Electrophoresis 2018, 39, 869–877 869 Arian Aghilinejad 1 Mohammad Aghaamoo 2 Xiaolin Chen 1 Jie Xu 3 1 Department of Mechanical Engineering, Washington State University, Vancouver, WA, USA 2 Department of Biomedical Engineering, University of California, Irvine, CA, USA 3 Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, Chicago, IL, USA Received June 26, 2017 Revised September 5, 2017 Accepted September 8, 2017 Research Article Effects of electrothermal vortices on insulator-based dielectrophoresis for circulating tumor cell separation Insulator-based dielectrophoresis (iDEP) is a powerful technique for separation and ma- nipulation of bioparticles. In recent years, iDEP designs using arrays of insulating posts have shown promising results toward reaching high-efficiency bioparticle manipulation. Joule heating (JH) and electrothermal (ET) flows have been observed in iDEP microdevices and significantly affecting their performances. In this research, we utilize mathematical modeling to study, iDEP technique and the effects of JH and ET flow on device perfor- mance and propose a separation scenario for selective trapping of circulating tumor cells (CTCs). A robust numerical model is developed to calculate the distribution of electric and fluid flow fields in the presence of JH and ET flow, and predict the cells’ trajectory inside the system. Our results indicate that JH not only induces temperature rise in the system, but also may alter the design iDEP separation scenario by inducing ET vortices that affect the cell’s trajectory. To investigate the impact of JH-induced ET flow charac- teristics and vortex generation on separation efficiency, we introduce a dimensionless force ratio encompassing the effects of electrical field, drag forces, JH, and ET flow. In- terestingly, it was found that ET flows can be used to significantly enhance the separation efficiency, even in higher inlet flow rates. Lastly, the effect of post geometry has been discussed. Keywords: Circulating tumor cell / Dielectrophoresis / Electrothermal flow / Joule heating DOI 10.1002/elps.201700264 Additional supporting information may be found in the online version of this article at the publisher’s web-site 1 Introduction In recent years, dielectrophoresis (DEP) has emerged as a promising technique for isolation and enrichment of tar- get cells from biological samples. One major application is in isolation of circulating tumor cells (CTCs) for can- cer diagnosis and prognosis [1]. DEP working principle is based on using a non-uniform electric field to induce mo- tion in polarizable particles or cells. This technique has been brought into biological applications for the separa- tion of blood cells [2], bacteria [3] and CTCs [4]. Recently, insulator based DEP (iDEP) has gained popularity due to its Correspondence: Dr. Jie Xu, Department of Mechanical and Indus- trial Engineering, University of Illinois at Chicago, 842 W Taylor St, Chicago, IL 60607, USA Fax: +1-312-413-0447 E-mail: [email protected]Abbreviations: CTC, Circulating Tumor Cell; ET, Electrother- mal; iDEP, insulator-based dielectrophoresis; JH, Joule Heating advantages in fabrication and low cost. In contrast to conven- tional DEP in which the non-uniform electric field is gener- ated by arrays of electrodes inside the microchannel, iDEP technique utilizes the combination of remote electrodes out- side the channel with insulating obstacles within the device to produce the spatial non uniformities in electrical field. This results in the independency of separation efficiency from cells’ distance to the electrodes [5]. Previously, there have been different types of insulating obstacles studied for iDEP such as single insulating constrictions [6], serpentine microchannel [7] and arrays of insulating posts [8]. Because of relatively uniform presence of DEP forces along the mi- crochannel, using arrays of microposts have become popular recently. Additionally, there are several studies investigating the effects of different parameters such as the spacing and shapes of the insulating posts [9,10]. Even though iDEP works with both DC [11] and AC [12] electric field, iDEP with AC electric field adds frequency as an extra degree of freedom to the design [13]; a unique feature that empowers separation of cells with minor differences in their intrinsic properties. Color Online: See the article online to view Fig. 1–8 in color. C 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.electrophoresis-journal.com
