Study of the bubble motion inside a peristaltic tube

Abstract

The motion of a long, axisymmetric bubble (fluid 1) inside a vertical peristaltic conduit containing a self-rewetting fluid (fluid 2) is discussed in this article. The fluid inside the tube and the floating bubble are immiscible, incompressible and have different densities. The peristaltic channel has two open ends. It is assumed that the bubble can move freely inside the tube without being restricted or deformed by the border wall. The effect of the density difference between the two fluids, Marangoni convection caused by the thermal and solutal gradient and an imposed back flow on the position and shape of the bubble have all been discussed. Motion of the bubble within a peristaltic tube, influenced by the Marangoni convection due to thermal and solutal gradients, has find various applications in the electrification of the atmosphere by sea bubbles, efficient mixing in microfluidic devices, improved cooling in heat exchangers, design of hydrophobic surfaces, spray coating thography techniques, enhanced mass transfer in chemical reactors, advancing various industrial and biomedical applications with precise fluid control. A mathematical model of the problem has been developed using a two-dimensional cylindrical polar coordinate system. The governing equations are in the form of linear partial differential equation and have been solved analytically. The effect of the thermo-solutal Marangoni convection in the microgravity region and the imposed back flow, impact of gravity-driven convection in the absence of the Marangoni convection or back flow, on the motion of bubble are discussed by plotting the position of the bubble. The initial radius and thermo-solutal Marangoni convection determine the bubble’s form as it evolves. When the initial radius falls below a critical value, the bubble becomes broader and shorter; conversely, when the original radius exceeds the crucial value, the bubble becomes longer and thinner.