Numerical simulation of adsorption and bubble interaction in protein foams using a lattice Boltzmann method

Abstract

The adsorption process and the resulting dynamic surface tension in the context of protein foams were studied. A diffusion–advection equation is solved using a lattice Boltzmann method (LBM) in order to simulate the adsorption of surfactants on a surface. With different adsorption isotherms, different surfactants can be modelled. The advection is driven by a flow field coming from the LBM. The phase transition is implemented with a free surface LBM approach where the liquid–gas two-phase flow is simplified to a single-phase free surface flow by using a volume of fluid approach. Looking at the different time scales for diffusion and advection, which are determined by the diffusion coefficient and the viscosity, respectively, the LBM is limited due to time and space resolution. The rates of protein transport to a surface by diffusion and by advection are investigated which indicate that diffusion is only relevant for modelling long-time studies. For those time ranges and low concentrations, the diffusion of proteins from a bulk to a surface of a droplet is simulated and compared with the literature. As a next step, situations as in protein foams are assumed. High concentrations of proteins, e.g. as in milk, result in a simplified scenario where neither diffusion nor advection is important. This is analysed theoretically which suggests an instantaneous change of surface tension. To examine the stability of foam lamellae, this is used for further simulations. Two bubbles rise close to each other with globally different surface tensions as for pure water and water with proteins. Depending on these surface tensions and the initial distance, the bubbles coalesce faster for high surface tensions and show less secondary motions for lower surface tension. It is concluded that bubbles in protein foams coalesce only at shorter distances than in pure water.