Article outline

In recent years, the study of the properties of anomalously viscous liquids has attracted the interest of many scientists from various fields of science, from oil refining to medicine. Unlike ordinary liquids, the viscosity of which decreases with increasing temperature, the viscosity of anomalously viscous media changes non-monotonically: it can increase sharply and then decrease in a certain temperature range. Under certain temperature conditions, an interesting phenomenon occurs in such liquids - a viscous barrier. This is a localized region with high viscosity, which can affect the movement of the main liquid flow, up to blockage. In this paper, we study the effect of a viscous barrier on the velocity of a droplet moving in a flow of an anomalously viscous liquid in a flat channel. Numerical modeling is performed using the phase field method, consisting of a system of Cahn–Hilliard–Navier–Stokes equations, supplemented by an equation for the temperature field. The purpose of the modeling is to study the effect of a viscous barrier located in the center of the channel on the velocity and deformation of a droplet. Three values of the capillary number Ca = 0.1, Ca = 1, Ca = 10 and three parameters of the viscosity anomaly A = 0 (without a viscous barrier), A = 5 (a small viscous barrier), A = 10 (a pronounced viscous barrier) are considered.

Graphs of the droplet velocity dependence on the capillary number are compiled. It is shown that for all cases of capillary numbers, the viscous barrier formed in the channel imparts additional acceleration to the droplet. For all calculations, the total normalized mass of the system was calculated over time, it is shown that the maximum error does not exceed 5%. Images of the droplet shape at the channel outlet for different cases of a viscous barrier are given. It is shown that if the capillary number is large (Ca > 1), then inclusions of the surrounding liquid can form in the droplet, however, if the droplet moves in a channel with a viscous barrier, then the highly viscous region does not allow inclusions of another liquid to form in the droplet due to more intense deformation of the droplet. It is established that the relative velocity of a drop in a flow of an abnormally viscous liquid is higher than in a flow of liquid with a constant minimum viscosity. Graphs of the dependence of the relative velocity of a drop on the liquid anomaly parameter for three capillary numbers are presented. It is shown that in a channel without a viscous barrier, the relative velocity of a drop is the lowest for all capillary numbers. In a channel with the largest viscous barrier (A = 10), the relative velocity of a drop is the highest. It is evident that the larger the viscous barrier, the stronger the acceleration it imparts to a drop: a viscous barrier acts as a kind of ”viscous gun“, imparting acceleration to a drop and increasing its velocity. It is established that a viscous barrier formed in a channel imparts acceleration to a drop and increases the relative velocity of a drop.