@article{Salem2024, 
author = {Ahmed G. Salem and Turki D. Alharbi and Abdulaziz H. Alharbi and Anwar Ali Aldhafeeri},
title = {Impact of a spherical interface on a concentrical spherical droplet},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {10},
pages = {28400-28420},
keywords = {micropolar fluid, axisymmetric motion, low Reynolds numbers, normalised hydrodynamic drag force, fluid-fluid interface effect},
url = {https://www.sciopen.com/article/10.3934/math.20241378},
doi = {10.3934/math.20241378},
abstract = {In this paper, an analytical and numerical technique are examined in order to analyse the Stokes flow determination problem due to a viscous sphere droplet moving at a concentric instantaneous position inside a spherical interface separating finite and semi-infinite immiscible fluid phases. Here, when only one of the three phases of the fluid (micropolar fluid) has a microstructure, attention is focused on this case. The motion is considered when Reynolds- and capillary-numbers are low, and the droplet surface and the fluid-fluid interface have insignificant deformation. A general solution is obtained in a spherical coordinate system based on a concentric position to analyse the slow axisymmetric movement of the micropolar fluid, considering microrotation and velocity components. Boundary conditions are initially fulfilled at the fluid-fluid interface and subsequently at the droplet surface. The normalised hydrodynamic drag force applying to a moving viscous droplet appears to be a function of the droplet-to-interface radius ratio, which increases monotonically and becomes unbounded when the droplet surface touches the fluid-fluid interface. The numerical outcomes of the normalised drag force acting on the viscous droplet are derived for different values of the parameters, and are presented in a tabular and graphical framework. A comparison was made between our numerical outcomes for the drag force and the pertinent data for the special cases found in the literature.}
}