The coating dynamics of a drying paint film with a yield stress is studied. The liquid is modeled as a binary mixture with one volatile component, solvent, and one nonvolatile component, resin. When the solvent has a different surface tension than the resin, solvent evaporation can lead to the creation of surface tension gradients which can potentially overcome the yield stress and dramatically affect the flow history. Using the lubrication approximations to derive the flux of the liquid film parallel to the substrate, we find that the presence of the yield stress causes several distinct flow regimes. The total flux of each of these regimes is summed, and using the continuity equation we derive an evolution equation giving the height of the free surface as a function of the distance along the substrate and time. The resulting equations are discretized and solved numerically using finite differences. High order derivative is treated implicitly, allowing for large time steps and reducing the computational requirements. We find that the presence of a yield stress greatly affects the leveling behavior of the coating. Critical yield stresses exist that can cause maximal leveling of the coating film.

中文翻译：

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用屈服应力使模型漆膜流平

研究了具有屈服应力的干燥漆膜的涂层动力学。将该液体建模为具有一种挥发性组分（溶剂）和一种非挥发性组分（树脂）的二元混合物。当溶剂的表面张力与树脂不同时，溶剂蒸发会导致表面张力梯度的产生，这可能会克服屈服应力并极大地影响流动历史。使用润滑近似来推导平行于基板的液膜通量，我们发现屈服应力的存在会导致几种不同的流动状态。对每个状态的总通量求和，并使用连续性方程式，我们得出了一个演化方程式，该方程式给出了自由表面的高度，该高度是沿着衬底的距离和时间的函数。使用有限差分将所得方程离散化并通过数值求解。高阶导数被隐式处理，从而允许较大的时间步长并减少了计算需求。我们发现屈服应力的存在极大地影响了涂层的流平行为。存在临界屈服应力，其可能导致涂膜达到最大水平。