(174bp) Dielectrophoresis-Based Motion for Switching of Microparticles: Numerical Modeling and Experimentation

In the current work, we present the finite-difference
method (FDM) based model and experiments to explain the motion of
microparticles in a phenomenon called Dielectrophoresis (DEP). In particular,
the current work aims to study the continuous-flow switching operation of
microparticles in a microchannel in which the steady-state location of the
target microparticles can be controlled to any desired position in the
microchannel. The numerical model is followed by a parametric study.
Furthermore, the work also presents experimental results of the switching of
Red Blood Cells (RBCs) in a microfluidic channel with an inlet and three
outlets. DEP has been selected to achieve the switching of microparticles
because of it being a non-contact, label-free method with great selectivity and
sensitivity.

1.    
Dielectrophoresis
Theory

DEP is defined as the migration of the neutral
polarizable particles in a conductive medium in a non-uniform electric field [1, 2]. The
time-averaged DEP force on a particle in a non-uniform electric field with
root-mean-squared value of  is
expressed as:

 The
term  represents the radius of the microparticle,  is the medium permittivity.  represents the real part of a
dimensionless number called the Clausius-Mossotti factor. Mathematically,  is written as:

where  is the complex permittivity of
the  particle and  is the complex permittivity of
the medium. The complex permittivity is calculated using:

where  is the electric conductivity,
and  is the angular operating frequency [3-5]. The particles undergo two
different behaviors: they either translate towards the maximum of the electric
field gradient in a phenomenon called positive DEP (pDEP), or they can move
towards the minimum of the electric field gradient, where their behavior is
termed as negative DEP (nDEP) [6, 7].

2.     Mathematical
Model

The mathematical model of the micro-device is developed
to study switching of the particles under the influence of nDEP. The complete
micro-device includes a 2 mm long microchannel having width and height of 50µm
and 35µm respectively. The schematic diagram of the microchannel with two
independently excitable electrode arrays (black blocks) is displayed in Fig.1.

Fig. 1: Schematic Diagram of
the microchannel with independently excitable microelectrodes.

Figure 2 displays a unit block of the microchannel. The
complete microchannel can be retrieved by duplicating the unit block over the
entire length of the channel; hence, all the calculations are based on the unit
block instead of the complete channel in order to effectively reduce the
computational time and memory.

Fig. 2: Schematics of the
unit block for the complete channel.

A non-uniform Electric Field (EF) is generated in the
unit block by applying an AC signal of alternating polarity to the electrodes
on each set of the side-wall at a fixed frequency. The calculated EF is used to
determine the DEP force using Eq. (1), and is projected on the complete length
of the channel. The Laplace equation (4) is utilized to describe the electric
potential in the channel.

where Δ represents the Laplace
operator and V represents the electric potential. Equation (4) assumes that no
electric charges reside inside the channel. The electric field is explained by
equation (5) as:      

A
Finite Difference Method using first-order and second-order central difference
schemes is used to solve Equations (4) and (5). The distance between
neighboring nodes is set to be 1.0 µm and the simulation is run with the time
step of 10^-4 s. Mathematically, the peak value of the applied signal
is stated in Eqs. (6) to (9). All other boundaries are considered as walls and
an insulated boundary condition is applied to those boundaries during the
calculations and are expressed in (10).

The second step involves the
trajectory calculations to demonstrate the switching capabilities of our
proposed microdevice. The equations of motion for the particles are solved
using Newton’s Law of Motion. The forces experienced by a particle during its
motion are stated in Eq. 11.

The first and second terms on the right side in eq
(10) represent the gravitational force vector and the buoyancy force
respectively, while the remaining two terms account for the forces due to DEP
and Drag respectively. x_p, y_p,
and z_p represent the displacement of the microparticle (radius = R_p)
in x, y, and z directions respectively. The terms ρ_p and ρ_m
are the densities of the microparticle and medium, respectively.  is the volume of the microparticle. Moreover, the
fluid and particle velocities are denoted by v_p and v_f.

