Saeid Movahed

Electrokinetic transport through the nanopores in cell membrane during electroporation

In electroporation, applied electric field creates hydrophilic nanopores in a cell membrane that can serve as a pathway for inserting biological samples to the cell. It is highly desirable to understand the ionic transfer and fluid flow through the nanopores in order to control and improve the cell transfection. Because of submicron dimensions, conventional theories of electrokinetics may lose their applicability in such nanopores. In the current study, the Poisson-Nernst-Planck equations along with modified Navier-Stokes equations and the continuity equation are solved in order to find electric potential, fluid flow, and ionic concentration through the nanopores. The results show that the electric potential, velocity field, and ionic concentration vary with the size of the nanopores and are different through the nanopores located at the front and backside of the cell membrane. However, on a given side of the cell membrane, angular position of nanopores has fewer influences on liquid flow and ionic transfer. By increasing the radius of the nanopores, the averaged velocity and ionic concentration through the nanopores are increased. It is also shown that, in the presence of electric pulse, electrokinetic effects (electroosmosis and electrophoresis) have significant influences on ionic mass transfer through the nanopores, while the effect of diffusion on ionic mass flux is negligible in comparison with electrokinetics. Increasing the radius of the nanopores intensifies the effect of convection (electroosmosis) in comparison with electrophoresis on ionic flux.

Electrokinetic transport through nanochannels.

This article presents a numerical study of the electrokinetic transport phenomena (electroosmosis and electrophoresis) in a three‐dimensional nanochannel with a circular cross‐section. Due to the nanometer dimensions, the Boltzmann distribution of the ions is not valid in the nanochannels. Therefore, the conventional theories of electrokinetic flow through the microchannels such as Poisson–Boltzmann equation and Helmholtz–Smoluchowski slip velocity approach are no longer applicable. In the current study, a set of coupled partial differential equations including Poisson–Nernst–Plank equation, Navier–Stokes, and continuity equations is solved to find the electric potential field, ionic concentration field, and the velocity field in the three‐dimensional nanochannel. The effects of surface electric charge and the radius of nanochannel on the electric potential, liquid flow, and ionic transport are investigated. Unlike the microchannels, the electric potential field, ionic concentration field, and velocity field are strongly size‐dependent in nanochannels. The electric potential gradient along the nanochannel also depends on the surface electric charge of the nanochannel. More counter ions than the coions are transported through the nanochannel. The ionic concentration enrichment at the entrance and the exit of the nanochannel is completely evident from the simulation results. The study also shows that the flow velocity in the nanochannel is higher when the surface electric charge is stronger or the radius of the nanochannel is larger.

A Theoretical Study of Single-Cell Electroporation in a Microchannel

Electroporation of a single cell in a microchannel was studied. The effects of electrical (e.g., strength of the electric pulse) and geometrical (e.g., microchannel height, electrode size and position) parameters on cell membrane permeabilization were investigated. The electrodes were assumed to be embedded in the walls of the microchannel; the cell was suspended between these two electrodes. By keeping the electric pulse constant, increasing the microchannel height reduces the number and the radius of the biggest nanopores, as well as the electroporated area of the cell membrane. If the width of the electrodes is bigger than the cell diameter, the transmembrane potential will be centralized and have a sinusoidal distribution around the cell if nanopores are not generated. As the width of the electrode decreases and becomes smaller than the cell diameter, the local transmembrane potential decreases; in the nonelectroporative area, the transmembrane potential distribution deviates from the sinusoidal behavior; the induced transmembrane potential also concentrates around the poles of the cell membrane (the nearest points of the cell membrane to the electrodes). During cell membrane permeabilization, the biggest nanopores are initially created at the poles and then the nanopore population expands toward the equator. The number of the created nanopores reaches its maximal value within a few microseconds; further presence of the electric pulse may not influence the number and location of the created nanopores anymore but will develop the generated nanopores. Strengthening the electric pulse intensifies the size and number of the created nanopores as well as the electroporated area on the cell membrane.

Electroosmotic flow in a water column surrounded by an immiscible liquid

In this paper, we conducted numerical simulation of the electroosmotic flow in a column of an aqueous solution surrounded by an immiscible liquid. While governing equations in this case are the same as that in the electroosmotic flow through a microchannel with solid walls, the main difference is the types of interfacial boundary conditions. The effects of electric double layer (EDL) and surface charge (SC) are considered to apply the most realistic model for the velocity boundary condition at the interface of the two fluids. Effects on the flow field of ς-potential and viscosity ratio of the two fluids were investigated. Similar to the electroosmotic flow in microchannels, an approximately flat velocity profile exists in the aqueous solution. In the immiscible fluid phase, the velocity decreases to zero from the interface toward the immiscible fluid phase. The velocity in both phases increases with ς-potential at the interface of the two fluids. The higher values of ς-potential also increase the slip velocity at the interface of the two fluids. For the same applied electric field and the same ς-potential at the interface of the two fluids, the more viscous immiscible fluid, the slower the system moves. The viscosity of the immiscible fluid phase also affects the flatness of the velocity profile in the aqueous solution.

