micromachines Article

Deformability-Based Electrokinetic Particle Separation Teng Zhou 1,2 , Li-Hsien Yeh 3 , Feng-Chen Li 4 , Benjamin Mauroy 5 and Sang Woo Joo 2, * 1 2 3 4 5

*

Mechanical and Electrical Engineering College, Hainan University, Haikou 570228, China; [email protected] School of Mechanical Engineering, Yeungnam University, Gyongsan 712-719, Korea Department of Chemical and Materials Engineering, National Yunlin University of Science and Technology, Yunlin 64002, Taiwan; [email protected] School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, China; [email protected] Laboratoire JA Dieudonné, UMR CNRS 7351, Université Côte d’Azur, Université de Nice Sophia Antipolis, Parc Valrose 06108 Nice Cedex 02, France; [email protected] Correspondence: [email protected]; Tel.: +82-53-810-2568

Academic Editors: Xiangchun Xuan and Shizhi Qian Received: 14 July 2016; Accepted: 7 September 2016; Published: 20 September 2016

Abstract: Deformability is an effective property that can be used in the separation of colloidal particles and cells. In this study, a microfluidic device is proposed and tested numerically for the sorting of deformable particles of various degrees. The separation process is numerically investigated by a direct numerical simulation of the fluid–particle–electric field interactions with an arbitrary Lagrangian–Eulerian finite-element method. The separation performance is investigated with the shear modulus of particles, the strength of the applied electric field, and the design of the contracted microfluidic devices as the main parameters. The results show that the particles with different shear moduli take different shapes and trajectories when passing through a microchannel contraction, enabling the separation of particles based on their difference in deformability. Keywords: arbitrary Lagrangian–Eulerian (ALE); dielectrophoresis; microfluidic; particle separation

1. Introduction The separation of small particles is one of the most important steps in many chemical and biological analyses [1–6]. Over the past decade, many microfluidic devices for the separation of particles have been developed, including passive and active types [7–12]. Passive methods incorporate the internal force and the fluid mechanism, such as hydrophoretic filtration [13,14], hydrodynamic filtration (HDF) [15–17], lateral displacement (DLD) [18–20], and inertial forces [3,6,21–23], while active methods involve electrophoresis or dielectrophoresis (DEP) [4,24–30], magnetophoresis [2,31–33], optical methods [34,35], and acoustophoresis [36]. DEP is a phenomenon in which a force is exerted on a dielectric particle when it is subjected to a non-uniform electric field. DEP has great advantages: it is label-free, based on simple instruments, and correlated to high selectivity and sensitivity. In association with new and efficient microfluidic devices [27], DEP has been widely used to manipulate various micro/nano-scale bio-entities, such as cells [37], bacteria [38], and viruses [39,40]. A number of physical or topological properties of cells or particles, including size, shape, and deformability, can be used for separation. Some microfluidic separation devices that use the deformability of the motioned object have been proposed and validated. They are based either on inertia [41], obstacles [42] or on the DLD method [19]. In a straight microchannel, Hur et al. [41] found that deformability affects the particle equilibrium position, and were able to enrich cells

Micromachines 2016, 7, 170; doi:10.3390/mi7090170

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using inertial force, cells’ deformability, and size acting as biomarkers. Zhu et al. [42] proposed found that deformability the particle equilibrium position, anddeformability, were able to enrich a microfluidic device that can affects sort elastic capsules according to their usingcells a channel using inertial force, cells’ deformability, and size acting as biomarkers. Zhu et al. [42] proposed a with a semi-cylindrical obstacle and a diffuser. Using three-dimensional immersed-boundary microfluidic device that can sort elastic capsules according to their deformability, using a channel finite-element lattice-Boltzmann simulations, Krueger et al. [19] demonstrated that DLD devices with a semi-cylindrical obstacle and a diffuser. Using three-dimensional immersed-boundary can be used to perform the deformability-based separation red blood cells (RBC). Lincan et al. [37] finite-element lattice-Boltzmann simulations, Krueger et al. [19]ofdemonstrated that DLD devices separated from based onseparation size and of deformability a microfluidic be cancer used to cells perform theleukocytes deformability-based red blood cellsusing (RBC). Lin et al. [37] ratchet separated cells from leukocytes based on size and deformability using adeformability microfluidic ratchet mechanism. The cancer aforementioned separation methods based on the particle are passive mechanism. The aforementioned separation methods based on the particle deformability are methods [19,37,41,42], and rely either on both size and deformability or on significant differences passive methods [19,37,41,42], and rely either on both size and deformability or on significant in deformability. differences in deformability. Here we present a microfluidic device electricseparation separation of particles Here we present a microfluidic devicefor for the the electric of particles based based on theiron their deformability, as shown Figure Separation is systematically investigated with numerical simulations. deformability, as in shown in 1.Figure 1. Separation is systematically investigated with numerical Fluid–structure interaction is simulated using finite elementsusing and an arbitrary Lagrangian–Eulerian simulations. Fluid–structure interaction is simulated finite elements and an arbitrary (ALE) method. The ALE method has been validated both experimentally and[5,12,13] method.Lagrangian–Eulerian The ALE method (ALE) has been validated both experimentally and theoretically for rigid theoretically for rigid [5,12,13] and deformable [43,44] particles. The proposed microfluidic device is and deformable [43,44] particles. The proposed microfluidic device is sensitive to the shear modulus sensitive to the shear modulus of deformable particles, and is capable of separating particles with of deformable particles, and is capable of separating particles with small differences in shear moduli. small differences in shear moduli. A parametric study is also conducted to optimize the A parametric studyof isthe also conducted to optimize the performance of the proposed device. performance proposed device.

