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.

Curvature estimation from a volume-of-fluid indicator function for the simulation of surface tension and wetting with a free-surface lattice Boltzmann method

“…Both the FD and the LSQR model seem to recapture approximately Eq. (20), however, with a smaller exponent < 0.5. This is acceptable, considering the low grid resolution and the static contact line model.…”

“…While the accuracy of the LBM is well-understood [16][17][18], only very few results have been reported addressing the accuracy of the FSLBM's advection scheme or its validity to simulate surface tension. Nevertheless, the approach has found numerous applications in surface tension driven complex flow scenarios [19][20][21][22][23] and even high Reynolds number flows [24,25]. Hence, in the present paper we evaluate the accuracy of the FSLBM in surface tension driven flows, and also discuss existing limitations due to the original advection scheme.…”

Boundary conditions for free interfaces with the lattice Boltzmann method

“…The method has been used successfully in the simulation of liquid-gas flows of high viscosity and density ratio. Examples can be found in Ammer et al (2014); Anderl et al (2014); Attar and Körner (2011); Donath et al (2010); Janßen (2010); Janssen et al (2010); N. Thürey (2004; Xing et al (2007a,b), and in Bogner and Rüde (2013); Svec et al (2012) for complex liquid-gas-solid flows. However, no theoretical analysis of the FSLBM is currently available.…”

waLBerla: A block-structured high-performance framework for multiphysics simulations

“…The simulations performed with the FSLBM have already provided new insights into a wide variety of physical applications. For instance, waLBerla's FSLBM extension was used to investigate complicated foaming processes that occur in the food industry [136,137] (cf. Figure 14a).…”