Continuous-Flow Separation of Malaria-Infected ... - ACS Publications

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Continuous-Flow Separation of Malaria-Infected Human Erythrocytes Using DC Dielectrophoresis: An Electrokinetic Modeling and Simulation Milad Nahavandi* Department of Chemical & Materials Engineering, University of Idaho, Moscow, Idaho 83844, United States S Supporting Information *

ABSTRACT: This paper presents a particle tracing numerical approach into direct current insulating dielectrophoretic (DC-iDEP) cell sorting using an innovative microfluidic device capable of continuously separating red blood cells infected in vitro by Plasmodium falciparum human−malaria parasites (Pf-iRBCs) from healthy red blood cells (h-RBCs), which is suitable for clinical diagnosis as well as biological and epidemiological research. The device operation is based on field flow fractionation (FFF) introduced by electrokinetic and DEP effects through the microchannel. After validation of numerical results with respective experimental data, a particle sorting model was developed to evaluate the simultaneous effects of channel geometry, applied voltage, and medium pH strength associated with the dynamic effects of electric and flow fields on separation performance. Computational investigations were performed on the basis of the proposed model and theoretical cell trajectory was calculated. Simulation results showed that RBCs with different dielectric responses perceived different dielectrophoretic force magnitudes while they were continuously pushed by electrophoretic force and the fluid stream generated by electroosmotic induced flow over the wall surface and were therefore focused to different streamlines in the microchannel. In addition, it was indicated that the pH of suspending medium substantially influenced the zeta potential and so an electric double layer (EDL) formed on the surface of the RBCs and the microchannel, which could widely change the electrokinetic movement of the cells. Results also showed that a perfect separation might be achieved at the pH and DC applied voltage of 5 and 13 V, respectively.

1. INTRODUCTION

including Plasmodium falciparum, P. malariae, P. ovale, and P. vivax. Among these, P. falciparum infection is the deadliest.2 Upon infection, P. falciparum parasites go through preerythrocytic and intraerythrocytic stages in the human host. In the pre-erythrocytic stages, sporozoites, which are transmitted by mosquitoes, invade liver cells and produce thousands of merozoites, which can then invade red blood cells (RBCs). In the intraerythrocyte stages, the red blood cells infected by P. falciparum (Pf-iRBCs) undergo

Malaria is still one of the world’s most common and serious tropical diseases and a great public health problem worldwide. According to The World Health Organization, every year, 3.2 billion people are at risk of malaria that leads to about 198 million malaria cases and an estimated 584 thousand malaria deaths, although people living in the poorest countries are the most vulnerable. In 2013, 90% of the world’s malaria deaths occurred in Africa and over 430 thousand African children died before their fifth birthday.1 Human malaria is caused by Plasmodium parasites that are spread to people through the bites of infected female Anopheles mosquito vectors.1 There are four types of Plasmodium parasites © XXXX American Chemical Society

Received: February 18, 2016 Revised: April 23, 2016 Accepted: April 24, 2016

A

DOI: 10.1021/acs.iecr.6b00660 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

Figure 1. Scheme of a DC-DEP device capable of separating h-RBCs from Pf-iRBCs.

Table 1. Boundary Conditions setting physics

variable

inlet

outlet

channel surface T

creeping flow

u

0

electric currents heat transfer particle tracing (fluid flow)

V T q v

V Tin q0 v0

various stages (ring, trophozoite, and schizont) in a 48 h cycle. At the end of the intraerythrocyte stages, roughly 16−18 merozoites are produced within a schizont, which subsequently bursts to release the merozoites, leading to infection of other RBCs.3−6 As this infection process repeats, the rate of infection of blood (the number of Pf-iRBCs in the total volume of a blood sample) increases exponentially. Therefore, development of techniques for early diagnosis of Pf-iRBCs at a low infection rate is necessary. The Giemsa staining method has been widely used for malaria diagnosis as the gold standard because of its high accuracy. However, the procedure for this method is complex, and well trained personnel are required for reliable evaluation. Besides, paper-based test kits based on antigen−antibody reactions have been developed commercially.7−11 These test kits are simple to use and easily detect the existence of Pf-iRBCs in blood, eliminating the need for a skilled technician. However, it is hard to achieve high detection accuracy at low infection rates (≲100 parasites/μL). Therefore, development of a precise Pf-iRBCs separation technique is needed for clinical applications and malaria research.12 Separation of Pf-iRBCs would enrich rare target cells from the low-infection-rate sample solution and noticeably augment the accuracy of malaria diagnosis in a clinical setting. In particular, it is important to separate the newly infected ring-stage Pf-iRBCs, because, despite late-stage Pf-iRBCs, ring-stage Pf-iRBCs circulate in the peripheral bloodstream of malaria-infected patients.13−15 Separation of Pf-iRBCs has been requested for biological and epidemiological research, such as for antimalarial drug assays and for studies of the invasion mechanism of the malarial parasite.16,17

