Composition gradients in miscible liquids can create volume forces resulting in variousinterfacial phenomena. Experimental observations of these phenomena are related to some difficultiesbecause they are transient, sufficiently weak and can be hidden by gravity driven flows.As a consequence, the question about their existence and about adequate mathematical models isnot yet completely elucidated. In this work we present some experimental evidences of interfacialphenomena in miscible liquids and numerical simulations of miscible drops and diffuse interfaces.

When two miscible fluids, such as glycerol (glycerin) and water,are brought in contact, they immediately diffuse in each other. However if the diffusion is sufficiently slow, large concentration gradients existduring some time. They can lead to the appearance of an “effective interfacial tension”. To study these phenomena we use the mathematical modelconsisting of the diffusion equation with convective terms and ofthe Navier-Stokes equations with the Korteweg stress.We prove the global existence and uniqueness of the solution for the associated initial-boundary value problem in a two-dimensional bounded domain.We study the longtime behavior of the solution and show that it convergesto the uniform composition distribution with zero velocity field.We also present numerical simulations of miscible drops and show howtransient interfacial phenomena can change their shape.