Figure 1. Electrokinetic motion of a deformable spherical particle of radius rp in a microfluidic chip

Figure 1. Electrokinetic motion of a deformable spherical particle of radius rp in a microfluidic chip with a contraction throat. w: width of the main channel. Widths of the channels with outlet IH and FE with a contraction throat. w: width of the main channel. Widths of the channels with outlet IH and FE are identical. r1 and r2 are the radii of the two quad-circles, respectively; dp is the distance between the are identical. andspherical r2 are the radiiand of the two quad-circles, center rof1 the particle the nearest channel wall.respectively; dp is the distance between the center of the spherical particle and the nearest channel wall. The paper is organized as follows: Section 2 includes the theory for the deformable particle trajectory and separation mechanism. Section 3 presents the simulated results of the particle The paper is organized as follows: Section 2 includes the theory for the deformable particle separation process and how the parametric studies—including the shear modulus, electric field trajectory and separation mechanism. Section 3the presents the simulated results of thethe particle intensity, and geometry parameters—affect particle trajectory. Section 4 concludes paper. separation

process and how the parametric studies—including the shear modulus, electric field intensity, and 2. Formulation and Numerical Methodtrajectory. Section 4 concludes the paper. geometry parameters—affect the particle 2.1. Mathematical Model 2. Formulation and Numerical Method In this study, we consider a two-dimensional (2D) channel that consists of a uniform inlet

2.1. Mathematical section withModel a converging-expansion part, and two uniform outlet sections. This geometry is used to study electrokinetic particle translation, as shown in Figure 1. The contraction part of the

In this study, we consider a two-dimensional (2D) channel that consists of a uniform inlet converging-expansion channel is generated by two quad-circles with different radii. The two outlet section sections with a are converging-expansion part, two uniform sections. geometry is designed to sort particles withand sufficiently different outlet trajectories into twoThis groups. A used to circular study electrokinetic particle translation, as shown in Figure 1. The particle with radius rp located at a distance dp from the channel wallcontraction is shown in part the of the magnified view below. An electric potentialby is two applied externally from AB to grounded outlets converging-expansion channel is generated quad-circles withinlet different radii. The two outlet IH and FE to an incompressible Newtonian fluid domain Ω f. The electric field E, generated in the sections are designed to sort particles with sufficiently different trajectories into two groups. A circular particle with radius rp located at a distance dp from the channel wall is shown in the magnified view below. An electric potential is applied externally from inlet AB to grounded outlets IH and FE to an incompressible Newtonian fluid domain Ωf . The electric field E, generated in the domain, induces the electrokinetic motion of a hyperelastic particle Ωp suspended in the fluid. Because the electric double layer (EDL) thicknesses adjacent to the charged particle and the channel wall are very thin

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in comparison to the particle radius and the channel widths, the thin-EDL approximation is applied. The electrical potential φ in the domain Ωf can be described by the Laplace equation,

∇2 φ = 0 in Ω f

(1)

The local electric field E can be calculated from the electric potential φ by E = −∇φ in Ω f

(2)

Because a potential shift is applied across the microfluidic chip, the boundary conditions for φ on the entrance and exits of the microchannel are φ = φ0 on AB

(3)

φ = 0 on IH and EF

(4)

and Solid boundaries—including the channel wall (Гw ) and particle surface (Гp )—are electrically insulating, yielding n·∇φ = 0 on Γw and Γ p (5) where n is the unit outward normal vector. The Reynolds number in the microchannel is very small, so that the conservation of momentum and mass can be described by the Stokes and the continuity equations: ρf

∂u = ∇·[− pI + µ(∇u + ∇uT )] in Ω f ∂t

(6)

and

∇·u = 0 in Ω f

(7)

where ρf and µ are the density and the viscosity of the fluid, respectively; u is the velocity vector; p is the hydrodynamic pressure; I is the unit tensor; and ∇uT is the transpose of the velocity gradient ∇u. An open boundary condition is specified at the inlet and the outlets:

∇·[−pI + µ(∇u + ∇uT )] = 0 on AB, IH and EF

(8)

The Smoluchowski slip boundary condition for Newtonian electroosmotic flow (EOF) is applied on the charged channel wall: u = uw =

