the transducer was recorded on a strip chart milli-volt recorder; the system was calibrated by adding knownweights of ferrofluid to the osmometer and recording the out-put.The COP was ascertained by adjustment of the height of

the capillary, Fig. 1A, in relation to the level surface of thesuspension until there was no drift in the meniscus as viewed

against an ocular scale with a 20-power microscope. The posi-tion of the meniscus could be determined within 4±0.1division (i 2.6 Mm). The COP was equal to the capillarypressuret minus the hydrostatic pressure. When 10 min wasallowed to detect zero drift in the meniscus, the height of thecapillary and the COP could be obtained with an accuracywithin ±0.03 cm of H20. Only when the COP changed slowlywas there sufficient time to obtain full accuracy by thismethod. When COP changed rapidly, another method wasused. Upon elevation of the magnet, the capillary was im-mediately raised to just below the height for the lowestanticipated COP. At this capillary level the meniscus driftedto the right in Fig. 1A (away from the membrane). As thetransient COP increased, the capillary pressure minus thepreset hydrostatic height became equal to the COP, and thedrift to the right became zero. Subsequently, the meniscusbegan to drift to the left at an accelerating rate. After a fewminutes, the capillary was adjusted to a lower level, and againthe COP was determined when the drift of the meniscus waszero. By this procedure, the COP was determined severaltimes after applying and removing the magnetic field.When the magnetic field was applied so that a pressure was

exerted against the membrane, there was an immediate smallshift in the meniscus, possibly due to compression of thespacer. This shift showed no hysteresis and was complete inless than 5 sec.The volume of the water on the water side of the membrane

was kept very small by the thin spacer, the small bore of thepolyethylene tubing, and the small volume of the capillary, soas to minimize thermal drifts. In a room without forced con-

t The capillaries used in this experiment were 20-,Al micropipettesfrom Yankee. The capillary pressure of each was 46.5 4t 0.1 mm ofH20.

Proc. Nat. Acad. Sci. USA 70 (1978)

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126 Physics: Scholander and Hammel

vection these drifts were negligible. The meniscus was dis-placed by 1 division by a change in volume of only 8.4 X 10-imm3.

In other experiments, the pressure transducer was mountedbelow the osmometer and the magnet was supported above theferrofluid in order to pull the ferrite particles away from themembrane and toward the surface of the ferrofluid. For theseexperiments the osmometer cup was filled to the rim. The rimwas coated with Vaseline and a film of Saran was loosely layedon the ferrofluid so as to exclude air. The cover pressed anO-ring onto the Saran film to maintain the film in a slackcondition, while it retained the ferrofluid. The spring wasadjusted so as to allow the pressure transducer to supportabout 40 g of the weight of the osmometer. As the magnet waslowered to the ferrofluid the weight decreased.

RESULTSMagnet below

When the magnet was raised beneath the ferrofluid so as todraw the ferrite particles away from the free surface andtoward the membrane, there was an immediate transient re-duction in the COP from -1.55 cm of H20 to +2.90 cm ofH20 (Fig. 2A). Subsequently, the COP increased rapidly, thengradually, until it read nearly zero after 33 hr. Conversely,when the magnet was removed, the COP increased immedi-ately to more than the equilibrium COP before it graduallyreturned toward the equilibrium value, as indicated in Fig.2A; the ferrofluid was stirred to hasten return to the finalequilibrium value of -1.70 cm of H20, indicating a drift ofonly 0.15 cm of H20 in 47 hr. Fig. 2A also shows the force(grams) and corresponding pressure (cm of H20) induced bythe magnetic field acting on the ferrofluid as a function oftime. There was an immediate increase in the magnetic pres-sure, followed by a period of rapid increase lasting about 30min, followed by a slow increase over many hours.The initial reduction in COP, as well as the subsequent

values, were dependent upon the proximity of the pole of themagnet to the suspension. The smaller the gap, the greater themagnetic pressure and the greater the reduction in the initialCOP. The initial reduction in COP was plotted for severalexperiments as a function of the magnetically induced pressureof the ferrite particles migrating toward the membrane (Fig. 3,upper-right quadrant). The equivalent line for COP andmagnetic pressure (both expressed as cm of H20) is drawn forcomparison. The data for the initial reduction in COP fall verynearly on the equivalent line. Also plotted in Fig. 3 (upper-right quadrant) is the net reduction in COP at 0.5 hr againstthe magnetic pressure.

