Dynamics of vapour bubbles in nucleate boiling

Abstract

This paper considers the behaviour of a vapour bubble formed at a nucleation site on a heated horizontal wall. This bubble is modeled as a spherical segment which is separated from the wall by a microlayer of intervening liquid. The liquid is presumed to be at rest at great distances from the bubble. In order to avoid unwarranted assumptions about forces acting on the bubble which are specific to all known models of bubble growth and detachment, we derive equations that govern bubble behaviour in a rigorous way from the variational equation that describes mechanical energy conservation for the whole system, which includes both the bubble and the liquid. The variational equation leads to a set of two mutually independent strongly nonlinear equations which govern bubble expansion and the motion of its centre of mass. Because these equations contain an extra unknown variable (the bubble vapour pressure), a supplementary equation that defines bubble vapour temperature must be formulated with allowance made for heat transfer to the bubble both from the bulk of the surrounding liquid and through the microlayer. The most important conclusion of this paper consists in the fact that surface tension effects result in an effective force that tends to transform the bubble into a sphere, thereby facilitating bubble detachment. This conclusion absolutely nullifies the generally, however erroneously, held belief that this effective force presses the bubble to the wall. By way of example, we consider the evolution of bubbles whose growth is thermally controlled. Our analysis provides quite a natural explanation for a number of repeatedly observed phenomena, such as the influence of gravity and surface tension on bubble growth rate and the dependence of bubble detachment size on thermophysical parameters.