CNRS, ILM Institut Lumière Matière, Université Claude Bernard Lyon 1 Campus LyonTech-La Doua Batiment Brillouin, 10 rue Ada Byron, F-69622 Villeurbanne, France.
Phys Rev E. 2018 Jan;97(1-1):012802. doi: 10.1103/PhysRevE.97.012802.
We present a continuum model describing dissolution and growth of a crystal contact confined against a substrate. Diffusion and hydrodynamics in the liquid film separating the crystal and the substrate are modeled within the lubrication approximation. The model also accounts for the disjoining pressure and surface tension. Within this framework, we obtain evolution equations which govern the nonequilibrium dynamics of the crystal interface. Based on this model, we explore the problem of dissolution under an external load, known as pressure solution. We find that in steady state, diverging (power-law) crystal-surface repulsions lead to flat contacts with a monotonic increase of the dissolution rate as a function of the load. Forces induced by viscous dissipation then surpass those due to disjoining pressure at large enough loads. In contrast, finite repulsions (exponential) lead to sharp pointy contacts with a dissolution rate independent of the load and the liquid viscosity. Ultimately, in steady state, the crystal never touches the substrate when pressed against it. This result is independent from the nature of the crystal-surface interaction due to the combined effects of viscosity and surface tension.
我们提出了一个连续统模型，描述了在基底限制下晶体接触的溶解和生长。在润滑近似下，对分离晶体和基底的液体膜中的扩散和流体动力学进行建模。该模型还考虑了离隙压力和表面张力。在这个框架内，我们得到了控制晶体界面非平衡动力学的演化方程。基于这个模型，我们探讨了在外载荷（称为压力溶解）下的溶解问题。我们发现，在稳态下，发散（幂律）的晶体-表面排斥导致平坦的接触，并且随着载荷的增加，溶解速率呈单调增加。在足够大的载荷下，粘性耗散引起的力超过离隙压力引起的力。相比之下，有限的排斥（指数）导致尖锐的接触，其溶解速率与载荷和液体粘度无关。最终，在稳态下，当晶体被压在基底上时，它永远不会接触到基底。由于粘度和表面张力的综合作用，这个结果与晶体-表面相互作用的性质无关。