Transcript
Electrophoresis 2018, 39, 869–877 869
Arian Aghilinejad1
Mohammad Aghaamoo2
Xiaolin Chen1
Jie Xu3
1Department of MechanicalEngineering, Washington StateUniversity, Vancouver, WA,USA
2Department of BiomedicalEngineering, University ofCalifornia, Irvine, CA, USA
3Department of Mechanical andIndustrial Engineering,University of Illinois at Chicago,Chicago, IL, USA
Received June 26, 2017Revised September 5, 2017Accepted September 8, 2017
Research Article
Effects of electrothermal vortices oninsulator-based dielectrophoresis forcirculating tumor cell separation
Insulator-based dielectrophoresis (iDEP) is a powerful technique for separation and ma-nipulation of bioparticles. In recent years, iDEP designs using arrays of insulating postshave shown promising results toward reaching high-efficiency bioparticle manipulation.Joule heating (JH) and electrothermal (ET) flows have been observed in iDEP microdevicesand significantly affecting their performances. In this research, we utilize mathematicalmodeling to study, iDEP technique and the effects of JH and ET flow on device perfor-mance and propose a separation scenario for selective trapping of circulating tumor cells(CTCs). A robust numerical model is developed to calculate the distribution of electricand fluid flow fields in the presence of JH and ET flow, and predict the cells’ trajectoryinside the system. Our results indicate that JH not only induces temperature rise in thesystem, but also may alter the design iDEP separation scenario by inducing ET vorticesthat affect the cell’s trajectory. To investigate the impact of JH-induced ET flow charac-teristics and vortex generation on separation efficiency, we introduce a dimensionlessforce ratio encompassing the effects of electrical field, drag forces, JH, and ET flow. In-terestingly, it was found that ET flows can be used to significantly enhance the separationefficiency, even in higher inlet flow rates. Lastly, the effect of post geometry has beendiscussed.
� Additional supporting information may be found in the online version of thisarticle at the publisher’s web-site
1 Introduction
In recent years, dielectrophoresis (DEP) has emerged as apromising technique for isolation and enrichment of tar-get cells from biological samples. One major applicationis in isolation of circulating tumor cells (CTCs) for can-cer diagnosis and prognosis [1]. DEP working principle isbased on using a non-uniform electric field to induce mo-tion in polarizable particles or cells. This technique hasbeen brought into biological applications for the separa-tion of blood cells [2], bacteria [3] and CTCs [4]. Recently,insulator based DEP (iDEP) has gained popularity due to its
Correspondence: Dr. Jie Xu, Department of Mechanical and Indus-trial Engineering, University of Illinois at Chicago, 842 W TaylorSt, Chicago, IL 60607, USAFax: +1-312-413-0447E-mail: [email protected]
advantages in fabrication and low cost. In contrast to conven-tional DEP in which the non-uniform electric field is gener-ated by arrays of electrodes inside the microchannel, iDEPtechnique utilizes the combination of remote electrodes out-side the channel with insulating obstacles within the deviceto produce the spatial non uniformities in electrical field.This results in the independency of separation efficiencyfrom cells’ distance to the electrodes [5]. Previously, therehave been different types of insulating obstacles studied foriDEP such as single insulating constrictions [6], serpentinemicrochannel [7] and arrays of insulating posts [8]. Becauseof relatively uniform presence of DEP forces along the mi-crochannel, using arrays of microposts have become popularrecently. Additionally, there are several studies investigatingthe effects of different parameters such as the spacing andshapes of the insulating posts [9,10]. Even though iDEP workswith both DC [11] and AC [12] electric field, iDEP with ACelectric field adds frequency as an extra degree of freedom tothe design [13]; a unique feature that empowers separation ofcells with minor differences in their intrinsic properties.
Color Online: See the article online to view Fig. 1–8 in color.
