Dey Mohar, Doumenc Frédéric, Guerrier Béatrice
Laboratoire FAST, Univ. Paris-Sud, CNRS, Université Paris-Saclay, F-91405, Orsay, France.
Sorbonne Universités, UPMC Univ Paris 06, UFR919, F-75005, Paris, France.
Eur Phys J E Soft Matter. 2016 Feb;39(2):19. doi: 10.1140/epje/i2016-16019-4. Epub 2016 Feb 25.
A hydrodynamic model is used for numerical simulations of a polymer solution in a dip-coating-like experiment. We focus on the regime of small capillary numbers where the liquid flow is driven by evaporation, in contrast to the well-known Landau-Levich regime dominated by viscous forces. Lubrication approximation is used to describe the flow in the liquid phase. Evaporation in stagnant air is considered (diffusion-limited evaporation), which results in a coupling between liquid and gas phases. Self-patterning due to the solutal Marangoni effect is observed for some ranges of the control parameters. We first investigate the effect of evaporation rate on the deposit morphology. Then the role of the spatial variations in the evaporative flux on the wavelength and mean thickness of the dried deposit is ascertained, by comparing the 2D and 1D diffusion models for the gas phase. Finally, for the very low substrate velocities, we discuss the relative importance of diffusive and advective components of the polymer flux, and consequences on the choice of the boundary conditions.
在类似浸涂实验中，采用流体动力学模型对聚合物溶液进行数值模拟。我们关注的是小毛细管数的情况，此时液体流动由蒸发驱动，这与由粘性力主导的著名的朗道 - 列维奇情况相反。采用润滑近似来描述液相中的流动。考虑了静止空气中的蒸发（扩散限制蒸发），这导致液相和气相之间的耦合。在某些控制参数范围内，观察到了由于溶质马兰戈尼效应引起的自图案化现象。我们首先研究蒸发速率对沉积物形态的影响。然后，通过比较气相的二维和一维扩散模型，确定蒸发通量的空间变化对干燥沉积物波长和平均厚度的作用。最后，对于非常低的基底速度，我们讨论聚合物通量的扩散和对流分量的相对重要性以及对边界条件选择的影响。
