Coalescence of two growing bubbles in a Hele–Shaw cell

Abstract

Abstract An understanding of the dynamics of growth-driven coalescence is important in diverse fields across natural science and engineering. Motivated by the bubble coalescence in magma during volcanic eruptions, we study both experimentally and theoretically the coalescence of two growing bubbles in a Hele–Shaw cell. In our system, bubbles grow by gas expansion due to decompression and the diffusional influx of dissolved gas in the liquid. Our experiments show that the evolution of film thickness and bubble shape depends on viscosity, decompression rate, and cell gap. Through a scaling analysis and a perturbation approximation, we find that the hydrodynamic interaction between two bubbles is characterized by a film capillary number $$Ca_f=(\eta {\dot{R}}/\sigma )(R/D)^2$$ C a f = ( η R ˙ / σ ) ( R / D ) 2 depending on viscosity $$\eta$$ η , bubble radius R, growth rate $${\dot{R}}$$ R ˙ , interfacial tension $$\sigma$$ σ , and cell gap D. The experimental results demonstrate that the film capillary number solely determines the bubble distortion just before coalescence. Under our experimental conditions, bubble coalescence occurs below a critical value of a nominal film capillary number defined as a film capillary number evaluated when two undeformed circular bubbles come into contact.