(483i) Bubble Shape Hysteresis: The Effect of Compressibility

The maximum bubble pressure method is a classical procedure to obtain the surface tension at liquid/air interfaces. Since surface tension is an important consideration for the stability of foams, this technique, which is valued because of its simplicity, is widely used. The name of the method is derived from the observation that a gas, when emerging from a capillary, undergoes a rapid expansion from a small, spherical cap within the capillary, to a much larger bubble. Associated with this transition, is a maximum in the pressure within the gas, which can be shown to be simply related to the surface tension. In this paper, we describe a more complete analysis of this shape transition that quantifies the effect of compressibility, previously not taken into account. This analysis is complemented by experimental measurements where the bubble volume was measured as a function of internal pressure for bubbles that are both emerging from capillaries and are being withdrawn into them. A principal finding of this work is the existence of a hysteresis in this relationship, depending on the geometry of the experimental system.

Experimentally, we observe that, as a result of compressibility, there are two regimes of bubble expansion and contraction. In the first regime, the bubble expands and contracts reversibly, with the bubble retracing the expansion profile obtained during contraction. However, in the second regime, expansion and contraction of the bubble is no longer reversible, thus exhibiting a hysteresis. In this second regime, the bubble undergoes a non-equilibrium jump in size between expansion and contraction.

Theoretically we show that the experimental observations are a consequence of compressibility influencing the equilibrium states of bubbles as a function of two non-dimensional parameters, A and P. A characterizes the relative magnitude of the volume of a hemispherical bubble to the dead volume in the system, and P characterizes the relative magnitude of the maximum capillary pressure to the ambient static pressure. We show that (at a given value of P) for values of A above a critical value, the bubble expands and contracts reversibly as in the first regime seen in our experiments. However for values of A below a critical value, the bubble shapes become hysteretic. Using a phase diagram of A and P, we show the two regimes of bubble formation (with and without hysteresis). Understanding bubble-shape hysteresis and its dependence on compressibility can have important consequences to the design of dilatational interfacial rheology experiments where bubbles are continuously compressed and expanded.