Dalimil Šnita

Parametrical studies of electroosmotic transport characteristics in submicrometer channels.

Spatially two-dimensional nonequilibrium mathematical model describing electroosmotic flow through a submicrometer channel with an electric charge fixed on the channel walls is presented. This system is governed by the hydrodynamic, electrostatic, and mass transport phenomena. The model is based on the coupled mass balances, Poisson, Navier-Stokes, and Nernst-Planck equations. Nonslip boundary conditions are employed. The effect of an imposed electric field on the system behavior is studied by means of a numerical analysis of the model equations. We have obtained the following findings. If the channel width is comparable to the thickness of the electric double layer, the system behaves as an ion-exchange membrane and the dependence of the electric current passing through the channel on the applied voltage is strongly nonlinear. In the case of negatively (positively) charged walls, a narrow region of very low conductivity (so-called ionic gate) is formed in the free electrolyte near the channel entry facing the anode (cathode) side. For a wide channel, the electric current is proportional to the applied voltage and the velocity of electrokinetic flow is linearly proportional to the electric field strength. Complex hydrodynamics (eddy formation and existence of ionic gates) is the most interesting characteristics of the studied system. Hence, current-voltage and velocity-voltage curves and the corresponding spatial distributions of the model variables at selected points are studied and described in detail.

Modelling of ionic systems with a narrow acid–base boundary

Formulation of a non-equilibrium model of an ionic system with a narrow acid–base boundary (representing the “electrolyte diode”) is introduced and its predictions are compared with those based on the traditional simplified model with a local electroneutrality and instantaneous local dissociation equilibria assumptions. Significant differences have been found in the spatial profiles around the acid–base boundary.

Transient behavior of an electrolytic diode

The transient behavior of an electrolytic diode system was studied. A gel-like electrolytic diode was incorporated in a capillary microfluidic chip. The microfluidic platform guaranteed a constant composition of solutions on the diode boundaries. The current responses of the electrolytic diode to step-like changes of the imposed DC electric voltage were measured. Some of these transients were accompanied by a short-time overshoot of electric current density. In order to explain this phenomenon, a mathematical model of the electrolytic diode system was developed. Dynamical analysis of the model equations confirmed the existence of the electric current overshoots. Because the results of the experimental and the numerical transient studies were quite similar, we have explained the physical meaning of three selected overshoots by means of an analysis of the reaction-transport processes inside the electrolytic diode system. The transient experiments carried out in this study indicate that our physical concept of the electrolytic diode system presented in previous papers is correct.

Three-phase slug flow in microchips can provide beneficial reaction conditions for enzyme liquid-liquid reactions

Here, we introduce a solution to low stability of a two-phase slug flow with a chemical reaction occurring at the phase interface in a microfluidic reactor where substantial merging of individual reacting slugs results in the loss of uniformity of the flow. We create a three-phase slug flow by introducing a third fluid phase into the originally two-phase liquid-liquid slug flow, which generates small two-phase liquid slugs separated by gas phase. Introduction of the third phase into our system efficiently prevents merging of slugs and provides beneficial reaction conditions, such as uniform flow pattern along the whole reaction capillary, interfacial area with good reproducibility, and intensive water-oil interface renewal. We tested the three-phase flow on an enzyme hydrolysis of soybean oil and compared the reaction conversion with those from unstable two-phase slug flows. We experimentally confirmed that the three-phase slug flow arrangement provides conversions and pressure drops comparable or even better with two-phase liquid-liquid arrangements.

Toward High Net Velocities in AC Electroosmotic Micropumps Based on Asymmetric Coplanar Electrodes

The most frequently studied ac electroosmotic micropumps exploit the coplanar asymmetric arrangements of the forcing electrodes. We analyze these systems by means of the following two mathematical models: 1) the classical slip model, which is based on a capacitor-resistor representation of the spatial domain, and 2) the nonslip model, which is based on the Poisson-Navier-Stokes-Nernst-Planck approach to the entire domain, including the electric double layers. Both the models predict similar results in many low-amplitude regimes. However, the nonslip model gives us a much better insight on the high-amplitude (nonlinear) behavior of the micropumps. Our most important findings obtained by the nonslip model can be summarized as follows: 1) There are optimal values of the electrode and gap size ratios that are generally different from those obtained by the slip model; 2) the micropump performance is relatively insensitive with respect to the electrode size ratio; 3) there is an optimal vertical confinement that enables us to attain high net velocities; 4) flow reversals on frequency, amplitude, and certain geometry characteristics are observed; 5) the energy efficiency of these pumps is very low; and 6) the Joule heating effect is negligible. The nonslip model characteristics are also discussed to explain the observed differences between predictions of the models. Convergence analysis dealing with the precision of numerical results obtained by the nonslip model is presented.

