I. V. Marchuk

Deformation of the Free Surface in a Moving Locally-Heated Thin Liquid Layer

Liquid film flow on a vertical surface is studied experimentally and theoretically under the determining influence of the thermocapillary forces. In the two-dimensional steady-state case the shape of the film surface is calculated numerically within the thin layer approximation with allowance for the temperature dependence of the viscosity of the liquid and redistribution of the heat flux in the heating element. A local heat source was used in the experiments to produce temperature gradients up to 10 K/mm on the liquid surface. The film thickness was determined by means of the schlieren method with reflection. The relative thickness of the roller in the upper heater edge zone, characteristic of the formation of regular structures, is measured. The thickness is h/h0=1.32 ±0.07, which agrees satisfactorily with the results of numerical calculations.

Thermocapillary Deformation of a Locally Heated Liquid Film Moving under the Action of a Gas Flow

We propose a two-dimensional model of a steady laminar flow of a liquid film in a channel in the presence of a cocurrent gas flow. An analytical solution for the problem of temperature distribution is obtained for a linear flow velocity profile. The linearized problem of thermocapillary deformation of the film surface caused by local heating at a constant heat flux is solved. It is established that a thermocapillary bump is formed in the region where a thermal boundary layer emerges on the film surface. Additional perturbations, decaying in the upstream direction, can be present on the free surface in front of the bump. A criterion determining this effect is found.

Role of vapor flow in the mechanism of levitation of a droplet-cluster dissipative structure

The rate of water evaporation has been experimentally determined under conditions that ensure the formation of a dissipative structure of the droplet cluster type [1, 2]. It is shown that, in the region of localization of a droplet cluster, the velocity of the vapor-air flow is sufficient to maintain the levitation of droplets over the liquid surface according to the Stokes mechanism.

Experimental Study of the Wave Flow of a Liquid Film on a Heated Surface

The wave flow of a water film over the surface of a vertical plate with a 150×150-mm heater has been experimentally studied. The action of heat flux on the wave flow of the liquid film is manifested by the formation of periodic flowing rivulets separated by thin film regions. The thickness of the film between rivulets was measured using a fiber optical reflection probe. As the heat flux grows, the average film thickness h continuously decreases. However, when the thickness reaches h≈0.5 h0, where h0 is the value given by the Nusselt formula for a laminar liquid film, the film exhibits spontaneous rupture. It was found that, as the local flow rate decreases, the wave amplitude in the region between rivulets drops more rapidly than expected according to the laws of “cold hydrodynamics.”

Determination of surface tension and contact angle by the axisymmetric bubble and droplet shape analysis

The algorithms of solution to the Young–Laplace equation, describing the shape of an axisymmetric droplet on a flat horizontal surface, with various ways of setting the initial data and geometric parameters of a droplet, were derived and tested. Analysis of the Young–Laplace equation showed that a family of curves that form the droplet surface is the single-parametric one with the accuracy of up to the scale factor, whose role is played by the capillary length, and the contact angle determines the curve turn at a contact point, but it does not affect the shape of the curve. The main natural parameter defining the family of the forming curve is the curvature at the droplet top. The droplet shape is uniquely determined by three independent geometric parameters. This fact allows us to calculate the physical properties, such as the capillary length and contact angle, measuring three independent values: height, droplet diameter, and diameter of the droplet base or the area of the axial cross section of the droplet or its volume.

Vapor condensation on nonisothermal curvilinear fins

An analytical expression is obtained for the optimum curvature of a nonisothermal fin featuring stationary condensation of motionless vapor under the conditions of a significant influence of the surface tension on the motion of a condensed liquid. An algorithm is proposed and realized that finds the optimum surface shape for an unknown temperature distribution in the nonisothermal fin. The algorithm is based on a joint solution of the equations of heat conduction and condensed liquid film flow on the fin surface. Allowance for the thermal conductivity of a material in optimization of the fin shape provides for a significant increase in the condensate outflow as compared to the case of the optimum isothermal fin shape and a finite thermal conductivity of the material.

Thermocapillary deformation of a thin locally heated horizontal liquid layer

In this paper, steady thermocapillary flow in a thin horizontal layer of a viscous incompressible liquid with a free surface is considered. An axially symmetric steady problem with a localized thermal action on a horizontal liquid layer with a deformable free surface is solved in a thin-layer approximation. In addition to the thermocapillary effect, the model takes into account the capillary pressure caused by the free surface variable curvature and the convective mechanism of heat transfer in the liquid. Analytical expressions for the velocity vector components as functions of the liquid layer thickness and surface temperature are obtained. The free surface and velocity profiles caused by various kinds of heating are calculated. The influence of convective heat transfer on the flow pattern is analyzed.

Condensation on Curvilinear Fins (Effect of Groove Flooding): EMERALD Experiment of ESA

Some aspects of the ESA space program EMERALD are presented. A problem of the film type condensation on curvilinear fin is considered with taking into account the essential influence of the capillary forces and non uniform temperature of the fin. Disjoining pressure effect on condensate film flow is studied numerically, because of very thin film of condensate on the fin tip. Value of the groove flooding depth changes significantly the condensate outflow from the condenser. Calculations for water condensation predict a very high value of the heat transfer coefficient, more than 50 kW/m2K, on a quite important part of the surface area and confirm the idea of proposed condenser and Double Capillary Pumped Loop.

Experimental investigation of the temperature field in the gas-liquid two-layer system

Results of an experimental investigation of the temperature field across the liquid-gas two-layer system are presented. The liquid layer is locally heated from the bottom substrate, and the intensive liquid evaporation is observed. A technique for measuring the temperature profile across the liquid and gas layers (including their interface) is developed. To do these measurements, the microthermocouple is moved across the layers with the help of precision micropositioner with a step of 1 μm. The temperature jump at the liquid-gas interface is measured, and its value increases with the temperature increase. Detailed information on the temperature field near the interface is obtained by using the precise thermocouple displacement with a small step.

On the role of capillary waves in the mechanism of coalescence of a droplet cluster

Packets of capillary waves on the surface of a horizontal water layer generated at coalescence with a layer of microdroplets (with a characteristic diameter of 50–100 μm) of the dissipative structure “droplet cluster” have been detected by high-speed video recording and the schlieren method. The shortest experimentally observed waves have a length of about 130 μm and their phase velocity exceeds 1.8 m/s. It has been found that the coalescence of a single drop initiates a self-sustained wave process, which induces the coalescence of hundreds of droplets in a time shorter than 1 ms, which form a cluster.