ε f ζw ( I − nn)·∇φ on Γw µ

(9)

where uw is the fluid velocity on the channel wall, and εf and ζw are, respectively, the fluid permittivity and the zeta potential of the channel wall. The velocity up on the particle consists two parts: (i) the Smoluchowski slip velocity arising from the particle surface charge; and (ii) the velocity of the particle motion. The boundary condition on the particle surface is then ε f ζw ∂S u = up = ( I − nn)·∇φ + on Γ p (10) µ ∂t where ζp is the zeta potential of the particle and S is the displacement of the deformable particle caused by the particle deformation and movement, governed by ρp

∂2 S − ∇·σ(S) = 0 in Ω p ∂t2

(11)

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Here ρp is the density of the deformable particle, and σ(S) is the Cauchy stress in the solid phase, which is a function of the displacement of the particle. In the following simulations, the particle is considered as an incompressible neo-Hookean material, described by a strain energy density function [43]. The force on the particle–fluid interface consists of hydrodynamic and electrokinetic stresses: Micromachines 2016, 7, 170

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σp ·np = σf ·nf + σE ·nf

Here ρp is the density of the deformable particle, and σ(S) is the Cauchy stress in the solid phase, which is a function of the displacement of the particle. In the following simulations, the particle is σf = −pI + µ(∇u + ∇uT ) considered as an incompressible neo-Hookean material, described by a strain energy density function [43]. 1 σE = ε f consists EE − of ε ( E· E) I The force on the particle–fluid interface 2 fhydrodynamic and electrokinetic stresses:

(12) (13) (14)

(12) σp·npstress = σf·nftensor + σE·nf on the particle surface, the hydrodynamic where σp , σf , and σE are, respectively, the total stress tensor, and the Maxwell stress tensor, (13) σf =respectively. −pI + μ(∇u + ∇uT)

2.2. Numerical Method and Code Validation σE = εfEE − 1 ε (E ⋅ E)I f

(14)

2

The above system is solved numerically using the commercial finite element package COMSOL where σp, σf, and σE are, respectively, the total stress tensor on the particle surface, the (Versionhydrodynamic 4.3a, COMSOL Group, Sweden) coupled with MATLAB (Version 8.2, MathWorks stress tensor,Stockholm, and the Maxwell stress tensor, respectively. Inc., Natick, MA, USA), operated in a high-performance cluster. The coupled system of hydrodynamic, 2.2.field, Numerical andmechanics Code Validation electrical and Method particle is solved simultaneously. As we are using the ALE method, the mesh is The deformed in orderis tosolved follow the motion of the andfinite the mesh quality decreases above system numerically using theparticle, commercial element package COMSOL (Version 4.3a, COMSOL Group,into Stockholm, Sweden) coupled with MATLAB (Version 8.2, falls progressively when the particle progresses the microfluidic device. When the mesh quality MathWorks Natick, MA, operated in a high-performance Thecurrent coupledparticle system ofposition, below 0.7 (out of aInc., maximum 1.0) USA), [1,6,13], the domain is re-meshed cluster. with the hydrodynamic, electrical field, and particle mechanics is solved simultaneously. As we are using step is the solution is mapped to the new mesh, and the computation is restarted. The previous the ALE method, the mesh is deformed in order to follow the motion of the particle, and the mesh repeated each time the mesh quality falls below 0.7. quality decreases progressively when the particle progresses into the microfluidic device. When the To mesh validate thefalls present compare 1.0) its predictions with the analyticalwith result quality belowmethod, 0.7 (out ofwe a maximum [1,6,13], the domain is re-meshed the of Keh and Anderson [45] for the electrophoresis of a rigid of diameterisdrestarted. along the axis current particle position, the solution is mapped to thespherical new mesh,particle and the computation The previous step isof repeated eacha.time the mesh falls below 0.7. EDL and negligible DEP force, of an infinite long tube diameter Under the quality conditions of thin To validate the present method, we compare its predictions with analytical particle result of (U Keh) is the approximate analytical solution for the electrophoretic velocity of the a spherical p and Anderson [45] for the electrophoresis of a rigid spherical particle of diameter d along the axis of # " tube of diameter  5 of thin EDL  and 6negligible  force, the   an infinite long α.3Under the conditions DEP d d ζw d approximate solution for the velocity of a spherical particle + electrophoretic 1.89632 − 1.02780 1 − (Up) is U0 U p = analytical 1 − 1.28987

a

a

a

ζp

(15)

 d d  d   ζ  Up = 1 − 1.28987   + 1.89632   − 1.02780     1 − w  U0 (15)  axial ζ p  strength of the external where U0 = εf ζp Ez/ µ is the Smoluchowski Ez being   a  velocity,  awith   a  the  3

