Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, United States.
J Colloid Interface Sci. 2010 Mar 1;343(1):306-13. doi: 10.1016/j.jcis.2009.11.044. Epub 2009 Nov 26.
We present an analysis of leveling in thin films of colloidal suspensions. The colloidal particles are assumed to be much smaller than the film thickness and influence the film rheology through a concentration-dependent viscosity and bulk diffusivity. A system of coupled nonlinear partial differential equations based on lubrication theory is used to describe the film height and the particle concentrations in the bulk and at the film surface. Linear stability analysis is applied to develop expressions for leveling rates in a number of limiting cases. It is found that for soluble particles, there exist regimes where increasing the Marangoni number slows down leveling at both short and long times, in contrast to the case of insoluble particles. Nonlinear simulations show that the linear theory accurately predicts leveling times even for large amplitude disturbances, and that the presence of a concentration-dependent viscosity and bulk diffusivity speed up leveling. The results of this work should be useful for estimating leveling rates in coatings laden with colloidal particles, and also in coatings containing soluble surfactant.
我们对胶体悬浮液薄膜的平整化过程进行了分析。假设胶体颗粒比薄膜厚度小得多，通过浓度相关的黏度和体相扩散系数对薄膜流变学产生影响。基于润滑理论的一个耦合非线性偏微分方程组被用来描述薄膜高度和体相以及薄膜表面的颗粒浓度。线性稳定性分析被用来推导一些极限情况下的平整化速率表达式。结果发现，对于可溶性颗粒，在短时间和长时间内，随着马兰戈尼数的增加，平整化速率都会减慢，这与不溶性颗粒的情况相反。非线性模拟表明，线性理论即使在大振幅干扰的情况下也能准确预测平整化时间，并且浓度相关的黏度和体相扩散系数会加快平整化进程。这项工作的结果对于估计含有胶体颗粒的涂层的平整化速率以及含有可溶性表面活性剂的涂层应该是有用的。