870 A. Aghilinejad et al. Electrophoresis 2018, 39, 869–877
Although iDEP is reliable and efficient for manipulatingparticles in lab-on-a-chip devices, Joule heating (JH) is a ma-jor concern when dealing with biological applications [14].This phenomenon, as a result of resistive power dissipationin conductive mediums, may impact device performance dueto variation in the medium’s temperature-dependent proper-ties, i.e. conductivity, permittivity, viscosity, and density [15].As a result of the temperature changes due to the JH, local gra-dients in conductivity and permittivity would be created in thesolution, and consequently cause bulk fluid forces and fluidmotion, known as electrothermal (ET) flow. Studying and uti-lizing ET flow in particle manipulation has been previouslyconducted for DEP-based devices with embedded electrodesinside the microchip [16].
Recently, JH and induced ET flows have been investi-gated in the context of iDEP mostly on single constrictionmicrochannels. Hawkins and Kirby modeled JH and the cor-responding ET flows in a single constriction iDEP device,with a DC-offset, and an AC electric field [17]. Their resultsdemonstrated the presence of ET vorticities around the chan-nel constriction, enhancing entrapment by affecting particles’deflection and decreasing fluid velocity. Sridharan et al. usedboth experimentation and numerical simulations to study theeffects of JH on electroosmotic flow in an iDEP microdevice,i.e. a constriction microchannel [18]. They found that JH-induced ET flow circulations form near channel constrictionsand recirculation vortices exist at AC voltages from 200 V to600 V. This group also experimentally investigated the JHon the electrokinetic particle transport and manipulation andhas developed a transient 3D numerical model to study theJH-induced ET flows on microdevice [19, 20]. Kale et al. hasinvestigated the effects of JH and ET streamlines experimen-tally by introducing the particle trapping number in singleconstriction microchannel [21]. Prabhakaran et al. has re-cently observed ET fluid circulations in polymer microfluidicchip and reported the presence of the fluid circulations at500 V AC and above [22]. Studying iDEP device with arraysof insulating posts, Gallo-Villanueva et al. observed reducedparticle trapping efficiency due to the decrease in electric fieldgradient because of JH in the posts’ region [23].
Despite the valuable research conducted on JH and ETflow in microfluidics devices, few has focused directly on ap-plications related to separation of biological samples, specifi-cally CTC separation. Moreover, the literature still lacks a thor-ough study that provides a detailed design guideline based onJH and ET flow for iDEP-based technique. To address theseissues, here, we define the problem as to study iDEP witharrays of insulating posts for trapping-based CTC separation.Specifically, we utilize numerical simulation to study exten-sively how JH and ET flow affect the system performanceand what critical design considerations should be takeninto account in decision makings. To achieve this goal, wedevelop a fully coupled electro-thermo-fluid numerical modelto investigate the relationship between the device operationparameters and the modelled JH and ET flows. In addition,particle tracing model is coupled with the developed numer-ical model to further predict the trajectories of cells in the
device. Utilizing such a numerical model platform, we studyin detail how different operation parameters such as elec-tric field, inlet velocity, medium properties, and post geome-tries contribute to JH and ET flows. This study is amongthe first to focus on the effects of JH and ET flows in iDEPdesigns for separation of CTCs from blood cells. It is worthnoting that although this research focus on iDEP with ar-rays of insulating posts, the developed numerical platformis easily extendible to any iDEP designs for bioparticleseparations.
2 Materials and methods
2.1 Governing equations
The dielectrophoresis (DEP) arises from the action of the ap-plied electric field on the dipole moment it induces in anobject. In the presence of a non-uniform electric field, theelectric forces acting on each side of the induced dipole areunequal, causing a net dielectrophoresis force to act on theobject. Induced polarization is the underlying phenomenonon which the DEP technique is based. Charges have to beinduced to guarantee the continuity of the normal compo-nent of total current density in a conductivity gradient, aphenomenon called Maxwell-Wagner interfacial charge relax-ation or structural polarization. The dielectrophoretic force isused here to separate the cells based on their differences indielectric properties. The time average of this force in an inho-mogeneous and time-varying electrical field E, is proportionalto the cell volume, as shown below:
F DE P = 2�εmr 3 Re (KC M) ∇|E |2 (1)
where εm is the permittivity of the medium, r the radius ofthe cell, and Re(KC M) is the real part of the Clausius-Mossottifactor defined as
KC M = ε̄cel l − ε̄m
ε̄cel l + 2ε̄m(2)
where ε̄ = ε − j ��
is the complex permittivity considering thepermittivity and conductivity of the cell and the medium andalso angular frequency (�) of the electrical field. Clausius-Mossotti factor varies between -0.5 to 1 depending on thebalance of complex permittivity of the particle and medium.When ε̄p�ε̄m, it means that the cell is more polarizable thanthe medium, the DEP force would be positive (pDEP) whichmakes the particles get attracted to the high electric fieldzones. Conversely, when ε̄p�ε̄m, the DEP force would benegative (nDEP), meaning particles get forced back from highelectric field regions. It is to be mentioned that at specificfrequency, called crossover frequency, the Clausius-Mossottifactor would be zero, resulting in no dielectrophoretic force.