5

6

electric field in the absence of particle. In the benchmark, Ez = 30 kV, ζw = 60 mV, ζp = 20 mV, 0 = εfζpEz/μ is the Smoluchowski velocity, with Ez being the axial strength of the external where − U10 εf = 7.08electric × 10 field F/m, ρf = 1000 kg/m3 , and µ = 0.001 Pa·s. To simulate a rigid particle, we used a in the absence of particle. In the benchmark, Ez = 30 kV, ζw = 60 mV, ζp = 20 mV, εf = 7.08 very large (G =kg/m 2000 Pa).μ As shown 2, athe numerical predictions Up using −10 F/m,for 3, and × 10value ρf =G1000 = 0.001 Pa·s.in ToFigure simulate rigid particle, we used a veryfor large our method are Pa). in good agreement analytical solution [45] value (symbols) for G (G = 2000 As shown in Figurewith 2, thethe numerical predictions forof UpKeh usingand our Anderson method (symbols) are in good agreement with the analytical solution of Keh and Anderson [45] (solid line). (solid line).

Figure 2. Velocity of a rigid sphere translatingalong along the a cylindrical tubetube as a function of the of the Figure 2. Velocity of a rigid sphere translating theaxis axisofof a cylindrical as a function ratio between the diameter d of the sphere and diameter a of the channel. The solid line and triangle ratio between the diameter d of the sphere and diameter a of the channel. The solid line and triangle symbols represent the analytical solution of Keh and Anderson [45] and the numerical results from symbolsthe represent the analytical solution of Keh and Anderson [45] and the numerical results from the present model, respectively. present model, respectively.

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3. Results and Discussion In the cases reported here, the geometric parameters are set to w = 200 µm, rp = 10 µm, and Micromachines 2016, 7, 170 5 of 11 dp = 10 µm, and the physical properties of the aqueous solution are ρf = 1000 kg/m3 , µ = 0.001 Pa·s, − 10 and ε3.f = 7.08 ×and 10Discussion F/m. The density and the permittivity of the neutrally buoyant deformable Results particle are assumed to be identical to those of the solution, ρp = 1000 kg/m3 and εp = 7.08 × 10−10 F/m. In the cases reported here, the geometric parameters are set to w = 200 μm, rp = 10 μm, The zeta potentials on the channel wall (ζw ) and particle (ζp ) are set to −60 mV and 20 mV, respectively; and dp = 10 μm, and the physical properties of the aqueous solution are ρf = 1000 kg/m3, μ = 0.001 Pa·s, the particle is to move−10 from left to right. and εf = 7.08 × 10 F/m. The density and the permittivity of the neutrally buoyant deformable In this section, the process is presented, afterρwhich a parametric study is performed to particle are assumedseparation to be identical to those of the solution, p = 1000 kg/m3 and εp = 7.08 × 10−10 F/m. investigate the effects of shear modulus, electric field intensity, and geometrical 1 and r2 ) The zeta potentials on the channel wall (ζw) and particle (ζp) are set to −60 parameters mV and 20(rmV, on the particle separation process. respectively; the particle is to move from left to right. In this section, the separation process is presented, after which a parametric study is

3.1. The Separation performed to Process investigate the effects of shear modulus, electric field intensity, and geometrical parameters (r1 and r2) on the particle separation process. The separation of dissimilar particles can be achieved by making their trajectories different. In this study,3.1. weThe chose to discriminate the particles using their shear modulus G as a marker. Particles with Separation Process different shear moduli reach different deformations and shapes, even if their volumes are identical. separation of dissimilar particles can be achieved by making their trajectories different. In Due to theThe difference in their shapes, the DEP force on the particles—which tends to push the particle this study, we chose to discriminate the particles using their shear modulus G as a marker. Particles away from the streamlines—is different, even if their location and surrounding electric field are with different shear moduli reach different deformations and shapes, even if their volumes are identical. To illustrate that the DEP force on the particles depends on the particle shape, we calculated identical. Due to the difference in their shapes, the DEP force on the particles—which tends to push the DEP force inaway the spanwise direction for two different with the volume: one with the particle from the streamlines—is different, even particles if their location and same surrounding electric circular shape and one with elliptical shape. The distances from the centers of the particles to field are identical. To illustrate that the DEP force on the particles depends on the particle shape, the we wall were calculated also set tothe beDEP identical. order to demonstrate role of DEP forces onsame the two different force inInthe spanwise direction forthe twosole different particles with the volume: one with shape and withFigure elliptical shape. The from of particle the particles particles, theycircular are first fixed inone space. 3 shows thatdistances the force on the the centers circular is larger to the wallon were set to one. be identical. In expected order to demonstrate the sole role ofwill DEPbe forces on the than the force the also elliptical It is then that the circular particle pushed farther two different particles, they are first fixed in space. Figure 3 shows that the force on the circular toward the center than the elliptical one. This also implies that the DEP focusing can be weakened by particle is larger than the force on the elliptical one. It is then expected that the circular particle will the particle deformation. In this way, particles with different shear moduli can be separated due to a be pushed farther toward the center than the elliptical one. This also implies that the DEP focusing difference in their deformations. can be weakened by the particle deformation. In this way, particles with different shear moduli can Figure 4 shows different trajectories for particles that exhibit only a difference in shear moduli. be separated due to a difference in their deformations. Shear moduli 20, 40,different 60, 80, trajectories 100, and 200 Pa are simulated, but only three cases are presented Figureof4 shows for particles that exhibit only a difference in shear moduli. here for themoduli sake of With different deformation and shape, particles experience different Shear of clarity. 20, 40, 60, 80, 100, and 200 Pa are simulated, but onlythe three cases are presented here hydrodynamic Maxwell stresses, resulting in different particle trajectories for particles for the sakeand of clarity. With different deformation and shape, the particles experience different with hydrodynamic and Maxwell stresses, resulting in different particle trajectories for particles with different shear moduli. different shear moduli.