Magnet above

In Fig. 2B is plotted the COP before, during, and after themagnet was placed above the ferrofluid. There was an im-mediate increase in the COP from a value of -1.1 cm of H20before placement of the magnet to -4.25 cm of H20, and afurther increase to - 5.45 cm of H20 after 2 hr, there was nofurther increase for another 2 hr. When the magnet was re-moved the COP snapped back to nearly the initial value(without the magnet). All points from Fig. 2B are replotted inFig. 3 (lower-left quadrant). With the magnet above thesuspension and drawing the magnetic particles away from themembrane and toward the free surface, all points fell on theequivalent line. The plot of the enhancement of colloidal

osmotic pressure versus induced magnetic pressure was nolonger time-dependent.

DISCUSSIONThe experiments on the colloidal osmotic pressure of a suspen-sion of magnetic particles demonstrate that (i) the role of thecolloidal particles was to exert a pressure of the solvatingwater to change the pressure of the water and (ii) it was thepressure of the water that determined the osmotic behavior ofthe colloidal suspension. It makes no difference (a) whetherthe pressure was transmitted to the water by the randomBrownian motion of the colloidal particles exerting a pressureat the free surface of the suspension, as when equilibriumosmotic pressures were observed, or (b) whether the pressureexerted by the colloidal particles was transmitted to the waterby viscous shear. Viscous shear transmitted pressure to thewater when the particles were forced by a magnetic field tomigrate toward or away from the membrane or when theparticles were dispersing toward or away from the membraneby diffusion after removal of the magnet.An explanation of osmosis found in current textbooks in

physiology (5, 6) is invalidated by these experiments. Itsuggests that the presence of the solute or colloidal particleslowers the concentration of the water at the membrane thatresults in the diffusion of water from the region of higher waterconcentration beyond the membrane to the region of lowerwater concentration on the solution side of the membrane.The fact that when the colloidal particles are forced to migratetoward the membrane generates a strongly negative COP,followed by an equilibrium osmotic pressure that approacheszero (or, if more than zero, then less positive than without themagnetic force) cannot be explained by supposed effects on theconcentration of water at the membrane.We conclude that the equilibrium effect of colloidal particles

is a positive pressure exerted on all boundaries retaining theparticles, first proposed by Van't Hoff for solutions as thebombardment pressure (7). The secondary effect is the re-sponse of the water to this colloidal particle pressure, that is, anegative hydrostatic pressure (with respect to the suspension'sambient pressure) in the water of the suspension, an effect thatwas first fully developed by Hulett (8) as a basis for explainingthe lowering of vapor pressure and osmosis. A similar view wasaccepted by Herzfeld (9), Mysels (10), and Duclaux (11), andby Scholander et al. (12) as a basis for osmosis. This secondaryeffect was first demonstrated experimentally by Scholanderand Perez (2). The effects of lowering the chemical potential ofwater on the colligative properties (osmotic pressure, vaporpressure, and melting point) in a solution at ambient pressureare entirely due to the lowering of the internal hydrostaticpressure in the water below ambient pressure. For example, themolecules of 1 mol of an ideal microsolute, which does notdissociate when dissolved in 1 liter of water at 00, woulddisperse throughout the volume and would exert a pressure of+22.4 atm on all boundaries, including the free surface of thesolution in an open container, and on the boundaries with allinclusions within the solution such as ice crystals or bubbles.As there are strong forces between the molecules of water, thepressure of the solute molecules against all surfaces develops atension in the water, i.e., an internal hydrostatic pressure of-22.4 atm in the water on the solution. The net pressure onany inclusion would be 0, or the same as the ambient pressure.The vapor pressure of the 1 molal solution would be lowered

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Proc. Nat. Acad. Sci. USA 70 (1973)

0"3eEU

2-

I..

=0 103E8; -Ia'a -2 CMHp=2 gmo 30o-L .-..----.U3L I Mooa

Hydrostatic Pressure in Solvent 127

cmHiOgm

010

-10---2 Magnetic-lo-1-2 O Pressure

-20-1._-40

0

E -IU

= -2S0

u 3._

E* -40

10~00

-6%15 20Hours

-4

B

-. .

