Rheological and electrokinetic regulation of peristaltic flow in a divergent channel carrying solid particles: Thermo-diffusive and wall flexibility impacts

Problem statement: This study addresses the complex transport mechanisms that arise in peristaltic systems when non-Newtonian behavior, wall flexibility and multi-phase interactions occur simultaneously. Limited research has explored the combined impacts of electroosmotic forces, chemical reactions and particulate suspensions within a nonuniform divergent channel bounded by compliant walls. The dynamics of a Carreau fluid carrying solid particles under these coupled effects, especially in relation to heat and mass transfer, remain largely unreported. This motivates the development of a detailed mathematical framework capable of capturing the interplay between fluid rheology of multiphase flow, electrokinetic forces and wall elasticity. Objective: The objective of this study is to develop the mathematical model of multiphase electroosmotic flow of Carreau fluid through the divergent channel that has compliant walls. The heat transfer and mass transfer analyses will also be discussed through energy and concentration equations, respectively. Solution methodology: The lubrication theory is used to simplify the developed nonlinear boundary value problem and obtain the analytical solution by using the regular perturbation method. The perturbation solution is compared with the numerical solution. The computational results are discussed through graphs, bar graphs and tables. Computation results: The outcomes revealed that both fluid and particle phase velocities are decreasing for increasing Weissenberg number and electroosmotic parameter, while temperature distribution is enhanced by the wall compliance. The size of the tapping bolus is maximized under the contribution of solid rigid particles in the carrier fluid. The heat transfer rate has increased and decreased to 65% and 14% for varying Brinkmann number and Weissenberg number, respectively. Applications: This study can be helpful for beginners to understand the basic modeling of fluid-particle suspension electroosmotic flow of Carreau fluid through the divergent channel. It can be useful in environmental, chemical processing and biomedical engineering (to design the efficient microfluidic drug systems) where heat and mass transportation of non-Newtonian fluid flows under the suspension of solid nanoparticles are important. An analytical solution can be helpful in the future when experimental data is available.