[− pI + μ(∇u + (∇u) )]n = − p0̂ n

μeo Et

p0̂ < p0

Et = E − (E ·n)n

0 (ground) −n·q = 0 V = Vc

n·J = 0 qconv = hamb × (Tamb − T) v = vc − 2(n·vc)n

So far, various techniques have been developed for the concentration and separation of Pf-iRBCs based on the difference between physical and electrical properties of Pf-iRBCs and healthy RBCs (h-RBCs). A density-gradient separation method using Percoll was suggested by Miao and Cui, and has commonly been used.18 However, this method requires an expensive working fluid (Percoll) and involves a complex process for the preparation of the density gradient. Also, Coronado et al. described a method to separate the late-stage Pf-iRBCs by magnetic columns.19 In addition, Nam et al. proposed a method for separating both the late-stage and early stage Pf-iRBCs on the basis of their paramagnetic characteristics due to the malaria byproduct, hemozoin, using a magnetic field gradient.20 Among these available methods, dielectrophoresis (DEP) has attracted the most attention due to its considerable advantages. The capability of performing continuous separation of biosamples with high efficiency and throughput is highly desirable in DEP microfluidic devices, so that most DEP devices can operate at about 1−10 μL/min.21 Unlike other techniques like magnetic separation in which the separation of cells is difficult and the cells recovery rate hardly gets to adequate levels due to the low paramagnetic characteristics of cells, DEP depends on the dielectric properties, which represent the structural, morphological, and chemical characteristics of bioparticles, allowing highly selective and sensitive analysis. Besides, even when in some cases Pf-iRBCs can be separated effectively using permanent magnets and ferromagnetic wire in a microchannel in various developmental stages, still there is no controllability on the strength of applied magnetic field,20 while DEP manipulation is straightforward and fully controllable by varying the electric conductivity of the B


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Figure 2. Variation of zeta potential versus medium pH for RBCs, PDMS, and glass surface.

suspending medium or the frequency and magnitude of the applied electric field. DEP is also easily and directly interfaced to conventional electronics, and can be used in the fabrication of Lab on a Chip (LOC) devices. In addition, DEP enables contact-free manipulation of particles (both charged and neutral) with lower sample consumption and fast speed.22 To our best knowledge, so far, a few number of works have been done only for discontinuous DEP isolation of Pf-iRBCs from h-RBCs. Gascoyne et al. developed dielectrophoretic devices for isolation of Pf-iRBCs based on the dielectric differences between Pf-iRBCs and h-RBCs using two types of interdigitated and spiral microelectrode arrays.23 Although in the both devices, Pf-iRBCs focus at the center of electrode arrays and then can be identified and counted, continuous separation of them is not possible. In the case of interdigitated microelectrodes, suspended Pf-iRBCs can only be washed free by flowing suspending medium through the microelectrode arrays, while the outlet washing medium still includes h-RBCs separated from channel surfaces due to shear stress. In this paper, for the first time, we present a modeling approach into an innovative LOC device capable of continuously separating h-RBCs and Pf-iRBCs based on the field flow fractionation (FFF) introduced by electrokinetic and DEP effects through a microchannel. In this device despite

other microdevices, particle motion benefited from the combined electrophoretic and electro-osmotic effect that eliminates the need for additional hydrodynamic flow, which results in a small scale device, process acceleration, and a noticeable decrease in operational costs. Also, the system has higher controllability than conventional microdevices as the applied voltage is the only adjustable variable. In addition, high purity and recovery rates can be achieved under certain operating conditions, which results in medical diagnosis with higher certainties. In the following, we first define a model for our suggested system based on the appropriate governing equations. Then, the model is slightly changed so that it can be validated with the most similar system with available experimental data published in literature. Finally, the effects of different operating parameters are examined on the basis of the initial proposed model to obtain optimum operational conditions.

2. MODELING AND SIMULATION Numerical modeling and simulation was performed based on the two-dimensional finite element method (FEM) analysis with the software package COMSOL Multiphysics version 5.2 to evaluate both types of viscous and electrical forces exerted on the cells and suspending medium, leading to desirable separation through the aforementioned microfluidic system that is described at the following. C


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Figure 3. Grid plot: triangular meshes inside model domain. NOH = 9; SOH = 28 μm; for other conditions, see Table 2.

right-hand side, respectively, beside the inlet and outlet of microchannel, to make a homogeneous DC electric field in the channel. The cell sample including a diluted mixture of RBCs is injected into the left upside inlet and buffer at the left downside inlet, which are defined as injection regions. RBCs are pushed by electrophoretic force into the focusing area while moving into a separation region to be under the effects of a dc-dielectrophoretic (DC-DEP) force formed around insulating hurdles, and fluid flow resulting from electro-osmotic surface flows through the microchannel and is known as electric-driven flow. After separation, h-RBCs and Pf-iRBCs move into collection regions that include upside and downside channels. Boundary conditions correspondent to different field variables governing the numerical solution of the indicated model are summarized in Table 1. 2.2. Subdomain Equations. Numerical modeling is performed based on the three differential forms of conservative equations including electric continuity, stokes flow, and particle tracing for fluid flow that stand for electric charge current, fluid, and particle momentum balance, respectively.

Table 2. Mesh Characteristics elements parameters type of elements bulk elements elements used for hurdles peak

min size [μm]

max size [μm]

max growth rate

curvature factor

0.646 0.01

14.5 1

1.15 1.05

0.3 0.2

2.1. Model Definition. A microdevice model capable of separating RBCs using dielectrophoretic technique and simultaneous application of both electrophoresis and electro-osmosis phenomena in the presence of fluid viscous effects was supposed and is shown in Figure 1. As a 3D model is only used where there are some changes in the third direction (-z), here there is no such change in that direction; therefore, we used the suggested 2D model in the x−y plane surface for our numerical modeling and simulation to increase the efficiency and reduce the time required for numerical solution. The proposed microchannel consists of four main parts including injection, focusing, separation, and collection regions. The device uses two electrodes, one placed at the left and other one at the

Figure 4. Grid independency analysis based on the maximum size of mesh used for hurdles peak. V = 10 V; pH = 5; for other conditions, see Figure 3. D


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Figure 5. Validation of simulation data: (a) an experimental image showing the separation of RBCs and PLTs in the design;35 (b) corresponding simulation results; and (c) validation of experimental and simulation results. Reprinted with permission from ref 35. Copyright 2011 American institute of Physics.

in width), the flow is laminar throughout the microchannel (Re < 0.05).