Figure 3. The spanwise component of dielectrophoretic (DEP) force along the channel for particles

Figure 3. The spanwise component of dielectrophoretic (DEP) force along the channel for particles with with two different shapes (identical volumes) with r1 = 60 μm, r2 = 120 μm. The radius of the circular two different shapes (identical volumes) with r1 = 60 µm, r2 = 120 µm. The radius of the circular particle particle is 5 μm, while the lengths of the major and minor axis of the ellipse are 6.25 and 4 μm, is 5 µm, while the lengths of the major and minor axis of the ellipse are 6.25 and 4 µm, respectively. respectively.

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Figure 4. Trajectories of particles with different shear moduli G with r1 = 60 μm, r2 = 120 μm, and the

Figure 4. Trajectories of particles with different shear moduli G with r1 = 60 µm, r2 = 120 µm, and strength of the axial electric field in the channel E = 30 V/m. An enlarged view of the contraction the strength of the electric fieldmodulus in the channel E = of 30NV/m. An view of the contraction region is onaxial the right. GN: shear of the particle Pa. (axis in enlarged μm). region is on the right. GN: shear modulus of the particle of N Pa. (axis in µm). 5, twoof different with G shear = 20 and 200 Pa start rfrom same As the FigureIn4.Figure Trajectories particlesparticles with different moduli G with 1 = 60the μm, r2 = location. 120 μm, and the channel width decreases, thefield electric field intensity At the electric fieldthe is Figure 4. of Trajectories of particles with different shear moduli with r1beginning, = 60 μm, = 120 μm, and strength the axial electric in the channel E =increases. 30 V/m.GAn enlarged viewr2the of the contraction In Figure 5, of twodeform different particles with Gthe = 20 200 Pa start from the same location. As the too weak as first and third positions in view Figure Thecontraction motion of strength axial the electric field in between the channel E =and 30 V/m. An enlarged of5.the region is ontothe the right. GN:particles, shear modulus of the particle of N Pa. (axis in μm). channel width the electric field intensity increases. At in the beginning, thevelocity electric field is the two particles is thus identical. The components of the region isdecreases, on the right. GN:almost shear modulus of thestreamwise particle of and N Pa.spanwise (axis μm). vectors (shown Figure 6) are almost identical. As the third progress through the channel, too weakIn to deform theinparticles, asalso between and positions insame Figure 5. TheAs motion of Figure 5, two different particles with the G = first 20 and 200particles Pa start from the location. the the electrical stressdifferent on the particle increases, inducing the200 particle with from the lowest shear location. modulus to In Figure 5, two particles with G = 20 and Pa start the same As the the two particles thus almost identical. The streamwise andAtspanwise components of the channel widthisdecreases, the electric field intensity increases. the beginning, the electric fieldvelocity is deform. In the fourth position in Figure 5, the electric field causes the particle with channel width decreases, the also electric field intensity increases. At the beginning, the electric fieldchannel, is too (shown weak to deform the particles, as between the first and third positions in Figure 5. The motion of vectors in Figure 6) are almost identical. As the particles progress through the G = 20 Pa to deform, while it has little effect on the one with G = 200 Pa. Due to the difference in too to deform the particles, as between the first and and thirdspanwise positionscomponents in Figure 5. of The motion of the weak two particles is identical. streamwise the velocity the electrical stress the particle increases, inducing the particle with the lowest shear modulus their shapes,on thethus totalalmost forces on the two The particles are different, as shown in Figure 3. Accordingly, the two particles is thus almost identical. The streamwise and spanwise components of the velocity vectors (shown incomponents Figure 6) are also almost identical. As the particles progress through thewith channel, the velocity (shown in Figure5, 6)the show conspicuous difference between particles to deform. In the fourth position in Figure electric field causes the particle with G = 20 Pa to vectors in Figure are almostcomponents identical. the particles through the electrical the6) particle increases, inducingAs the particle withprogress lowest shear modulus to G (shown = 20 Pastress and Gon = 200 Pa. Thealso spanwise in particular show athe negative value forthe G =channel, 20 deform, while it has little effect on the one with G = 200 Pa. Due to the difference in their shapes, the electrical onGthe particle inducing theelectric particle with shear modulus to Pa, while that for = 200 Pa hasincreases, a positive value. particles’ trajectories arelowest fully separated upon with deform. In stress the fourth position in Figure 5,Thethe field the causes the particle the total forces on twoconstriction, particles are different, as shown in Figure 3. Accordingly, thewith velocity thethe channel where the electric field the strongest. deform. the fourth in effect Figure causes thetheparticle G = 20reaching PaIn to deform, whileposition it has little on5,thethe oneiselectric with G =field 200 Pa. Due to difference in