In this study, the calculations were performed, usingbreast cancer cell and white blood cells as a model, in view ofthe major importance of these cells in biotechnology. Here,single shell model is used to consider the cell’s thin mem-brane effect on its overall dielectric performance [24]. In this
model, equivalent cell complex permittivity can be calcu-lated using cytoplasm and membrane complex permittivity(εcyt and (εmem):
εcel l = εmem
3 + 2(
εcyt −εmem
εcyt +2εmem
)
3 −(
εcyt −εmem
εcyt +2εmem
) (3)
where = rcel lrcel l −d and d is the cell membrane thickness.
The dielectric properties of breast cancer cells and gran-ulocytes are reported by Becker et al. [25] and Yanget al. [26], respectively, and are listed in Table 1. Basedon these dielectric properties, the real part of Clausius-Mossotti is plotted with respect to different applied elec-tric field frequency and medium conductivities (Fig. 1).According to Fig. 1A, by increasing the frequency, the crit-ical conductivity at which the cells change behavior frompDEP to nDEP will be increased. As shown in Fig. 1B,MDA-231 and WBC behave differently at different frequen-cies for two representative conductivities. For the purpose ofCTC separation, we take the advantage of such a differenceto trap one type of cells while allowing the other ones to passthrough the device. To achieve this, if the applied frequencyis more than the crossover frequency for MDA-231, pDEPwill be applied to CTCs. On the other hand, when the fre-quency is less than the crossover frequency for white bloodcell, it experiences nDEP; hence in this middle range, breastcancer cells would experience pDEP which attracts them tothe microposts and possibly results in trapping while whiteblood cells would experience nDEP. Generally, it is easier toattract particles using pDEP rather than repelling them bynDEP [14]. Furthermore, working in pDEP regime is morestraight-forward especially in low conductive mediums [27].
Most of the previous studies approximated medium con-ductivity dependency to temperature as a linear function [15].However, Porras et al. demonstrate that it is more accurate touse quadratic equation as [28]
� = �0
[1 + P1 (Tmean − T0) + P2(Tmean − T0)2] (4)
where �0 is conductivity at reference temperature (T0) andparameters P1 and P2 were determined experimentally byPorras et al. which here would be 0.02071 1
K and 4.3 ×10−5 1
K 2 respectively.For the permittivity and viscosity of the medium, same
as previous studies, we have [15, 18, 20, 29]
ε (T ) = ε0 (1 + (T − T0)) (5)
� = 2.761 × 10−3exp(
1713K
T
)(6)
where ε0 is fluid permittivity at reference temperature and is temperature coefficient of fluid permittivity which is-0.0046 1
K in this study. Other properties such as thermal con-ductivity and heat capacity can be safely assumed as constantas DI water in our study.
2.2 Numerical model description
Joule heating modelling with associated ET flows requirescoupling three physics: thermal, electric, and fluid flow. Inthis regard, COMSOL Multiphysics (Fluid Flow, Heat transferin fluids, and AC/DC) was used to solve for the flow, temper-ature, and electric fields in the system. Also, we have usedparticle tracing module in COMSOL Multiphysics to trackthe trajectory of the bioparticles. The geometry is shown inFig. 2. For calculating flow rates, we assumed the height ofthe channel as 100 �m.