The steady-state form of the charge continuity equation expressing the differential conservation law of charge in dielectric material was used to define the stationary electric current within the microchannel, where constitutive equations including the point form of Ohm’s law and electric displacement account for electric conductivity and relative permittivity, respectively, according to eq 1.24

∇·[−pI + η(∇u + (∇u)T )] + Fb = 0 ρm ∇·u = 0

The stationary heat transfer equation for nonisothermal flow was used to describe the temperature variation of blood throughout the microchannel and is shown in eq 3. Also, to take into account electrothermal effects, Joule heating, also known as ohmic or resistive heating, was used as a heat source term, eq 4.

∇·J = 0 J = σE + Je = σ( −∇V) + Je D = ε0εrE = ε0εr( −∇V )

(2)

(1)

The stationary incompressible Stokes equation and its mass continuity equation for momentum balance were used to describe a steady-state laminar flow of suspending medium through the microchannel and were solved simultaneously based on eq 2. Because of the small channel dimensions (only 40 μm

ρb Cpu·∇T + ∇·( −k∇T ) = Q J

(3)

Q J = J ·E

(4)

Electro-osmotic flow is induced over the entire surface of the microchannel due to double layer formation besides the charged E


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Figure 6. Effect of insulating hurdles; velocity profile within the microchannel. V = 15 V; pH = 5; for other conditions, see Figure 3.

Figure 7. Effect of insulating hurdles: (a) variation of velocity along cross section (shown in Figure 6) for different size of hurdles, and (b) maximum velocity difference: (V − V21)/V21. For other conditions, see Figure 6.

surface. Electro-osmotic velocity is calculated by the Helmholtz− Smoluchowski equation based on the electro-osmotic mobility of counterions over the charged surface with small Debye length, eq 5.25

UEO = μEOE =

−ε0εmζs E η

(5)

To trace the trajectories of particles moving in fluid in the presence of an external field (i.e., electric field, fluid flow, etc.), a particle F


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Figure 8. Effect of insulating hurdles: RBCs separation level for different size of hurdles: (a) SOH = 22 μm, (b) SOH = 24 μm, (c) SOH = 26 μm, (d) SOH = 28 μm; for other conditions, see Figure 6.

tracing equation is used. The particle momentum comes from Newton’s second law, which states that the net force on a particle is equal to its time rate of change of its linear momentum in an inertial reference frame according to eq 6.26 d(mpv) dt

= Fb

(6)

Drag force is one of the external forces acting on particles moving in fluid flow and caused by fluid viscous stress, eq 7. The particle velocity response time for spherical particles in a laminar flow that is frequently known as Stokes drag law is defined based on eq 8. Fd =

τp =

1 m p (u − v ) τp

(7)

2ρp rp2 9η

(8)

The particle tracing physics interface is also coupled with the electric current interface to predict the effects of dielectrophoresis (DEP), which is the motion of uncharged polarizable particles in a nonuniform electric field. The dielectrophoretic force results from the interaction of the electric field with the induced dipole moment. Depending on the dielectric properties of the particle and the medium, the motion is directed either toward or away from regions of high electric-field intensity, which results in positive or negative dielectrophoresis, p-DEP and n-DEP, respectively.26−28 The DEP force can be obtained directly in Eulerian form from divergence of the Maxwell Stress Tensor (MST) based on electric field distribution.29−32 However, it is usually approximated through its first dipole moment contribution that is expressed by eq 9.26−28 In this equation, the Clausius−Mossotti factor stands for electrical properties of particles, eq 10, while equivalent relative permittivity

Figure 9. Effect of insulating hurdles: (a) variation of velocity along cross section (shown in Figure 6) for different number of hurdles, and (b) maximum velocity difference: (V − V10)/V10. For other conditions, see Figure 6.

accounts for geometrical characteristics of particles (i.e., bioparticle with single, double, or triple shells). Here, the equivalent G


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Figure 10. Effect of insulating hurdles: RBCs separation level for different number of hurdles. (a) NOH = 2, (b) NOH = 4, (c) NOH = 6, (d) NOH = 8; for other conditions, see Figure 6.

membrane electrical properties due to the loss of conductive electrolytes (i.e., water with ions as charge carriers), although these changes do not influence on electric permittivity in the same level as it is merely contingent upon dipole moment. In addition, the electrophoretic effect resulted from the balance between the applied electric field and viscous resistance exerted by the liquid on the suspended particles is taken into account in the form of electrophoretic mobility defined by eq 14.

permittivity of RBCs as single shell bioparticles is given by eq 11. Also, frequency-dependent polarization is described by complex permittivity of particle and suspending medium according to eq 12, while eq 13 is used for nonfrequency electric field. FDEP = P∇E = 2πrp3ε0 Re(εm*) Re(fCM)∇|E|2

fCM =

* − εm* εpe * + 2εm* εpe

(10)

⎛ +2 ( ) ⎝ ε * = ε* ⎛ ( ) −⎝ ro ri

pe

s

εj* = εj −

εj* = εj

ro ri

3

⎜

3

(9)