0 5Hou rs

FIG. 2. (A) Colloidal osmotic pressure (COP) and magnetic force induced by the magnetc field (gin) as a function of time after raisingand lowering magnet from below osmometer. The magnetic force is also expressed as the corresponding magnetic pressure in cm of H20.S indicates COP after ferrofluid is stirred in osmometer. (B) COP and magnetic pressure as a function of time before and after lowering mag-net from above the osmometer and then raising it again.

by exactly the same amount as the lowering caused by a ten-sion of 22.4 atm in pure water at O0, and for exactly the samereason, i.e., the water in the solution is under a tension of 22.4atm, a view first proposed by Hulett (8). Lowering of the

melting point of a solution is also a consequence of the tensionin the water of the solution. Hydrostatic tension in the waterlowers its vapor pressure, whereas the vapor pressure ofice is not lowered since the net pressure at its boundary

EU

magnet below

W~~~~~~~~~~~~~~~~oo -43 'Dob-4a. AA0U2 0-O -30

0~~~~~~~~~02 0

0~~~~~

-4 -3 -2 -1/ 2 3 4 5 6

Magnetic Pressure cm H20

magnet above

.2

.3

4

J5FIG. 3. Upper-right quadrant. Reduction in COP against magnetic pressure initially (solid triangles) and after 0.5 hr (open circles). Data

were obtained by raising magnet from below up to several levels beneath the osmometer. The solid line is the equivalent pressure line.Lower-left quadrant. Enhancement of COP versus magnetic pressure at several times after the magnet was lowered to osmometer fromabove (solid circles, data from Fig. 2B).

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128 Physics: Scholander and Hammel

is ambient pressure, as for all inclusions. Thus, the tempera-

ture at which the vapor pressures of the water and ice are

equal is lowered by the tension in the water.The results shown in Fig. 2A, after removal of the magnet,

and in Fig. 2B demonstrate that one sufficient condition for a

COP is the dispersal of particles away from the membrane.By their viscous shear these dispersing particles transmittedto the solvating water a negative hydrostatic pressure, whichwas the transient portion of the COP. Fig. 2A also shows thatpulling the particles away from the free surface reduced thepressure exerted by the particles against the free surface and,thereby, reduced the COP toward zero. The magnetic force onthe particles also caused them to migrate toward the mem-

brane, transmitting by viscous shear hydrostatic pressure tothe solvating water that could yield, if sufficient, a COP thatwas negative. For strong magnetic forces, the COP remainednegative so long as the particles migrated toward the mem-

brane. In time, the particles distributed themselves in themagnetic field in accordance with the Boltzman distribution,i.e., highest concentration at the membrane and lowestconcentration at the free surface and no net migration. As themagnetic field gradient increased, the initial migration of theparticles toward the membrane increased and the initial nega-

tive COP decreased without limit, but the equilibrium COPonly decreased toward zero as the equilibrium distribution ofparticles left fewer and fewer particles at the free surface.The overshooting and undershooting of the COP about itsequilibrium value in Fig. 2A also illustrates that the pull on

the magnetic particles by the magnet could cause the particlesto migrate toward the membrane at a higher rate than was therate of migration away from the membrane by thermaldispersal when the magnet was removed.Only the qualitative features of the curves in Fig. 2A and

B were subject to analysis. The unknown distribution of themagnetic particle size and dipole moment in the ferrofluid andassymetries in the heterogenous magnet field used in theseexperiments prevented a quantitative analysis of the curves.