components in Figure 6) show conspicuous between with G = 20 in Pa and G = 20shapes, Pa(shown to deform, while has effect on the one with Gas = shown 200 Pa.particles to the difference their the total forcesit on thelittle two particles aredifference different, inDue Figure 3. Accordingly, G = 200 Pa. The spanwise components in particular show a negative value for G = 20 Pa, while their shapes, the total forces on the two particles are different, as shown in Figure 3. Accordingly, the velocity components (shown in Figure 6) show conspicuous difference between particles with that the velocity components in Figure 6) show conspicuous between particles for GG==200 Paand has value. The particles’ trajectories aredifference fully aseparated upon reaching 20 Pa Ga =positive 200 Pa.(shown The spanwise components in particular show negative value for Gwith = 20 the G = 20 Pa and G = 200 Pa. The spanwise components in particular show a negative value for G = 20 Pa, while that for G = 200 the Pa has a positive particles’ trajectories are fully separated upon channel constriction, where electric fieldvalue. is theThe strongest. Pa, whilethe thatchannel for G = constriction, 200 Pa has a where positive Thefield particles’ trajectories are fully separated upon reaching thevalue. electric is the strongest. reaching the channel constriction, where the electric field is the strongest. Figure 5. Time trace of a deformable particle passing through the contraction with the shear modulus (a) G = 20 Pa and (b) 200 Pa while r1 = 60 μm, r2 = 120 μm, and E = 30 V/m. The positions from left to right represent time lapse of 0, 25, 40, 46, 51, 53.5, 55, 60, and 80 ms.

Figure 5. Time trace of a deformable particle passing through the contraction with the shear

Figure 5. Time trace trace of a deformable particle passing through the contraction withwith the shear modulus Figure 5. (a) Time deformable particle shear μm, r2 through = 120 μm,the andcontraction E = 30 V/m. Thethe positions modulus G = 20 Pa of anda (b) 200 Pa while r1 = 60passing (a) G modulus = 20 Pa and (b) G = 200 Pa while r = 60 µm, r = 120 µm, and E = 30 V/m. The positions from left 2 μm, = 60 r2 = 120 μm,and and80Ems. = 30 V/m. The positions (a)right G = 20 Pa and time (b) 200 Pa1of while from left to represent lapse 0, 25,r140, 46, 51, 53.5, 55, 60, to right represent time lapse of 0, 25, 40, 46, 51, 53.5, 55, 60, and 80 ms. from left to right represent time lapse of 0, 25, 40, 46, 51, 53.5, 55, 60, and 80 ms.

Figure 6. Velocity components of particles with different shear moduli in motion. (a) u, main flow direction; (b) v, orthogonal to main flow direction. Here r1 = 60 μm, r2 = 120 μm, and the electric field intensity in the channel is E = 30 V/m.

Figure 6. Velocity components of particles with different shear moduli in motion. (a) u, main flow Figure 6. Velocity components of particles with different shear moduli in motion. (a) u, main flow

60 μm,moduli r2 = 120 in μm, and the (a) electric field flow direction; (b) v, components orthogonal to of main flow direction. Here r1 =shear Figure 6. Velocity particles with different motion. u, main direction; (b) v, channel orthogonal main flow direction. Here r1 = 60 μm, r2 = 120 μm, and the electric field intensity in the is Eto = 30 V/m. direction; (b) v, orthogonal to main flow direction. Here r1 = 60 µm, r2 = 120 µm, and the electric field intensity in the channel is E = 30 V/m. intensity in the channel is E = 30 V/m.

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3.2. Effect of Shear Modulus The effect of particle Micromachines 2016, 7, 170 compliance is studied by varying the shear modulus G. Considering 7 of 11 that many engineering materials have shear modulus in the MPa or GPa range, most cells are in the kPa 3.2. Effect of Shear Modulus range, and some artificial liposomes can be as small as on the order of unity in Pa, a wide range of G was used the experiment. Here weisonly report the results for Gmodulus = 20 to G. 200Considering Pa becausethat for the Theineffect of particle compliance studied by varying the shear many engineering have shear modulus in the MPa or GPa range, most cells are inranging the kPafrom electric potential used,materials it is sufficiently wide to exhibit representative particle behaviors range, to and some Between artificial liposomes bethe as small as on the intensity order of unity in Pa, aenough wide range of G the compliant rigid. 20 and 60can Pa, electric field is strong to cause was used in the experiment. Here we only report the results for G = 20 to 200 Pa because for theleave particle to deform. The trajectories are not very different up to the contraction. As the particles electric potential used, it is sufficiently wide to exhibit representative particle behaviors ranging the contraction and reach the expansion channel, the differences become notable. Due to the elasticity, from compliant to rigid. Between 20 and 60 Pa, the electric field intensity is strong enough to cause the particle tends to recover its original shape as the electrical stress fades away. This relaxation process the particle to deform. The trajectories are not very different up to the contraction. As the particles is slow, however, and the differences in trajectories persist. For this reason, we can separate particles leave the contraction and reach the expansion channel, the differences become notable. Due to the basedelasticity, on their the shear moduli with their as trajectories in the tested configuration, particle tends to difference recover its between original shape the electrical stress fades away. This as shown in Figure 4. relaxation process is slow, however, and the differences in trajectories persist. For this reason, we can separate particles based on their shear moduli with difference between their trajectories in the