εp* − εs*

μep =

⎞

⎟

εp* + 2εs* ⎠

εp* − εs* ⎞ ⎜ ⎟ εp* + 2εs* ⎠

iσj ω

j = p, m

j = p, m

DC

AC

(14)

E

The electrophoretic velocity of particles is coupled to particle velocity previously shown in eq 7. As, electrophoretic mobility depends strongly on the electrical diffuse double layer around the particles and the particle zeta potential, for spherical particles with low zeta potential and arbitrary Debye length, electrophoretic mobility is defined by Henry equations, eqs 15 and 16.33

(11)

ω = 2π f

Uep

(12)

μep =

(13)

Respective electrical properties of both the healthy and infected RBCs with their associated empirical tolerances (errors) are presented in Table S1, although only their absolute values without the indicated tolerances were used in our simulation. Also, it should be noted that in practice, RBCs are rather negatively charged, flexible, and slightly varying in size. However, the size diversity of cells as well as particle−particle interactions due to their slight charges can be fairly negligible in the presence of certain applied voltages and a diluted concentration of cells with a low level of medium pH, even though it makes a minor level of uncertainty in experimental applications. In addition, as shown in Table S1, the conductivity of host cells varies through the penetration of parasite and the consequent changes in

ε0εm ζc f (kdrp) η

(15)

⎡ ⎛ ⎞−3⎤ 2⎢ 2.5 ⎟⎟ ⎥ f (kdrp) = 1 + 0.5⎜⎜1 + ⎥ 3 ⎣⎢ k r (1 + 2exp( − k r )) ⎝ d p d p ⎠ ⎦ (16)

For an aqueous solution with multivalent ions, the inverse Debye length that is called the Debye−Hückel parameter, is given by eq 17.34 kd = H

1 = λD

e2 εmKBT

n

∑ ci0Zi2 i

(17) DOI: 10.1021/acs.iecr.6b00660 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 11. Effect of insulating hurdles; variation of RBCs separation level for different size and number of hurdles. V = 20 V; for other conditions, see Figure 6.

Figure 13. Effect of applied voltage; variation of electric field and DEP force along the cross section (shown in Figure 12b) in different electric potentials. For conditions, see Figure 6.

Figure 12. Electric field strength within the microfluidic device. For conditions, see Figure 6.

The components properties of human blood plasma required for calculating the Debye length of RBCs at a particular temperature are presented in Table S2. Since the microfluidic device correspondent to the model shown in Figure 1 is usually composed of a polydimethylsiloxane (PDMS) block placed on top of a glass chip to seal the microchannels and is mechanically fixated using plasma treatment,35 the electric double layer (EDL) formed on these surfaces and their equivalent zeta potentials are of great importance. As shown in eq 5 and 15, zeta potentials of the surface and also RBCs are determining parameters in both the electro-osmotic and electrophoretic mobility expressions, respectively. This potential refers to the strength and polarity of the EDL of the solid−liquid interface where the bound Stern layer ends and the mobile diffuse layer known as the Gouy−Chapman layer begins.34 As the decrease of pH exponentially increases the concentration of H+ ions in suspending medium, the selective adsorption of H+ ions onto the solid-buffer interfaces slightly counteracts the original negative zeta potential that leads to a decrease in zeta potential with smaller negative values. In contrast, at higher pH values, OH− ions become the potential−determining ions (P.D.I) and their adsorption onto the solid-buffer interface results in stronger negative zeta potential at the interface and so an increase in zeta potential.36−40 As shown in Figure 2, the zeta potential of RBCs, PDMS, and glass increases by increasing the pH value of suspending medium. These trends are also used to determine the effect of pH on RBCs separation as discussed later in a following section.

Figure 14. Effect of applied voltage; variation of velocity along the cross section (shown in Figure 12b) in different electric potentials. For conditions, see Figure 6.

2.3. Mesh. Triangular elements were used to mesh the domain shown in Figure 1 in which RBCs are carried by electrophoresis and suspending fluid flow through microchannel. Mesh contribution pattern within the microchannel is presented in Figure 3a. As the solution stability is significantly reduced by application of an electric field, a greater number of elements with smaller size must be used in areas with a stronger electric field to produce a more stable and accurate solution. As can be seen in Figure 3b, finer meshes are used around hurdle peaks than the bulk of domain. The size and distribution parameters of different elements within the proposed microchannel are also presented in Table 2. 2.3.1. Grid Independency Analysis. To investigate the independency of the grid from the solution of the problem, the recovery percentage of h-RBCs was calculated for different element sizes and is depicted in Figure 4. This evaluation is done in low applied voltage of 10 V where the level of separation is very I


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Industrial & Engineering Chemistry Research Table 3. Volumetric Flow Rate and RBCs Throughput voltage [V] RBCs/s = 60

10

11

12

13

14

15

16

17

18

19

20

Qmedium (μL/s) CRBCs (particle/ μL)

1.9 31.5

2.1 28.7

2.2 26.7

2.4 24.9

2.7 22.1

2.9 20.2

3.1 19.3

3.2 18.7

3.4 17.6

3.5 16.8

3.7 15.9

Figure 15. Effect of applied voltage: RBCs separation level for different electric potentials. (a) V = 14 V, (b) V = 16 V, (c) V = 18 V, (d) V = 20 V; SOH = 25 μm; for other conditions, see Figure 6.