However, an important quantitative feature revealed by Fig.3 is that when all of the magnetic particles were exerting a

pressure on the solvating water, there was an exact equivalencebetween the COP and the induced magnetic pressure mea-

sured by the transducer. This effect always occurred when themagnet was above. When the magnet was below the colloidalsuspension, the only time when all the magnetic particles were

exerting a pressure on the water was before any of the migrat-ing particles had arrived at the membrane. When the magnetwas above the colloidal suspension and pulling the colloidalparticles toward the free surface and away from the mem-

brane, then the magnetic particles were always exerting a

pressure on the solvating water, either by viscous shear as theywere migrating toward the free surface or by pressure appliedto the free surface as they were reflected from the free surface.Since the particles were either migrating toward the surfaceor exerting their pressure at the surface, the equivalence of theenhanced COP and the magnetic pressure demonstrates thatthe pressure in the water caused by the viscous shear of themigrating particles was indistinguishable from the pressure inthe water caused by the equilibrium pressure of the particlesagainst the free surface.When the magnet was below the suspension and pulling the

particles toward the membrane, there was an approximateproportionality between the colloidal osmotic pressure and the

induced magnetic pressure when they were measured at a fixedinterval after application of the magnetic field, e.g., at 30 minin Fig. 3. The proportionality constant diminished with timefrom the initial value, rapidly at first and then more slowly asmore and more particles arrived at the membrane and couldexert no further influence on the water.Even the monomers and polymers of pure water must be

exerting a pressure against all boundaries, causing the bindingforces between these moieties to be under tension. If all thewater were monomeric, the maximum internal tension wouldbe 55.5 X 22.4 = 1243 atm at 00, well under the tensilestrength of water, which has been estimated at some 2000atm (13). At temperatures between 0 and 250, the majority ofthe water molecules are considered to be combined in clustersof various sizes (14). However, the molecules of water in acluster may be so loosely joined that they exhibit their ownBrownian motion. At the free surface of the water they wouldthen exert a pressure against the surface as if they were

monomers. If this model is correct, then the internal hydro-static tension of pure water would be approximately RT/VW,,where the partial molar volume V0,, is not a function oftemperature.

CONCLUSIONS

The primary effect of the colloidal particles in a water suspen-sion is the outward pressure they exert against all boundaries.The colligative properties are the consequences of the negativehydrostatic pressure generated in the solvating water. AsPerrin (15) recognized in his studies on the molecular basis ofBrownian motion, the effects on the solvent in a solution ofmicrosolutes must be the same as for a colloidal suspension.Thus, we can generalize from our experiments on the colloidalsuspensions that (i) microsolutes also exert a pressure on allboundaries of the solution, (ii) the solvating water opposesthis pressure by a negative hydrostatic pressure within thewater, a tension made possible by the strong binding forcesbetween molecules of water, and (iii) the colligative propertiesof the solution are a direct consequence of the hydrostatictension in the water of the solution.

We thank J. Raymond and Dr. A. A. Yayanos for reading themanuscript and suggesting improvements. This work was sup-ported by NSF Grant GB 8343 and NIH Grant HE 13893-01.

1. Scholander, P. F. (1971) Microvascular Res. 3, 215-232.2. Scholander, P. F. & Perez, M. (1971) Proc. Nat. Acad. Sci.

USA 68, 1093-1094.3. Hargens, A. R. & Scholander, P. F. (1969) Microvascular Res.

1,417-419.4. Rosensweig, R. E. (1966) Int. Sci. Technol. 55.5.- Guyton, A. (1971) in Textbook of Medical Physiology (W. B.

Saunders Co., Phila.), pp 44-47.6. Gordon, M. S. (1972) in Animal Function: Principles and

Adaptations (MacMillan Co., London), pp. 243-245.7. Van't Hoff, J. H. (1887) Z. Phys. Chem. 1, 481-508.8. Hulett, G. A. (1902) Z. Phys. Chem. 42, 353-368.9. Herzfeld, K. F. (1937) Phys. Z. 38, 58-64.

10. Mysels, K. J. (1959) in Introduction to Colloid Chemistry(Intersciences Publishers Inc., New York), pp. 134-136.

11. Duclaux, J. (1965) J. Chim. Phys. Physicochem. Biol. 62,435-438.

12. Scholander, P. F., Hammel, H. T., Bradstreet, E. D. &Hemmingsen, E. A. (1965) Science 148, 339-346.

13. Yayanos, A. A. (1970) J. Appl. Phys. 41, 2259-2260.14. Nemethy, G. & Scheraga. H. A.(1962) J. Chem. Phys. 36,

3382-3400.15. Perrin, M. J. (1910) in Brownian Movement and Molecular

Reality (Taylor and Francis, London).

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