Prediction of dynamic contact angle histories of a bubble growing at a wall

A fast growing boiling bubble at the verge of detaching from a plane wall is usually shaped as a truncated sphere, and experiences various hydrodynamic forces due to its expansion and the motion of its center of mass. In a homogeneous flow field, one of the forces is the so-called bubble growth force that is essentially due to inertia. This force is usually evaluated with the aid of approximate expressions [Int. J. Heat Mass Transfer 36 (1993) 651, Int. J. Heat Mass Transfer 38 (1995) 2075]. In the present study an exact expression for the expansion force is derived for the case of a truncated sphere attached to a plane, infinite wall. The Lagrange–Thomson formalism is applied. Two Euler–Lagrange equations are derived, one governing the motion of the center of mass, the other governing expansion a kind of extended Rayleigh–Plesset equation. If a constitutive equation for the gas–vapor content of the bubble is given, initial conditions and these two differential equations determine the dynamics of the growing truncated sphere that has its foot on a plane, infinite wall. Simulations are carried out for a given expansion rate to predict the history of the dynamic contact angle. The simulations increase the understanding of mechanisms controlling detachment, and yield realistic times of detachment.