Elizaveta Ya. Gatapova

Slip Effect on Shear-Driven Evaporating Liquid Film in Microchannel

The development of compact, advanced cooling technology leads to problems involving two-phase flows at micro-scales. We investigate the effect of slip on heated liquid film driven by its own vapor in microchannel. The macroscopic interface shape is found to be sensitive to slip length comparable with the initial film thickness. The slip at the wall tends to elongate the transition film, and can have an effect on the mass flow rate. Calculations reveal that the maximum of the slip velocity is located in the transition region. The present work is a part of the preparation of the SAFIR experiment of the European Space Agency onboard the International Space Station.

Application of Floquet theory to the stability of liquid films on structured surfaces

We consider instability of a liquid film on a substrate structured by an array of gas-filled grooves. The instability is driven by disjoining pressure, while the effect of structuring on viscous flow in the film is modeled by a square-wave variation of the slip length along the substrate. Linear stability criteria are established analytically using Floquet theory and compared with the predictions of a straightforward numerical approach, all in the framework of a lubrication-type model. Then, stability is analyzed for a more general model based on Stokes flow approximation; validity of the lubrication-type approach is discussed. The structuring is found to enhance the instability for a wide range of conditions. Resonant interaction between the interfacial deformations and the substrate structuring pattern leads to discontinuities in the dispersion curves, a situation analogous to appearance of gaps in the energy spectra seen in the applications of Floquet theory in solid state physics.

THE THERMOCAPILLARY CONVECTION IN LOCALLY HEATED LAMINAR LIQUID FILM FLOW CAUSED BY A CO-CURRENT GAS FLOW IN NARROW CHANNEL

A two-dimensional model of a steady laminar flow of liquid film and co-current gas flow in a plane channel is considered. It is supposed that the height of a channel is much less than its width. There is a local heat source on the bottom wall of the channel. An analytical solution for the temperature distribution problem in locally heated liquid film is obtained, when the velocity profile is linear. An analytical solution of the linearized equation for thermocapillary film surface deformation is found. A liquid bump caused by the thermocapillary effect in the region where thermal boundary layer reaches the film surface is obtained. Damped oscillations of the free surface may exist before the bump. This is obtained according to the solution of the problem in an inclined channel. It depends on the forces balance in the film. The defining criterion is found for this effect. The oscillations of free surface do not exist for horizontally located channel.

Annular Liquid Film Flow Under Local Heating in Microchannel

In our previous investigations the formation of liquid bump of locally heated laminar liquid film with co-current gas flow was obtained [1,2]. The evaporation of liquid was left out of account. Heat transfer to the gas phase was approximately specified by a constant Biot number [2,3]. The aim of this work is an investigation of the evaporation effect, the hydrodynamics and the heat transfer of liquid film flow in a channel 0.2-1 mm height. The 2-D model of locally heated liquid film moving under gravity and the action of co-current gas flow with low viscosity in a channel are considered. The channel can be inclined at an angle with respect to horizon. It is supposed that the height of the channel is much less than its width. Surface tension is assumed to depend on temperature. The velocity profiles for gas and liquid regions are found from problem of joint motion of isothermal non-deformable liquid film and gas flow. Using the findings the joint solution of heat transfer and diffusion problem with corresponding boundary condition is calculated. Having the temperature field in the whole of liquid and gas flow region we find a local heat transfer coefficient on the gasliquid interface and Biot number as a function of flow parameters and spatial variables.

ROLE OF THERMOCAPILLARY CONVECTION IN RUPTURE OF A FALLING LIQUID FILM HEATED FROM BELOW

The present work is aimed to describe and explain the physical mechanism of the rupture of a liquid film of moderate thickness falling down a heated substrate. Our investigations are based on the experimental data obtained using IR thermography, fiber optical technique as well as theoretical estimation of critical values. We show that thermocapillary convection may be responsible for critical film thickness. By investigating the instability of thermocapillary cells we demonstrate that thermocapillary forces play a dominant role in the first and the second stages of the dry patch formation process.Copyright

THE INFLUENCE OF EVAPORATION IN SHEAR-DRIVEN LIQUID FILM ON HEAT REMOVAL FROM LOCAL HEATER

The present work focuses upon shear-driven liquid film evaporative cooling of high heat flux local heater. Thin evaporating liquid films may provide very high heat transfer rates and can be used for cooling of high power microelectronic systems. Thermocapillary convection in a liquid film falling down a locally heated substrate has recently been extensively studied. However, non-uniform heating effects remain only partially understood for shear-driven liquid films. The combined effects of evaporation, thermocapillarity and gas dynamics as well as formation of microscopic adsorbed film have not been studied. The effect of evaporation on heat and mass transfer for 2D joint flow of a liquid film and gas is theoretically and numerically investigated. The convective terms in the energy equations are taken into account. The calculations reveal that evaporation from film surface essential influences on heat removal from local heater. It is shown that the thermal boundary layer plays significant role for cooling local heater by evaporating thin liquid film. Measured by an infrared scanner temperature distribution at the film surface is compared with numerical data. Calculations satisfactorily describe the maximal surface temperature value.Copyright