The Fate of Chemical Species from a Sample Introduced into a Redox-Magnetohydrodynamics (R-MHD) Microfluidics Chamber: Influence of Diffusion within Flow Fields Near Pumping Electrodes and Walls and Under Different Experimental Conditions
Authors: Hesan Shirin , Khan Foysal Z. , König Jörg , Abrego Tello Miguel Angel , Johnson James , Cierpka Christian , Mutschke Gerd , Fritsch Ingrid 
Published: September 2023

Redox-magnetohydrodynamics (MHD) offers unique capabilities for pumping liquids on a small scale where other microfluidic pumps are ineffective or unsuitable. It can vary speed, change direction, stir and pump in a loop by controlling the magnitude and direction of ionic current, j, between two or more electrodes having desired geometries in the presence of a perpendicular magnetic field, B. This interaction generates a force, FB
, orthogonal to j and B, following the right hand rule. The localized volume of liquid then moves in the same direction as FB
due to momentum transfer. MHD is compatible with a variety of solvents and solution compositions. In principle, MHD does not require valves or channel sidewalls to move fluid in a path. For applications involving analysis or imaging of single entities, like nanoparticles, microbeads, and biological cells, the focus is on inspection of the entities in a specific region of moving fluid. However, in applications where there is a collection of species, such as a concentration of an analyte in a sample introduced into the fluid having a different composition, it is important to understand how the analyte disperses from both the fluid dynamics and diffusion. Numerical approximations were performed using COMSOL Multiphysics® to analyze the 3D velocity profiles generated experimentally by redox magnetohydrodynamics (R-MHD) microfluidics and to predict the fate of analyte molecules in a sample that is introduced into that fluid.
Simulations were first compared to experimental data from parallel band, pumping electrodes, where uniform horizontal flow profiles are possible when sidewalls are far away. Experimentally obtained velocities involved an R-MHD chamber with a rectangular geometry of 30 mm x 17 mm formed from a cutout in a poly(dimethyl siloxane) (PDMS) gasket placed onto a microfabricated chip containing individually-addressable electrodes, filled with an electrolyte solution, and capped with a glass coverslip. The gasket thickness defined the chamber height. To generate an ionic current, an electronic current was applied between two poly(3,4-ethylenedioxythiophene) (PEDOT) modified, parallel band electrodes with dimensions of ~890 µm width and 15 mm length (along the x-direction), separated by a 2.76 mm gap. A magnetic flux density of 0.37 T was produced by a permanent magnet placed beneath the chamber. Astigmatism particle tracking velocimetry (APTV) was used to interrogate the fluid velocity between the electrodes where only a single camera was needed to capture all three velocity components in a 3D volume. This technique measures the astigmatic aberration to encode the out-of-plane position of a tracer particles in the measurement volume. In some experiments, microparticle image velocimetry (μPIV) was used to evaluate particle velocity by measuring displacement of tracer particles along horizontal planes. Velocity profiles with high spatial resolution from the APTV and µPIV measurements provided a detailed look at the effects on fluid motion in three dimensions as a function of applied current (from ± 50 µA to ± 1000 µA), electrolyte concentration (from 0.1 NaCl + 10% glycerol to keep the density constant, to 1.3 M NaCl + 0% glycerol), and chamber height (from 429 µm to 1690 µm). Simulated velocity profiles between electrodes in the x-direction are within 95.8 of those of APTV experiments involving variation in currents for a fixed chamber height and different chamber heights for a single applied current. In studies involving µPIV and variation of electrolyte concentrations, the magnitude of maximum fluid velocity is higher than for simulations. (We will present studies where this discrepancy is addressed.)
Then, using simulations we “introduced” a sample, 20-µm across centered between pumping electrodes, with initial concentration of 0.1 M and diffusion coefficient of 8.75 x 10-6 cm2/s. Time-dependent evolution of molecule transport was superimposed on the steady-state R-MHD. The spread and direction of molecular species outside of the pumping path greatly depends on location of chamber sidewalls from the outer edges and ends of band electrodes.
Diffusional and fluid dynamic spread of sample after introduction between pumping electrodes having concentric circular geometries was then studied by simulations. Here, fluid pumps in a loop. Wall and sample location and electronic current magnitude were taken into consideration. Knowledge from these configurations are of interest for chip-based, circular chemical separations, with an “infinite” number of plates and goal of higher separation efficiencies. Horizontal flow profiles for R-MHD at concentric ring electrodes are not uniform, because of unequal ionic current densities across the curved flow path. Results from these numerical approximations and implications for designing lab on a chip applications for pumping sample plugs by R-MHD microfluidics with and without side walls for chemical applications will be discussed.