elements were used to form the finite element interpolation functions. To solve the system of equations, the time dependent GMRES solver known as generalized minimal residual algorithm for solving nonsymmetrical linear systems was used.41 Also, the maximum iteration number of 103 as well as the relative and absolute tolerance of 10−3 and 10−6, respectively, were set as operational solver parameters for the setting of a nonlinear method module with a constant Newton and damping factor of 1 to solve possible nonlinearities in the system of equations. Furthermore, a generalized alpha was chosen for the time stepping module with free steps taken by the solver, which was adequate to guarantee the stable solution of the problem. 2.5. Validation. To evaluate the validation of simulation data, the proposed model shown in Figure 1 was slightly changed so that the trajectory of h-RBCs through the microchannel can be compared with available empirical results gathered from published experiments for the DEP separation of human h-RBCs from platelets (PLTs) under effects of AC electric potential. Experimental and simulation data are respectively presented in Figure 5 panels a and b, and validated in Figure 5c. As we can see, simulated values agree well with the experimental results with the maximum average deviation of about 1%. 2.6. Simulation Results. The set of stationary and transient governing equations for our proposed model was solved and returned the distributions of the electric field and fluid flow inside the device geometry. According to simulation results, application of a dielectrophoretic force combined with electrokinetic and flow field effects led to the desirable separation of healthy and

sensitive to the magnitude of electric potential, and any rough division of domain by using course meshes, specifically at the peak of hurdles with strong electric fields, can significantly result in instability of the solution. As shown, by increasing mesh size at the peak of hurdles, the separation of h-RBCs decreases moderately, and for mesh sizes bigger than 9 μm it starts to fluctuate because of the lack of accuracy, while it increases and starts to level off in smaller mesh sizes, which in turn indicates the independency of the numerical solution from the size of the elements. 2.4. Solution Methodology. In general, modeling an electrokinetic flow together with induced effects of DEP is not a trivial task. The modeling becomes complicated in a microfluidic device as it is described by a system of coupled nonlinear equations consisting of Ohm’s law and electric displacement equations for the electric charge current field; Stokes and Helmholtz−Smoluchowski equations respectively for the momentum balance and electro-osmotic velocity of the suspending medium; the Henry equation and Newton’s second law respectively for the electrophoretic mobility and momentum balance of RBCs; and equations accounting for Stokes drag and the DEP force acting on moving RBCs through the microchannel. Because analytical solutions can be obtained for only a very limited number of cases with the simplest geometry, in the case of such complex systems the application of those analytical methods is almost impossible. Therefore, in this study, the finite element method (FEM) was used to solve the system of equations without any simplification. Moreover, Lagrange quadratic interpolation J


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Industrial & Engineering Chemistry Research infected RBCs, which is substantially under effect of different geometrical and operational conditions. As can be seen at the following, this system benefited from electric driven flow which eliminates the need for an external flow producer (i.e., electroosmotic pump) in addition to its ability to work controllably with an external source of electrical energy. Besides, the model of this system is fairly tunable with some design and operational tuning parameters such as size of hurdles (SOH), number of hurdles (NOH), applied voltage, and medium pH. Therefore, optimum conditions are provided based on the obtained results, where the maximum separation can be achieved at the lowest applied voltages and thereby Joule heating effects, which paves the way for the future manufacturing of such a device. Nevertheless, as there are no empirical data available to further corroborate the subsequent numerical results, in terms of practical purposes, it should be noted that these data are obtained from the simulation of our proposed model at the specific operating conditions, which might not be practically feasible in many operational applications. However, to increase the level of certainty, choosing the value of tunable parameters in the certain given ranges is highly recommended to compensate the inevitable differences between experimental and numerical outputs, 2.6.1. Effect of Insulating Hurdles. The required spatial electric nonuniformities for the DEP effect can be generated by insulating hurdles. As the moving RBCs are restricted between the hurdles and surface of the microchannel in the separation region, the height of hurdles can vary the pattern of fluid flow (i.e., the region of maximum velocity) so that RBCs move at different crosswise positions, undertaking different DEP forces resulting from strong nonuniform electric field around the needles of the hurdles. The velocity profile through the proposed microchannel is shown in Figure 6, which consists of three velocity regions between two facing surfaces: (1) electro-osmotic flow beside the surface that resulted from ion movement in the diffuse layer adjacent to the stern layer fixed on the surface in adouble layer; (2) electro-osmotic bulk flow arising from fluid viscous flow and through shear stress (momentum diffusion) perpendicular to the surface; and (3) a stagnant zone with almost zero velocity above the double layer due to the momentum transverse balance beside the microchannel surface. As shown, fluid in bulk flow reaches maximum velocity at the region between the surface and peak of the hurdles. Also, the velocity profile across the cross section shown in Figure 6 is presented in Figure 7a. As we can see, by increasing the size of the hurdle, the area of maximum velocity approaches both the surface and peak of the hurdle (H1 > H2 and S1 > S2), while the magnitude of maximum velocity increases by almost 24% at the hurdle size of 28 μm, Figure 7b). Although the consequent increase of velocity magnitude has negative effect on the separation process by limiting the exposure time required for the n-DEP force to effectively repel the cells, the general effects of increasing the hurdle size intensify separation performance as RBCs, particularly healthy ones, undergo higher repulsive effects from the n-DEP force by approaching the hurdle peak with an intensive electric field. However, since the infected RBCs (Pf -iRBCs) have more relative permittivity than healthy ones, which based on Table S1 is closer to the relative permittivity of diluted blood plasma, they undergo lower n-DEP force according to eq 10 and so deviate slightly from their initial path when passing the hurdles, which results in appropriate separation of cells. The effect of hurdle size on the separation of RBCs is illustrated in Figure 8. As shown, by raising the height of hurdles, higher numbers of h-RBCs move into downstream, while

Figure 16. Effect of applied voltage: variation of h-RBCs separation versus electric potential for different number and size of hurdles. (a) SOH = 25 μm, (b) SOH = 26 μm, (c) SOH = 27 μm, (d) SOH = 28 μm; for other conditions, see Figure 6.

