Impact of the wetting length on flexible blade coating

We study a common industrial problem: the spreading of a Newtonian fluid by a deformable blade, which is also paradigmatic of elasto-hydrodynamic interactions. This question has been seen in the light of an elasticity-capillarity analogy, and a parallel with dip coating experiments was proposed to predict the deposited film thickness [1]. To do so, the liquid reservoir was always considered as infinite. Here, we consider the case of a finite reservoir of liquid, emptying as the liquid is spread, a situation corresponding to a large majority of everyday situations, such as the spreading of paint on a wall, or cream on the skin. We evidence the role of a central variable: the wetting length lw, which sets a boundary between the wet and dry parts of the blade. We show that the deposited film thickness depends quadratically with lw. We study this problem experimentally and numerically by integration of the elasto-hydrodynamic equations, and finally propose a scaling law model to explain how lw influences the spreading dynamics.
[1] Seiwert, J., Quéré, D., Clanet, C., Flexible scraping of viscous fluids. J. Fluid Mech. 715: 424–435, 2013.