Type: Semester project
A bubble of fluid with negligible viscosity is moving with some constant velocity U in a tube filled with fluid of viscosity μ at low Reynolds number. The interfacial tension between the two fluids is denoted by γ. In the case of a horizontal capillary tube of small radius r such that the gravitational effect on the motion can be neglected, the bubble has a thin fluid film denoted h between it and the wall of the tube that is given by
and the velocity of the bubble U exceeds the average velocity of the fluid V by an amount UW where W is
What happens if we consider two bubbles following each other? Do they move faster or slower?
We will use Basilisk [1], an open-source software for the solution of partial differential equations, to solve the unsteady, incompressible, variable density, Navier-Stokes equations in axisymmetric formulation. An initial validation on the classical case with one bubble in a horizontal tube and vertical tube (where gravity is no longer neglected) will be followed by a numerical study on the two bubbles motion.
[1] http://basilisk.fr/
[2] Bretherton FP. The motion of long bubbles in tubes. Journal of Fluid Mechanics. 1961;10(2):166-188. doi:10.1017/S0022112061000160
Supervisors: Tomas Fullana & François Gallaire