Figure 1. (A) Clausius-Mossoti factor for MDA-231in different conductivities,(B) The behavior of Breastcancer cell (blue) and Whiteblood cell (red) for differentfrequencies.
872 A. Aghilinejad et al. Electrophoresis 2018, 39, 869–877
Figure 2. (A) Isometric view of the iDEP device, (B) Geometry ofthe microchip and design parameters.
The equations and numerical method to solve them areillustrated in detail in the supporting document.
To solve these coupled physics, three sets of boundaryconditions are required, and summarized in Table 2.
3 Results and discussion
3.1 Single constriction iDEP; Validation study
To validate our developed numerical model, the ET flows,as a result of the non-uniform temperature rise in thechannel, were modeled and compared with experimen-tal and numerical results reported by Sridharan et al.[18] (Fig. 3) in the special case of 600 V AC appliedvoltage.
According to the results, our model can predict wellthe ET flows associated with Joule heating. Specifically,as shown in Fig. 3B, the model can accurately predictthe ET vortices with specific circulation directions at in-let and outlet of the microchannel. In order to validateof our simulation, we mainly focus on ET flow patternand the presence of vortices rather than focusing on mag-nitude. Sridharen et al. [18] used very high convectiveheat transfer coefficient in their research in order to beconsistent with their experimental results. Therefore compar-ing the magnitudes would not be helpful to compare our sim-ulation with their results. However, for the current study, theability of our developed numerical model for predicting bothJoule heating and the pattern of ET flows would be sufficientenough.
3.2 Effect of joule heating on temperature,
conductivity, and electrical field
One of the major phenomena of iDEP technique is the re-sulting high temperature gradients that would rise due to thehigh electric field gradients.
In Fig. 4A, the temperature profile on the centerlineof the microchannel is depicted. Due to heat flux boundarycondition that is applied on the outlet, the temperature firststarted to increase to its maximum and after that decrease.Figure 4B depicts the maximum temperature inside thechannel for different initial conductivities with respect tothe applied voltage. Because our goal here was to separateMDA-231 from WBCs, for different conductivities, the fre-quency should be changed in order to have different typeof DEP forces (pDEP and nDEP). We used 20 kHz for0.01 S/m, 100 kHz for 0.05 S/m and 300 kHz for 0.075 S/mand 0.1 S/m conductivities according to Fig. 1. These fre-quencies are in line with the ranges which were previously
Figure 3. Comparison of the ET flows, as a result of Joule heating,between (A) the work by Sridharan et al., and (B) our developednumerical model. The results shows the capability of our modelto predict such phenomenon.
Table 2. Summary of the utilized boundary conditions for modeling Joule heating and the corresponding electrothermal flow
Physics Inlet Outlet Channel walls
Electric field Electric potential (V = Vi n ) Ground (V = 0) Electric insulation (n · (�E ) = 0)Fluid flow Velocity inlet (v = U i n ) Pressure outlet (Pout = 0) No slip (v = 0)Heat transfer (T = T0) Outflow (−n · (k∇T ) = 0) Constant Temperature T = T0 (Room Temperature)
Figure 4. (A) Temperatureprofile on the centerline ofthe microdevice, (B) Maxi-mum temperature value fordifferent conductivities forcommon range of appliedvoltage in iDEP devices, (C)changes in conductivity dueto the temperature gradi-ent inside the microchip,(D) Deviation from the electricfield by comparing the gradi-ent of electric field squaredwhen Joule heating is con-sidered (∇|E |2JH) neglected(∇|E |2).
reported from the experiments done by Das et al. [35]. Notethat although we focused on MDA-231 for separation in thisstudy, most of CTCs behave with a similar trend in the pres-ence of electrical field. Therefore the strategy deployed inthis research, can also be applied for different types of CTCs.In Fig. 4C, the maximum amount of conductivity for differ-ent applied voltages has been presented in different initialconductivities. Even for moderate voltage differences, therewould be a significant change in conductivity. Such a highlynon-linear trend and its effects should be considered in thedevice behavior specially for trapping the particles as it altersthe Classius-Mossoti factor. Figure 4D represents the varia-tion in ∇|E |2 when JH is considered (∇|E |2JH) by comparingthe values obtained by neglecting JH (∇|E |2). By consideringthese changes in conductivity and electric field gradient dueto the temperature in design step, we would be able to pre-dict the influence of the JH on electrical performance of thedevice.