Pf-iRBCs move still into upstream with a small downward shift. As we can see at the following, the increase of voltage in low buffer pH may cause Pf-iRBCs to move through downstream, which has a converse effect on desirable separation. In addition to hurdle height, the number of hurdles can change the velocity of fluid flow and also the number of DEP repulsion. K


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Figure 17. Effect of Joule heating: (a) Joule heating within the device, (b) Joule heating around the hurdle, (c) Joule heating value around the hurdle peak and along the cross section; NOH = 8, V = 13 V, hamb = 10.45 W/(m2·K), Tamb = 293.15 K, Tin = 293.15 K; for other conditions see Figure 6.

hurdles with a height of more than 25 μm maximum separation of cells is attainable without any decline in trends, which indicates the independency of separation from the number of hurdles. 2.6.2. Effect of Applied Voltage. As mentioned earlier, insulating hurdles make a nonuniform electric field that is stronger around their peaks. The contour plot of electric field strength through microfluidic channel is shown in Figure 12. As we can see, h-RBCs are repelled further than infected ones when passing beside the hurdles, which results in their eventual separation by reaching to the collection area. On the basis of the second law of thermodynamics, when dielectric materials, here known as diluted blood plasma as suspending medium and RBCs, approach toward hurdles, they move in a way to minimize the total energy of system. Therefore, dipole moments flip their directions the extent to which is proportional to the electric permittivity value of the dielectric material. As the relative permittivity of diluted blood plasma is more than that of both the infected and h-RBCs according to Table S1, the suspending medium moves toward hurdle peaks with a stronger electric field to neutralize the strong electric field as much as possible, which results in RBCs repulsion away from hurdles and so their eventual separation. This repulsive effect that is due to nonuniformity of the electric field near the peaks of the hurdles comprises the so-called DEP force, which based on eq 9 consists in the electric permittivity of the dielectric particles and suspending medium as well as the electric field. Hence, the DEP force considerably depends on the electric field strength determined by the magnitude of the applied voltage.

The variation of velocity for different numbers of hurdles along the cross section shown in Figure 6, is presented in Figure 9a. As we can see, by increasing the number of hurdles, fluid velocity decreases due to the significant friction loss confronting the fluid passing through the separation zone with zigzag flow pattern. This deceleration is specifically more obvious for maximum velocity at the middle of the channel where most of the cells prefer to pass through. As shown in Figure 9b, the maximum velocity diminishes by almost 70% when hurdle number increases up to 10 times. Although a higher number of hurdles decelerates fluid flow through the microchannel, it increases the number of times cells are pushed down by DEP force when they approach the peak of hurdles and also provides more time available for cells to intake DEP repulsive effects, which brings about a greater level of separation. As can be seen in Figure 10, higher numbers of h-RBCs are separated with a greater number of hurdles and perfect separation can take place using eight hurdles according to Figure 10d). However, a higher number of hurdles is not always favorable and sometimes can decrease the level of separation by making torque and circulation in fluid flow and so generating some sort of cell mixing instead of separation. This incident occurs especially in a higher number of hurdles with small sizes. Simultaneous effects of hurdles height and number are illustrated in Figure 11. As we can see, by increasing the number of hurdles with small heights (21−25 μm) the percentage of recovered h-RBCs rises, and by reaching a certain number of hurdles it starts to fall. However, these trends increase more steeply in the presence of bigger hurdles so that by raising the number of L


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Figure 18. Effect of Joule heating: (a) temperature field throughout the device, (b) variation of temperature along the cross section; for conditions see Figure 17.

The value of the electric field and its corresponding n-DEP force along the cross section shown in Figure 12b for different applied voltages are illustrated in Figure 13 panels a and b, respectively. As can be seen, by raising the electric potential at a certain distance from the peak of the hurdle, both the electric field strength and its equivalent negative value of n-DEP force increase, while by taking distance from the peak of hurdles, electric field strength declines which leads to a consequent decrease in n-DEP force magnitude at different applied voltages. As shown in Figure 13b, the negative values of n-DEP force acting on h-RBCs are higher than their corresponding forces acting on infected RBCs at different electric potentials. Also, as indicated before, this device benefited from electrokinetic driven flow in the form of electro-osmotic fluid flow and electrophoresis of cells through a microchannel, which depends substantially on the strength of the electric field resulting from the gradient of applied voltage. Therefore, by applying higher electric voltages, the electrophoretic mobility of cells and the velocity of both the electro-osmotic surface flow and its consequent bulk flow increase, which leads to faster movement of cells and therefore the time restriction for n-DEP repulsive effects required for perfect separation. The variation of fluid velocity in different applied voltages along the cross section shown in Figure 12b is presented in Figure 14. As expected, by raising the applied voltage both the surface and bulk electro-osmotic velocities increase through the microchannel. Also, various volumetric medium flow rates and the consequent RBCs concentrations at different applied voltages are summarized in Table 3. Although faster movement of RBCs in higher applied voltages has negative effects on their desirable separation, it is substantially

