Immiscible fluids flow driven by membrane pumping mechanism

Immiscible fluids play a crucial role in various fluid dynamics applications, particularly in microfluidics, biomedical devices, and industrial transport systems, where their distinct properties enable controlled separation and flow dynamics. The present study investigates the behavior of two immiscible, incompressible fluids flow driven by membrane pumping with different dynamic viscosities in a circular tube. This research uniquely examines how variations in amplitude and diameter of a deformable membrane influence the interfaces of immiscible fluids, flow characteristics, and pumping characteristics providing insights under realistic conditions. Using axisymmetric cylindrical coordinates, the study analyses the impact of membrane deformation modeled through a spatial membrane function, on pressure gradients, velocity profiles, wall shear stress, and interface dynamics between the core and peripheral layers. The governing equations are simplified using the lubrication approximation, enabling a comprehensive numerical investigation via MATLAB. The results revealed that increasing the viscosity ratio reduces the core layer and expands the peripheral layer, shifting the interface downward with greater membrane amplitude and diameter. Higher viscosity ratio and membrane deformation enhance the pressure gradient, shear stress, and flow resistance. These outcomes provide critical insights for optimizing membrane-based systems in microfluidics, biomedical applications, and industrial fluid transport. The enhanced understanding of viscosity and geometric influences on flow dynamics offers a foundation for future studies to investigate non-Newtonian fluids and more complex geometries, paving the way for improved performance in practical applications.