3.3. Effect External Electric Field in Figure 4. testedofconfiguration, as shown

The effect of the electric field intensity is studied by varying its amplitude in the straight channel 3.3. Effect of External Electric Field by adjusting the electric potential between the inlet and outlet, before the contraction channel to 20, effect the to electric intensity is studied by varying its in theshear straight 30, and 40The V/m. In of order showfield the clear separation performance, theamplitude particles with moduli channel by adjusting the electric potential between the inlet and outlet, before the contraction G = 20 and 200 Pa are used (Figure 7). The result shows that particles with the same shear modulus channel to 20, 30, and 40 V/m. In order to show the clear separation performance, the particles with move nearer to the upper wall when the electric field intensity increases. In Figure 7, the trajectories of shear moduli G = 20 and 200 Pa are used (Figure 7). The result shows that particles with the same particles with G = 200 Pa are the first, second, and fifth lines from top to bottom, with electric field shear modulus move nearer to the upper wall when the electric field intensity increases. In Figure 7, intensities E = 30, 20, and 10 V/m. thesecond, trajectories forlines different G increases the trajectories of particles with GThe = 200difference Pa are the in first, and fifth from top to bottom,when the electric field intensity increases. In order to amplify the difference, high electric field intensities with electric field intensities E = 30, 20, and 10 V/m. The difference in the trajectories for different G are needed. Inwhen practice, however, highincreases. electric field intensity might be possible, depending increases the electric fieldusing intensity In order to amplify thenot difference, high electric intensities needed. In practice, however, using high electric field shows intensity might be on thefield nature of the are particles (e.g., biological particles). The present result that Ex =not 20 V/m is possible, depending the nature of the (e.g., biological particles). The result sufficient to separate the on particles (Figure 7). particles The differences in the trajectories are, present however, already shows that with Ex = E 20=V/m is sufficient to aseparate the particles (Figure 7). Theshould differences in the for very significant 20 V/m, and such reasonable electric field intensity be sufficient trajectories are, however, already very significant with E = 20 V/m, and such a reasonable electric any actual applications [25–27]. field intensity should be sufficient for any actual applications [25–27].

Figure 7. Trajectories of aof particle for for various combinations G and andstrength strengthofof the Figure 7. Trajectories a particle various combinationsofofthe theshear shearmodulus modulus G axial the electric in the channel 60 µm = 120 theμm. right an enlargement x with r1Ex= with axialfield electric field in theEchannel r1 and = 60r2μm andµm. r2 =On 120 Onisthe right is an of the contraction region. stands for the electric field in the V/m and the enlargement of the Ei_Gj contraction region. Ei_Gj stands forstrength the electric fieldchannel strengthatini the channel at ishear V/m of and theparticle shear modulus the particle at j Pa. Axes are in μm. modulus the at j Pa. of Axes are in µm.

3.4. Effect of Geometrical Parameters of the Contraction Region: r1 and r2

3.4. Effect of Geometrical Parameters of the Contraction Region: r1 and r2 The geometrical parameters r1 and r2 can be used to control the particle trajectory (Figure 8).

The geometrical parameters r and r2 can be used to control the particle trajectory (Figure 8). Due to the repelling force on the1 channel wall, the particle cannot stay very close to the channel Due to the repelling force on the channel wall, the particle cannot stay very close to the channel wall in the contraction. The starting point of the particle is set to very close to the downward wall of wall in thethe contraction. The starting of moves the particle setcontraction to very close to the downward wall of the expansion channel. As thepoint particle towardisthe channel, the particle gradually expansion As the particle moves toward the contraction channel, the particle gradually moves moveschannel. away from wall. There is thus a non-negligible distance between the particle and the channel wall. The particle position will be adjusted by the channel wall, composed of two circles. away from the wall. There is thus a non-negligible distance between the particle and the channel wall.

