Friedrich-Alexander University Erlangen-Nuremberg, Chair of Fluid Mechanics, Cauerstr. 4, Erlangen, Germany.
Food Funct. 2014 Apr;5(4):755-63. doi: 10.1039/c3fo60374a.
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.
研究了蛋白质泡沫中的吸附过程和由此产生的动态表面张力。为了模拟表面活性剂的吸附，使用格子玻尔兹曼方法（LBM）求解扩散-对流方程。通过使用不同的吸附等温线，可以模拟不同的表面活性剂。对流由来自 LBM 的流场驱动。通过自由表面 LBM 方法实现相变，其中通过使用体积流体方法将液-气两相流简化为单相自由表面流。观察到扩散和对流的不同时间尺度，它们分别由扩散系数和粘度决定，LBM 受到时间和空间分辨率的限制。研究了扩散和对流将蛋白质运送到表面的速率，这表明扩散仅适用于模拟长时间研究。对于那些时间范围和低浓度，模拟了蛋白质从本体扩散到液滴表面的情况，并与文献进行了比较。作为下一步，假设蛋白质泡沫等情况。例如，在牛奶中，蛋白质的高浓度导致简化的情况，其中扩散和对流都不重要。这从理论上进行了分析，表明表面张力会发生瞬时变化。为了检查泡沫薄片的稳定性，将其用于进一步的模拟。两个气泡彼此靠近上升，表面张力全局不同，如纯水和含蛋白质的水。根据这些表面张力和初始距离，表面张力较高的气泡会更快地聚结，表面张力较低的气泡会较少出现二次运动。结论是，蛋白质泡沫中的气泡仅在比纯水中更短的距离内聚结。
