Boundary conditions of sliding during the motion of bodies in a dilute emulsion of gas bubbles

B. V. Boshenyatov

Institute of Applied Mechanics of Russian Academy of Sciences, Moscow

Abstract: It is shown that the reason for the slip boundary conditions of during the movement of bodies in a viscous and incompressible emulsion of gas bubbles is the hydrodynamic interaction of the bubbles with the surface of the body. The influence of hydrodynamic interaction on the slip parameter $\xi$ increases with an increase in the volume concentration of bubbles $\varphi$ and with a decrease in the size of the body $R$ compared to the size of the bubbles $a$. Limit analytical dependences of the slip parameter $\xi$ for a ball moving in an emulsion of identical gas bubbles were obtained – $\xi_{down}<\xi(a/R,\varphi)<\xi_{up}$.

Keywords: slip boundary conditions, Stokes equations, emulsion of gas bubbles, hydrodynamic interaction.

Received: 02.12.2024
Revised: 23.03.2025
Accepted: 27.03.2025

DOI: 10.61011/PJTF.2025.12.60615.20208

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