Figure 3 provide the distributions of the electrical
potential in the unit block from an applied voltage of 4V (peak-to-peak).

Fig. 3: Distribution of Electric Potential
in (i) the complete unit block and (ii) the bottom surface of the unit block

The switching of microparticles is successfully shown
in Fig. 4 as a consequence of manipulating the operating voltage. In the
simulation, the particles are allowed to start from a fixed location at the
inlet and they possess the same velocity as that of the carrying medium. For
the equal applied signal (V₁ = V₂ = 4 V_p-p)
case shown in Fig. 4a, the equilibrium locations lie in the vertical plane
passing through the center along the width of the channel (y-direction), and
hence, the micro-entities can be seen progressing towards the middle before
settling down at the same level as they traverse the microchannel. However, the
micro-objects advance closer to the left wall of the channel if the left
electrode set is energized at a lower voltage (V₂ = 8 V_p-p)
as compared the right one (V₁ = 2 V_p-p) as shown in Fig.
4b. On the contrary, the cells traverse near the right wall, Fig. 4c, on
applying a greater voltage signal on the electrode pairs at the bottom of the
left sidewall (V₁ = 8 V_p-p; V₂ = 2 V_p-p).

Fig. 4: The trace of the micro-scale
entities in the Finite Difference simulation. The objects are switched to (a)
the center, (b) left-sidewall, and (c) right-sidewall

3.    Future Work

In the full-length paper, we plan to perform a number
of parametric studies to investigate the influence of numerous geometric and
operating parameters on the trajectories of microparticles, and in turn, switching
behaviour of these particles. For instance, the influence of radius of
the particulates, volumetric flow rate, and the width of the electrodes inside
the microchannel will be studied in the simulations.
Furthermore, the microdevice will also be fabricated using standard
microfabrication technique and the experiments will be performed to validate
the numerical model.

References:

[1]          B. Mathew, A. Alazzam, M. Abutayeh, and I. Stiharu, "Model‐based
analysis of a dielectrophoretic microfluidic device for field‐flow
fractionation," Journal of separation science, vol. 39, pp.
3028-3036, 2016.

[2]          K.
Chan, H. Morgan, E. Morgan, I. Cameron, and M. Thomas, "Measurements of
the dielectric properties of peripheral blood mononuclear cells and trophoblast
cells using AC electrokinetic techniques," Biochimica et Biophysica
Acta (BBA)-Molecular Basis of Disease, vol. 1500, pp. 313-322, 2000.

[3]          Y.
Huang, X.-B. Wang, F. F. Becker, and P. R. Gascoyne, "Membrane changes
associated with the temperature-sensitive P85gag-mos-dependent transformation
of rat kidney cells as determined by dielectrophoresis and
electrorotation," Biochimica et Biophysica Acta (BBA)-Biomembranes, vol.
1282, pp. 76-84, 1996.

[4]          T.
Z. Jubery, S. K. Srivastava, and P. Dutta, "Dielectrophoretic separation
of bioparticles in microdevices: A review," Electrophoresis, vol.
35, pp. 691-713, 2014.

[5]          B.
Mathew, A. Alazzam, S. Khashan, and B. El-Khasawneh, "Path of
microparticles in a microfluidic device employing dielectrophoresis for
hyperlayer field-flow fractionation," Microsystem Technologies, vol.
22, pp. 1721-1732, 2016.

[6]          V.
Nerguizian, A. Alazzam, D. Roman, I. Stiharu, and M. Burnier Jr,
"Analytical solutions and validation of electric field and
dielectrophoretic force in a bio‐microfluidic channel," Electrophoresis,
vol. 33, pp. 426-435, 2012.

[7]          J.
Ko, E. Carpenter, and D. Issadore, "Detection and isolation of circulating
exosomes and microvesicles for cancer monitoring and diagnostics using
micro-/nano-based devices," Analyst, vol. 141, pp. 450-460, 2016.