Rhythmic membrane contraction effects on inclined microchannel flow of Newtonian fluids with velocity slip

Microscale fluid flow is a critical aspect of various biomedical applications, including lab-on-a-chip devices, microfluidic systems, and biomedical implants. Understanding the behavior of fluids at the microscale is essential for designing and optimizing these devices. However, the complex interactions between fluid flow, channel geometry, and surface properties at the microscale pose significant challenges. This study develops a mathematical model to investigate microscale fluid flow in an inclined microchannel, incorporating slip effects and Newtonian fluids. By simplifying the governing nonlinear equations using low Reynolds number and long wavelength approximations, the research provides an analytical solution to the dimensionless conservation equations. The results are validated using both the Shooting method and the bvp5c solver, ensuring the accuracy and reliability of the findings. The study offers comprehensive insights into various fluid characteristics, including: pressure gradients, velocity profiles, volumetric flow rates, skin friction, and stream function patterns. These were analyzed across a range of parameters, such as inclination angle ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>α</mml:mi> </mml:mrow> </mml:math> ), slip parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> ), Froude number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Fr</mml:mi> </mml:mrow> </mml:math> ), and Reynolds number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Re</mml:mi> </mml:mrow> </mml:math> ). The inclination angle significantly influences fluid motion, particularly in gravity-driven flows and biomedical devices. Slip effects reduce friction at channel walls, enhancing pumping efficacy and optimizing microfluidic systems. This study provides valuable insights for biomedical applications, including controlled drug delivery, diagnostic devices, and organ-on-a-chip technologies. Additionally, understanding slip effects can improve industrial processes, such as lubricant coatings, heat exchangers, and filtration systems, by minimizing energy losses and optimizing performance.