Vorobev A, Ivantsov A, Lyubimova T
Faculty of Engineering and the Environment, University of Southampton, Southampton, UK.
Institute of Continuous Media Mechanics Ural Branch RAS, Perm Federal Research Centre, Perm, Russia.
Eur Phys J E Soft Matter. 2017 Nov 20;40(11):99. doi: 10.1140/epje/i2017-11589-1.
Using the approach of direct numerical simulations we investigate the gravity-capillary waves induced on a horizontal interface between two slowly miscible liquids. It is assumed that the liquids are just brought into contact, and thus the interface is slowly smeared by the action of interfacial diffusion. It is also assumed that the initial shape of the interface is distorted by harmonic perturbations, which results in the development of the gravity-capillary surface waves. The evolution of the binary mixture is modelled on the basis of the phase-field method. Our results show that in the limiting case of negligible diffusion the classical dispersion relations for immiscible interfaces can be reproduced. Although, for the waves with shorter wavelengths such an agreement is more difficult to obtain. The interfacial diffusion brings an additional dissipation to the fluid system, strongly damping the development of the shorter waves. We also show that the mixing (or the transition of a binary system to the state of thermodynamic equilibrium) is intensified by the presence of the surface waves, and this effect is more important when the liquids are slowly miscible, i.e. when the interfacial diffusion is weak.
我们采用直接数值模拟的方法，研究了两种缓慢互溶液体之间水平界面上产生的重力 - 毛细波。假设两种液体刚刚接触，因此界面在界面扩散作用下会缓慢模糊。还假设界面的初始形状因谐波扰动而变形，这导致了重力 - 毛细表面波的发展。二元混合物的演化基于相场方法进行建模。我们的结果表明，在扩散可忽略不计的极限情况下，可以重现不混溶界面的经典色散关系。然而，对于波长较短的波，这种一致性更难获得。界面扩散给流体系统带来了额外的耗散，强烈地阻尼了短波的发展。我们还表明，表面波的存在会加剧混合（或二元系统向热力学平衡状态的转变），并且当液体缓慢互溶时，即界面扩散较弱时，这种效应更为重要。
