The nucleation and growth of gas bubbles in a Newtonian fluid: an energetic variational phase field approach

Abstract

Abstract.In this paper, we study the nucleation and growth of gas bubbles in a Newtonian fluid. We employ a general energetic variational formulation with a phase-field method, and compare the analytical and numerical predictions of this new formulation with those of classical models. The new approach allows the study of bubble nucleation, growth and coalescence in a unified framework, and has the capability of modeling complex situations in polymer foaming, with multiple-bubble interaction, interaction with an external flow field, complex non-Newtonian rheology and non-Fickian diffusion.

Bran‐induced effects on the evolution of bubbles and rheological properties in bread dough

“…The relationship between foam rheology and bubble coalescence is associated with the solid dough phase or layer in between bubbles. This is because, coalescence between two entities occurs when the viscous binding constituent is squeezed out from the film that separates the bubbles (Naber, Liu, & Feng, ), resulting in energy dissipation. If the energy loss due to this dissipation exceeds the initial kinetic energy, the bubbles will coalesce to form a larger bubble (Liu, Lister, Iveson, & Ennis, ).…”

“…The relationship between foam rheology and bubble coalescence is associated with the solid dough phase or layer in between bubbles. This is because, coalescence between two entities occurs when the viscous binding constituent is squeezed out from the film that separates the bubbles (Naber, Liu, & Feng, 2008), resulting in energy dissipation.…”

Instant coffee foam: An investigation on factors controlling foamability, foam drainage, coalescence, and disproportionation

“…The high and low coalescence rates were observed in Trial 5 and Trial 14, respectively (Table ). The inverse relationship between solid content of coffee solution and coalescence rate can be ascribed to the following reason: coalescence between two bubbles occurs when the viscous constituent in between is pinched off the film that separates the bubbles (Naber, Liu, & Feng, ). Higher solid content of the coffee feed solution (as in Trial 14) might have increased the viscosity of liquid phase surrounding the bubbles.…”

Two-component viscous flows with density-dependent transition layer

“…Thus, we enforce the ansatz for the non-inert system (see [1], [17], [22]) ρ(∂ t Φ + v · ∇Φ) = −λδ δf δΦ .…”

“…In the subsequent considerations the transformation to Lagrangian coordinates is essential. The free boundary problem (12), (13), (17), (18)- (23) is transformed into a phase field problem with fixed boundary. Then we can show that regions with zero mass density in the interior of the domain are impossible.…”