3.3 Effect of fluid circulations on particle separation
Presence of ET forces inside the device causes motion in thefluid and creates vortices. By modeling the ET force in the mi-crochip, we can predict these motions inside the microchan-nel. An important implication of these modeling would beto enable the designers to control the effects of ET flow and
even use these vortices inside their devices for separation.Figure 5 shows an example case illustrating the JH-induceET flows in the microchip with an applied voltage of 500 V.
The presence of these vortices could change the regulartrajectory of the particles that is predicted by DEP force. Forquantitatively showing the effect of these vortices on the mainflow, the velocity profile is depicted for two different cases onthe centerline: one that considers ET flows and one that ne-glects ET flows (Fig. 5B and 5C). Note that the velocity profileis depicted for two cases as well, one with 0.05 S/m conduc-tivity for media and another with 0.01 S/m conductivity. It isclear that in lower conductivity, the effect of vortices is neg-ligible (Fig. 5C), as previously reported by Gallo-Villanuevaet al. [23] while the effect of ET flow on higher conductivity(Fig. 5B) is significant. Hereafter, all the further studies areconducted in a medium with 0.05 S/m conductivity becauseof investigating the effects of ET vortices in physiologicalrange on particle separation.
To investigate the effect of ET flow on particle trajectory,the trajectory of particles was modeled in the absence andpresence of ET flow (Fig. 6). The inlet velocity of the flowwas 500 �m/s which is among the highest inlet velocities foriDEP devices corresponded to 0.1 mL/h flow rate.
Figure 6 represents the difference in particle trapping inthe presence of electrothermal flow. Comparing Fig. 6A and6B, presence of ET flow decreases the velocity of particles inthe first columns of posts and cause more particles to trap.
874 A. Aghilinejad et al. Electrophoresis 2018, 39, 869–877
Figure 5. (A) Fluid streamlines inside the microchannel which causes vortices to arise due to electrothermal forces between the postsin a medium with 0.05 S/m conductivity, velocity profile on the centerline (B) For 0.05 S/m initial conductivity, (C) For 0.01 S/m initialconductivity.
Figure 6. Simulation results obtained using COMSOL Multi-physics software. A comparison of cell (MDA-231) trajectory in-side the channel: (A) In the absence of ET flow, (B) In the presenceof ET flow. Note that more cells are getting trapped in the pres-ence of ET flow.
These simulations could show the significance of the effectof ET flow even in high flow rates. As it could be noticedfrom Fig. 6, in the absence of ET flow, more cells are run-ning away from pDEP traps. Hence, the presence of ET flowcould enhance the separation of the cells. With respect tothis point that significant temperature rise will threaten thecells’ viability, decreasing the cells’ residual time in DEP trapscompensates this issue while allowing us to take advantage ofJH-induced ET vortices. One way to achieve this is to periodi-cally apply perpendicular flow to release the trapped cells [36].
To gain an accurate and quantified comprehension onhow JH and corresponding ET flow would affect cell separa-tion and manipulation, we define a dimensionless force ratioas the ratio between the DEP force and surrounding fluidforce. The surrounding fluid force used in the force ratio is
caused by the fluid flow due to the ET and pressure gradienteffects. This force is calculated based on Eq. S-10 consideringonly the fluid velocity and neglecting the cell velocity. To trapthe target cells, higher value of the force ratio experienced bythose cells is more desirable. The main advantage of usingthis parameter is to simultaneously investigate the effects oftemperature and JH on electrical field, conductivity, ET forceand velocity which could define the functionality and perfor-mance of the design. Using Eqs. (1) and S-10, , the forceratio, would be
= FDE P
F f low
= r 2cel l
3
(εm Re(KC M)
�
) ∇|E |2|v| (7)
Figure 7 represents the force ratio along the centerlineof the microchip for 0.02 mL
hr , 0.04 mLhr and 0.06 mL
hr inletflow rates at 500 V applied voltage in 100 kHz to trap theMDA-231 cancer cell. In Fig. 7A to 7C, the effect of ETflow was neglected while in the rests, the ET flow effect wasconsidered.