Numerical studies of continuous nutrient delivery for tumour spheroid culture in a microchannel by electrokinetically-induced pressure-driven flow

Continuous nutrient delivery to cells by pressure-driven flow is desirable for cell culture in lab-on-a-chip devices. An innovative method is proposed to generate an induced pressure-driven flow by using an electrokinetically-driven pump in a H-shape microchannel. A three-dimensional numerical model is developed to study the effectiveness of the proposed mechanism. It is shown that the average velocity of the generated pressure-driven flow is linearly dependent on the applied voltage. Considering the culture of a multicellular tumour spheroid (MTS) in such a microfluidic system, numerical simulations based on EMT6/Ro tumour cells is performed to find the effects of the nutrient distribution (oxygen and glucose), bulk velocity and channel size on the cell growth. Using an empirical formula, the growth of the tumour cell is studied. For low nutrient concentrations and low speed flows, it is found that the MTS grows faster in larger channels. It is also shown that, for low nutrient concentrations, a higher bulk liquid velocity provide better environment for MTS to grow. For lower velocities, it is found that the local MTS growth along the flow direction deviates from the average growth.

Electrokinetic motion of a rectangular nanoparticle in a nanochannel

This article presents a theoretical study of electrokinetic motion of a negatively charged cubic nanoparticle in a three-dimensional nanochannel with a circular cross-section. Effects of the electrophoretic and the hydrodynamic forces on the nanoparticle motion are examined. Because of the large applied electric field over the nanochannel, the impact of the Brownian force is negligible in comparison with the electrophoretic and the hydrodynamic forces. The conventional theories of electrokinetics such as the Poisson–Boltzmann equation and the Helmholtz–Smoluchowski slip velocity approach are no longer applicable in the small nanochannels. In this study, and at each time step, first, a set of highly coupled partial differential equations including the Poisson–Nernst–Plank equation, the Navier–Stokes equations, and the continuity equation was solved to find the electric potential, ionic concentration field, and the flow field around the nanoparticle. Then, the electrophoretic and hydrodynamic forces acting on the negatively charged nanoparticle were determined. Following that, the Newton second law was utilized to find the velocity of the nanoparticle. Using this model, effects of surface electric charge of the nanochannel, bulk ionic concentration, the size of the nanoparticle, and the radius of the nanochannel on the nanoparticle motion were investigated. Increasing the bulk ionic concentration or the surface charge of the nanochannel will increase the electroosmotic flow, and hence affect the particle’s motion. It was also shown that, unlike microchannels with thin EDL, the change in nanochannel size will change the EDL field and the ionic concentration field in the nanochannel, affecting the particle’s motion. If the nanochannel size is fixed, a larger particle will move faster than a smaller particle under the same conditions.

Feedback/feedforward modeling and control of electroosmotic flow in a T-shape microchannel

Electroosmotic effect is usually utilized to generate the flow field in microfluidic systems. In many of these microdevices, an accurate control over the output flow rate of the microfluidic part is necessary for the successful operation of the whole system. In this study, a combined feedback/feedforward strategy is proposed to control the output flow rate in a micro-T-junction. First, finite element model of the electroosmotic flow in the T-junction is generated; second, using the adaptive neural fuzzy inference system, the finite element model forms a basis for generating training data for building an inverse model of the flow in the micro-T-junction. This inverse model serves as a controller in the feedforward part of the system. Then, in order to make the controller robust against disturbances and uncertainties such as dimensional tolerances, a Mamdani-type fuzzy logic controller is incorporated in the feedback part of the controller. Finally, simulation results are presented in order to proof the performance of the designed controller.

Combined Feedback/Feedforward Velocity Control of Electrokinetically Driven Flow in a Network of Planar Microchannels

Abstract In the present study, a combined feedback/feedforward strategy will be utilized in order to control the output flow rate in a micro-T junction. First, Finite Element Model (FEM) of the electroosmotic flow in the T-junction will be generated and then this model will form a basis for generating training data for building an inverse model of the flow in the T-junction based on Adaptive Neural Fuzzy Inference System (ANFIS). This inverse model serves as a controller in the feedforward part of the system. Also, in order to make the controller robust against disturbances and uncertainties such as dimensional tolerances, a Mamdani-type fuzzy logic controller is incorporated in the feedback part of the controller. Finally, simulation results will be presented in order to establish the performance of the designed controller.