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The particle position will be adjusted by the channel wall, composed of two circles. Then, 8changing Micromachines 2016, 7, 170 of 11 the size of r1 and r2 can be used to control the outlet as the particle leaves the channel. Then,particles changing the different size of r1 shear and r2moduli can be still usedhave to control the trajectories, outlet as the even particle leaves The with different when the the sizes of channel. r1 and r2 are varied. In Figure 8a, the particles with shear moduli G = 20 and 200 Pa all exit from the The particles with different shear moduli still have different trajectories, even when the sizes of downward outlet with r1 = 90 µm and r2 = 90 µm. The figure shows that the repelling force is not r1 and r2 are varied. In Figure 8a, the particles with shear moduli G = 20 and 200 Pa all exit from the strong enough to push the particle up to the centerline of the channel. In order to separate the particles, downward outlet with r1 = 90 μm and r2 = 90 μm. The figure shows that the repelling force is not the sizes of enough r1 and rto2 should adjusted in the order to make 200 to Paseparate shear modulus strong push thebeparticle up to centerline of the the particle channel. with In order the cross particles, the centerline andoftor1 keep particle with 20 in Paorder sheartomodulus thewith centerline. After we the sizes and rthe 2 should be adjusted make thebelow particle 200 Pa shear reduced r1 to cross 80 µmtheand increased 100 µm, the particle Pa modulus shear modulus crosses modulus centerline andr2totokeep the particle with with 20 Pa200 shear below the centerline.and Afterexits we reduced to 80 μm and increased 2 to 100 μm, the particle 200 Pa shear exits the centerline throughr1the upper outlet, whilerthe particle with 20 Pawith shear modulus modulus crosses the outlet centerline and 8b). exitsWe through the upper while the rparticle withincrements. 20 Pa through the downward (Figure then sweep theoutlet, sizes of r1 and 2 in 10 µm shear modulus exits through the downward outlet (Figure 8b). We then sweep the sizes of r 1 and r2 When r1 = 40 µm and r2 = 140 µm, the particles with shear moduli G = 20 and 200 Pa can still be in 10 μm increments. When r1 = 40 μm and r2 = 140 μm, the particles with shear moduli G = 20 Pa separated in the tested configuration. However, the particles all leave the channel through the upper and 200 Pa can still be separated in the tested configuration. However, the particles all leave the outlet when r1 = 30 µm and r2 = 150 µm. This method shows that we can count on a 40 µm tolerance channel through the upper outlet when r1 = 30 μm and r2 = 150 μm. This method shows that we can for the design of r1 and r2 . count on a 40 μm tolerance for the design of r1 and r2.

Figure 8. Trajectories of particles shearmoduli moduliG Gforfor various values r1 and r2 Figure 8. Trajectories of particleswith withtwo twodifferent different shear various values of r1ofand r2 whenwhen the axial electric field in the channel is E = 30 V/m. (a) r = 90 µm and r = 90 µm; (b) r = 80 µm 1 μm the axial electric field in the channel is E = 30 V/m. (a) r11= 90 μm and r2 =290 μm; (b) r1 = 80 and rand µm;μm; (c) (c) r1 =r1 40 140μm; µm;(d) (d)r1r=1 30 = 30 150 Axes µm. are Axes = 40µm μmand andrr22 = = 140 μmµm andand r2 = r150 in are μm.in µm. r2 = 100 2 = 100 2 =μm.

4. Conclusions 4. Conclusions An electrokinetic microfluidic device for particle separation is designed and analyzed using an

An electrokinetic microfluidic device for particle separation is designed and analyzed using ALE-based finite elements computation. Separation is controlled with the particles’ shear modulus, an ALE-based finite elements computation. Separation is controlled with the particles’ shear modulus, which affects the particles’ deformation, in turn affecting the particles’ trajectories. The present whichstudy affects the particles’ deformation, turn affecting particles’ trajectories. suggests that if the microfluidicin device is properlythe designed, shear modulus The is anpresent effectivestudy suggests that if the microfluidic device is properly designed, shear modulus is an effective separation separation marker for deformable particles. Furthermore, the proposed design exhibits a reasonable marker for deformable particles. the proposed design exhibitsthat a reasonable tolerance, which might ease anyFurthermore, fabrication process. Additionally, we showed low electrictolerance, field whichintensities might ease fabrication we showed that low the electric field intensities canany be used withoutprocess. reducingAdditionally, separation efficiency, which allows safeguarding of fragile such as biological cells. Finally, which we showed that parameters ofparticles, the can be used particles, without reducing separation efficiency, allows thegeometrical safeguarding of fragile channel in thethat design of the device proposed. of the contraction channel such contraction as biological cells.provide Finally,flexibility we showed geometrical parameters provide flexibility in the design of the device proposed.

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Acknowledgments: This work is funded by the Yeungnam University Research Grant. Author Contributions: T.Z. and B.M. conceived and designed the experiments; T.Z. performed the experiments; T.Z. and F.L. analyzed the data; S.W.J. contributed reagents/materials/analysis tools; T.Z., L.Y., B.M. and S.W.J. wrote the paper. Conflicts of Interest: The authors declare no conflicts of interest.

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