As it is shown in Fig. 7, in all the cases we can achievehigher force ratios by using the ET flow on the centerline ofthe microchannel at first columns of posts which generallyare more important than others for trapping the particles.Due to the presence of ET flow, the magnitude of particlesvelocity would decrease and cause higher force ratio. Notethat force ratio decreases by moving along the centerlinetoward the outlet. The main reason is the decrease in ∇|E |2due to the JH-induced increase in conductivity according toFig. 4. Although the force ratio decreases by moving alongthe channel, we are still capable to get higher force ratios andtrap the cells in first rows.
Figure 7. Force ratio for (A) 0.02 mLhr , (B) 0.04 mL
hr and (C) 0.06 mLhr inlet flow rates and 500 V applied voltage for breast cancer cell. These
results show the effect of ET flow which enhances the cell separation by decreasing the cell’s velocity.
3.4 Effect of geometry on fluid circulations
Post shape and configuration has a direct effect on iDEP trap-ping efficiency as it affects electric and flow field distributionthroughout the system. In Fig. 8, the comparison for threebasic geometries (circle, diamond, square) has been done. Asshown in Fig. 8, ∇|E |2 for diamond shape post is higher thanothers as confirmed by previous researches [10, 37]. How-ever, the force ratio for diamond shape microposts is smallerthan circular and square shape posts. The reason is that inthe presence of the ET vortices inside the channel, the veloc-ity profile is affected by these vortices and shape of microp-osts has influence on this profile. In Fig. 8D, the maximumforce ratio for square shape post is higher than circular and
diamond for different inlet flow rates. Note that thesevalues are calculated along the centerline of the de-vice which are located at the largest distance fromthe posts. This means that trapping of the par-ticles can also happen in values less than one.Figure 8E compares the temperature rise in square anddiamond shape post relative to circular one. The neg-ative percent for diamond represents that in these de-signs, the temperature rise is less than the circularposts.
These graphs provide a thorough view for using the dif-ferent shape post depends to the application and can be servedas a design guideline. For instance, dealing with particleswhich are not temperature sensitive, choosing a square shape
Figure 8. (A, B, C) The gradient of the electric field squared for different geometries along the centerline, (D) Force ratio for differentgeometries in different flow rates, (E) Temperature rise inside the channel for square and diamond shape microposts relative to circularpost.
876 A. Aghilinejad et al. Electrophoresis 2018, 39, 869–877
post would provide higher efficiency and trapping ratio whiledealing with temperature sensitive bioparticles such as mam-malian cells, diamond would be the best option for keepingthe temperature low and does not decrease the force ratiosignificantly compare to circular posts.
4 Concluding remarks
In this study, mathematical modeling was used to simulatethe iDEP device performance and design scenario for CTCtrapping and separation. To achieve a comprehensive con-ception toward the technique, JH and induced ET flows wasmodeled and studied. We developed a fully coupled electro-thermo-fluid numerical tool via temperature dependent ma-terial properties and particle tracing modeling to predict thecell trajectory and device performance for different condi-tions. We also demonstrated that by choosing appropriatefrequency, the selective trapping of CTCs become possible,according to its dielectric properties.
The implication of our finding is that ET flows are notalways a disadvantage but also can be used to enhance the per-formance for separation. To quantify this effect, dimension-less force ratio was introduced and utilized in the modelingto show the effects of ET flow and facilitate the compari-son between different embedded insulating post geometrieswhich is very critical for iDEP devices. Results show that al-though the diamond shape posts provide higher electric fieldgradient, square shape microposts have higher force ratioin presence of ET flows. The systematic research work con-ducted here provides the fundamental groundwork as well asdesign guidelines for developing efficient iDEP devices forbioparticles and cells separation.
The authors have declared no conflict of interest.
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