Figure 19. Effect of medium pH; variation of h-RBCs separation level versus the pH of suspending medium in different applied voltages. For conditions, see Figure 6.

conpensated by a considerable increase in the n-DEP repulsive force acting on the cells. So, concurrent effects of electro-osmotic driven flow together with electrophoretic and DEP force over moving RBCs in higher electric potentials bring about a further level of separation. As shown in Figure 15, more h-RBCs are separated by applying higher voltages, so that perfect separation is achieved at an electric potential of 20 V. The application of higher electric potential with its overall enhancing effect on the separation of h-RBCs and Pf-iRBCs for hurdles with different heights and numbers is also shown in Figure 16. As we can see, by raising electric potential the percentage of separated h-RBCs has an overall increasing trend for different hurdle numbers, although these trends increase M


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Industrial & Engineering Chemistry Research Table 4. Percentage of Pf-iRBCs Recovery voltage [V] pH

10

11

12

13

14

15

16

17

18

19

20

4.5 4.75 5−7.5

2.5 100 100

0 100 100

0 100 100

0 100 100

0 100 100

0 79 100

0 7 100

0 0 100

0 0 100

0 0 100

0 0 100

that the use of excessively low operating temperatures has its own detrimental effects on separation performance as it increases significantly the viscosity of the medium and stickiness of cells to each other. 2.6.4. Effect of Medium pH. As mentioned earlier, zeta potential is an important parameter in the electro-osmotic and electrophoretic mobility of fluid and RBCs which determined by the pH level of suspending medium. Therefore, the change of pH level can influence the performance and magnitude of electric field effects,43 and so vary the h-RBCs separation performance through our microfluidic device. The variation of h-RBCs recovery versus different levels of medium pH for a certain range of applied voltages is shown in Figure 19. As we can see, by raising medium pH from 4.5 to 7.5 the recovery percentage of h-RBCs diminishes by almost 50% in 20 V while it drops more steeply to a low of almost 5% by decreasing electric potential to 10 V. Also, as shown in Table 4, the absolute recovery of Pf-iRBCs is achieved for most of the presented pH values, except in some cases with pH values lower than 5 and applied voltages higher than 10 V.

more steeply for hurdles with higher heights where more levels of separation can be achieved at the same applied voltages. Also, by increasing the height of hurdles, perfect separation of h-RBCs is obtained in lower applied voltages for different numbers of hurdles. As shown in Figure 16d, perfect recovery of h-RBCs is achieved at around 18 V for different numbers of hurdles with 25 μm in size in comparison to almost 12 V required for the complete separation in the presence of hurdles with 28 μm in size. 2.6.3. Effect of Joule Heating. Joule heating, is a significant problem in electrokinetically driven microfluidic chips, particularly polymeric systems (i.e., PDMS) where low thermal conductivities amplify the difficulty in rejecting this internally generated heat.42 According to eq 4, the high conductivity of injected blood and its consequent effect on increasing the charge current density of blood mixture with suspending medium in the presence of a strong electric field can result in substantial Joule heating, which may result in a number of significant secondary effects including a rise in volumetric flow rate followed by lower separation performance or even destroying cells at high electric potentials. Although the dilution of blood and low applied voltages can diminish these electrothermal effects, some amount of heat is generated that necessitates the examination of Joule heating and heat transfer through the device. Total generated heat resulting from Joule heating throughout the device is depicted in Figure 17a. As shown, the maximum of heat was generated at the vicinity of the hurdle peaks with the strongest electric field. The variation of Joule heating around the peak of a hurdle is more visible in Figure 17b and also illustrated quantitatively in Figure 17c along the cross section. As can be seen, by approaching the hurdle peak the amount of generated heat increases smoothly and it starts to rise more steeply for the distances lower than 2 μm. Therefore, the maximum of heat produced is in the separation zone with a certain numbers of insulating hurdles, which results in the highest rate of convective heat flux released from this zone into the ambient. Hence, to overcome the more amount of heat generated in higher applied voltages, one can suggest the enhancement of surface heat flux using force or natural convective coolers such as those described in the literature for microchannel applications.32 Also, the profile of temperature throughout the device as well as its variation along the cross section are shown in Figure 18a and Figure 18b, respectively. As we can see, by taking distance from inlet to outlet, temperature increases more steeply at higher electric potentials, while due to the aforementioned reason it shows some fluctuations at the peaks of hurdles. In addition, as RBCs can fairly bear temperatures up to the normal body temperature of 37 C (∼310 K) and application of 20 V engenders an increase in the medium temperature by the maximum of almost 10 K, the operation of a device at the applied voltages below 20 V and inlet temperatures lower than 27 C (300 K) make an adequate level of operational certainty. Also, as shown, the effect of temperature is almost negligible at applied voltages lower than 15 V, in which the temperature rises by less than 5 K in reaching the device outlet. In addition, it is worth mentioning

