Mathematical Modeling and Analysis of the Steady Electro-Osmotic Flow of Two Immiscible Fluids: A Biomedical Application

The in vitro fabrication of big osteoarticular implants integrating biomaterials and cells is of tremendous interest because these tissues have a limited ability to regenerate. However, the growth of such cells in vitro is highly problematic, especially later in the culture, when the extracellular matrix has almost filled the initial porous network. Thus, the fluid flow required to properly perfuse the sample cannot be obtained by the hydraulic driving force alone. Fluid pumping is a central concern of a microfluidic system and electro-osmotic pumps (EOPs) are commonly employed for this purpose. Using electro-kinetic equations as a basis, this study analyzed the variations of a two-fluid electro-osmotic flow of viscoelastic fluid flow through a channel. The behavior of the fluid was studied through the Ellis equation. This is how the electro-osmotic pump functions, as demonstrated in the literature that it electrically drags a conducting fluid across a non-conducting fluid through interfacial dragging force along the channel. A steady-state analytical solution for the system in a conducting fluid channel was studied by undertaking an interface planner for fluids exhibiting Newtonian rheological properties. The pumping characteristics were studied in detail by using the Ellis model’s parameters. The fluid rheology was studied, which showed the viability of this technique.