Adaptive mesh simulations of ionic systems in microcapillaries based on the estimation of transport times

Abstract We present results of testing an empirical algorithm of mesh adaptation for modeling of spatially one-dimensional reaction-transport systems with initially separated components and large moving gradients. The algorithm combines newly developed procedures of r -refinement and standard FEMLAB procedures. The developed method uses an expansion of a dense mesh in neighborhoods of localized large gradients and estimates the mesh adaptation interval (based on the evaluation of transport times). The size of the neighborhood is dynamically controlled. The adaptation method has been tested on systems of parabolic–elliptic PDEs with extremely large moving gradients of concentrations and electric potential. We have found that CPU time requirements are comparable to other mesh adaptation solvers. The simplicity of the empirical procedure of the mesh adaptation and its easy implementation in standard dynamic solvers represent main advantages of the proposed method. The studied system, called an “electrolyte diode”, is described by four mass balances of the electrolyte components (parabolic PDEs) and by Poisson equation of electrostatics (an elliptic PDE). Dynamics of formation of open and closed modes of the electrolyte diode are described and current–voltage characteristics are explained. The results obtained with the developed solver agree with the results of steady state analysis. Our tests prove that the proposed algorithm of mesh adaptation can be used in modeling of microfluidics application, e.g., DNA chips, capillary electrophoresis and isoelectrical focusing, where formation of extremely large gradients of electric potential and concentrations of the electrolyte components is expected.

AC electric sensing of slug-flow properties with exposed gold microelectrodes

A new method for slug-flow (segmented flow) characterization by means of ac electric sensing is proposed. Water segments regularly dispersed in kerosene are used as an experimental system. The sensing procedure is carried out in a plexiglass microchip with embedded gold microelectrodes. The presence of passing slugs over a measurement spot is determined from impedance variations. A square-shaped signal resulting from the slug flow is acquired and flow properties such as the mean velocity and length of the slugs are calculated. Complex behaviour of the corresponding electrochemical system is studied. Dependence of the impedance signal on the flow rate, ion concentration in the dispersed water slug and electric field strength are discussed and explained in detail. Advantages and disadvantages of the suggested method, in comparison with existing capacitive noncontact methods, are also clarified. Unlike the noncontact methods of electric sensing, with the insulation dielectric layer over the electrodes, our electrodes are in a direct contact with the carrier phase. The results show that the method is promising for process applications and will be further improved.

Traveling wave electroosmosis: The influence of electrode array geometry

We used a mathematical model describing traveling‐wave electroosmotic micropumps to explain their rather poor ability to work against pressure loads. The mathematical model is based upon the Poisson–Nernst–Planck–Navier–Stokes approach, that is, a direct numerical simulation, which allows a detail study of the energy transformations and the charging dynamics of the electric double layers. Using Matlab and COMSOL Multiphysics, we performed a set of extensive parametric studies to determine the dependence of generated electroosmotic flow on the geometric arrangement of the pump. The results suggest that the performance of AC electroosmotic pumps should improve with miniaturization. The AC electroosmosis is likely to be suitable only at submicrometer scale, as the pumps ability to work against pressure load diminishes rapidly when increasing the channel diameter.

Mathematical Modeling of Traveling Wave Micropumps: Analysis of Energy Transformation

In this paper, we assess the performance and efficiency of an ideal traveling wave electroosmotic micropump with a continuous electrode. All simulations were performed in the combination of Matlab and COMSOL Multiphysics using a weak form. The mathematical model is based on the Poisson-Nernst-Planck-Navier-Stokes approach with fully coupled governing equations. Our results suggest that the pumping efficiency depends strongly on the voltage amplitude, system scale, or electrolyte concentration. This analysis aims to find a window of opportunity, with reasonable pump throughput and efficiency.

Mathematical modeling of traveling wave micropumps: Analysis of energy transformation

In this paper, we assess the performance and efficiency of an ideal traveling wave electroosmotic micropump with a continuous electrode. All simulations were performed in the combination of Matlab and COMSOL Multiphysics using a weak form. The mathematical model is based on the Poisson-Nernst-Planck-Navier-Stokes approach with fully coupled governing equations. Our results suggest that the pumping efficiency depends strongly on the voltage amplitude, system scale, or electrolyte concentration. This analysis aims to find a window of opportunity, with reasonable pump throughput and efficiency.