Numerical Modelling of Liquid Film Spreading Dynamics over Smooth Vertical Surface under Isothermal Conditions

The paper presents numerical modelling of the liquid film spreading dynamics of the R21 (mol. fraction: 0.9) and R114 refrigerants mixture. We considered an outer flow along a round vertical cylinder at Reynolds number of 104 and various contact angles. The simulation was performed in OpenFOAM software on the basis of the volume of fluid (VOF) method. We have shown that the wetting front deforms at wetting angles of 30 and 50 degrees, and regular jets form. At the same time, it was demonstrated that at the wetting angle of 10 degrees the spreading front has practically a flat shape, but one may see some regular thickenings of the liquid film along the contact line of the front.

On Capabilities of Tracking Marine Surface Currents Using Artificial Film Slicks

It is known that films on the sea surface can appear due to ship pollution, river and collector drains, as well as natural biological processes. Marine film slicks can indicate various geophysical processes in the upper layer of the ocean and in the atmosphere. In particular, slick signatures in SAR-imagery of the sea surface at low and moderate wind speeds are often associated with marine currents. Apart from the current itself, other factors such as wind and the physical characteristics of films can significantly influence the dynamics of slick structures. In this paper, a prospective approach aimed at measuring surface currents is developed. The approach is based on the investigation of the geometry of artificial banded slicks formed under the action of marine currents and on the retrieval of the current characteristics from this geometry. The developed approach is applied to quasi stationary slick bands under conditions when the influence of the film spreading effects can be neglected. For the stationary part of the slick band where transition processes of the band formation, e.g., methods of application of surfactants on water, film spreading processes, possible wind transformation etc., become negligible, some empirical relations between the band geometrical characteristics and the characteristics of the surface currents are obtained. The advantage of the approach is a possibility of getting information concerning the spatial structure of marine currents along the entire slick band. The suggested approach can be efficient for remote sensing data verification.

Film spreading from a miscible drop on a deep liquid layer

We study the spreading of a film from ethanol–water droplets of radii $0.9~\text{mm}<r_{d}<1.1~\text{mm}$ on the surface of a deep water layer for various concentrations of ethanol in the drop. Since the drop is lighter ($\unicode[STIX]{x1D709}=\unicode[STIX]{x1D70C}_{l}/\unicode[STIX]{x1D70C}_{d}>1.03$), it stays at the surface of the water layer during the spreading of the film from the drop; the film is more viscous than the underlying water layer since $\unicode[STIX]{x1D712}=\unicode[STIX]{x1D707}_{l}/\unicode[STIX]{x1D707}_{d}>0.38$. Inertial forces are not dominant in the spreading since the Reynolds numbers based on the film thickness $h_{f}$ are in the range $0.02<Re_{f}<1.4$. The spreading is surface-tension-driven since the film capillary numbers are in the range $0.0005<Ca_{f}<0.0069$ and the drop Bond numbers are in the range $0.19<Bo_{d}<0.56$. We observe that, when the drop is brought in contact with the water surface, capillary waves propagate from the point of contact, followed by a radially expanding, thin circular film of ethanol–water mixture. The film develops instabilities at some radius to form outward-moving fingers at its periphery while it is still expanding, till the expansion stops at a larger radius. The film then retracts, during which time the remaining major part of the drop, which stays at the centre of the expanding film, thins and develops holes and eventually mixes completely with water. The radius of the expanding front of the film scales as $r_{f}\sim t^{1/4}$ and shows a dependence on the concentration of ethanol in the drop as well as on $r_{d}$, and is independent of the layer height $h_{l}$. Using a balance of surface tension and viscous forces within the film, along with a model for the fraction of the drop that forms the thin film, we obtain an expression for the dimensionless film radius $r_{f}^{\ast }=r_{f}/r_{d}$, in the form $fr_{f}^{\ast }={t_{\unicode[STIX]{x1D707}d}^{\ast }}^{1/4}$, where $t_{\unicode[STIX]{x1D707}d}^{\ast }=t/t_{\unicode[STIX]{x1D707}d}$, with the time scale $t_{\unicode[STIX]{x1D707}d}=\unicode[STIX]{x1D707}_{d}r_{d}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$ and $f$ is a function of $Bo_{d}$. Similarly, we show that the dimensionless velocity of film spreading, $Ca_{d}=u_{f}\unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$, scales as $4f^{4}Ca_{d}={r_{f}^{\ast }}^{-3}$.