3. CONCLUSION In this work, initially the importance of separation of h-RBCs from Pf-iRBCs in medical diagnosis of malaria infection was illustrated. Next, a model geometry capable of manipulating RBCs using the simultaneous effects of electrokinetics and DEP through a microchannel was proposed and appropriate governing equations for mathematical modeling of the problem were presented. Then, a computational study was conducted under various operational conditions to verify the extent to which this method was effective and also examine the effects of different parameters on DEP separation of cells in the proposed model. On the basis of acquired simulation results, perfect separation can be achieved at the pH and DC applied voltage of 5 and 13 V, respectively. However, it is worth mentioning that in practice, although working with such a device with the proposed geometrical and operational values might not result in the exact numerical outputs, it gives us useful criteria for future manufacturing. In addition, as there are several inevitable degrees of uncertainty in experimental applications, a higher level of certainty can be achieved by choosing the value of parameters from the hypothetical results placed in assured operational ranges. In general, the following conclusions can be drawn from this investigation: (1) Application of electric field in the proposed microdevice results in formation of electric double layer and therefore electro-osmotic flow over the microchannel surface, which eventually leads to bulk flow that carries RBCs ahead through the channel. RBCs are also pushed by electrophoretic effects as they have slight negative charges, and are repelled by the DEP force when passing near the peaks of the hurdles in the separation zone. Therefore, particle motion in this device takes advantage of the combined N


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(2)

(3)

(4)

(5)

(6)

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η = dynamic viscosity [Pa·s] E = electric field [V/m] Et = tangential electric field [V/m] V = electric potential [V] n = normal unit vector q = particle position J = electric current [C/s] or [A] Je = externally generated current density [A/m2] σ = electric conductivity [μS/cm] εr = relative electric permittivity ε0 = electric permittivity of vacuum = 8.85× 10−12 [C/(V·m)] or [F/m] εm = relative electric permittivity of medium ε*m = relative complex electric permittivity of medium εp* = relative complex electric permittivity of parasite εs* = relative complex electric permittivity of shell ε*pe = equivalent complex relative electric permittivity of particle D = charge displacement [V/m2] Fb = body force [N] ρm = medium density [kg/m3] Ueo = electroosmotic velocity [m/s] ξs = surface zeta potential [V] ξc = cell zeta potential [V] t = time [s] ρp = particle density [kg/m3] τp = particle velocity response time [s] rp = particle radius Fd = drag force [N] FDEP = dielectrophoretic force [N] P = dipole moment [(N·m2)/V] f CM = Clausius−Mossotti factor RE = real part operator ri = particle inside diameter [m] ro = particle outside diameter [m] ω = angular frequency [rad/s] f = frequency [Hz] i = imaginary number (√−1) μep = electrophoretic mobility [m2/(V·s)] Uep = electrophoretic velocity [m/s] kd = Debye−Hückel parameter mp = particle mass [kg] λD = Debye length [m] e = electron charge= 1.6 × 10−19 [C] Z = ion charge number T = temperature [K] KB = Boltzmann constant= 1.38× 10−23 [m2.kg/(s2.K)] ci = component concentration [mol/m3] ρb = blood density [kg/m3] Cp = heat capacity at constant pressure [J/(kg·K)] k = thermal conductivity [W/(m·K)] QJ = heat generated by Joule heating (W/m3) QMedium = medium volume rate (μL/s) hamb = convective heat transfer coefficient (W/(m2·K))

electrophoretic and electro-osmotic effects that eliminate the need for additional hydrodynamic flow. Increasing the height of hurdles results in a narrower channel width and therefore a rise in velocity magnitude that leads to lower separation performance by limiting the exposure time required for n-DEP force to effectively repel the cells. However, it can generally enhance the level of separation as RBCs, h-RBCs in particular, undergo higher repulsive effects from the n-DEP force and so can be separated further. Although higher number of hurdles decelerates the fluid flow through the microchannel, it increases the number of times cells are pushed down by DEP force and also provides more time for cells to intake DEP repulsive effects, which leads to a greater level of separation. However, raising the number of hurdles is not always favorable as it can create torque and circulation in fluid flow and so brings about the mixing of cells instead of separation. Raising the applied voltage leads to an overall rise in the separation level for different hurdle numbers, even though it increases more steeply for hurdles with bigger sizes. Hence, the perfect separation of h-RBCs is achieved for the hurdle size of 28 μm at low electric potential of 13 V. High conductivity of injected blood engenders an increase in medium temperature due to Joule heating, which may lead to a number of considerable secondary effects such as rise in volumetric flow rate, lowering the separation performance, or even destroying cells at high applied voltages. However, the rise in temperature is negligible at low electric potentials so that based on obtained results temperature rises by less than 5 K for the applied voltages lower than 15 V. pH level is a determining factor in the proposed separation process and applied voltage substantially affects its level of effectiveness, so that by raising the pH of the suspending medium from 4.5 to 7.5 the level of h-RBCs separation diminishes by almost 50% in 20 V while it drops more steeply to a low of almost 5% by decreasing electric potential to 10 V.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.6b00660. Table S1: Typical electrical properties of parameters used to calculate fCM of h-RBCs and Pf-iRBCs. Table S2: Human blood plasma components (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +1-2088749061. E-mail: [email protected]. Notes

Abbreviation

The authors declare no competing financial interest.

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DC-iDEP = direct current insulating dielectrophoresis DC = direct current AC = alternating current p-DEP = positive dielectrophoresis n-DEP = negative dielectrophoresis LOC = lab on a chip h-RBCs = healthy red blood cells

NOMENCLATURE u = medium velocity [m/s] v = particle velocity [m/s] vc = particle velocity when striking the wall [m/s] p = pressure [Pa] μeo = electroosmotic mobility [m2/(V·s)] O


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Pf-iRBCs = rbcs infected in vitro by plasmodium falciparum human−malaria parasites PLTs = platelets FFF = field flow fractionation EDL = electric double layer FEM = finite element method MST = Maxwell stress tensor PDMS = polydimethylsiloxane P.D.I = potential−determining ions GMRES = generalized minimal residual NOH = number of hurdles SOH = size of hurdles

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