Evaporating meniscus

For a while now, the problem of flow and heat transfer in heated capillaries has attracted attention from a number of research groups, with several applications to engineering. The knowledge of the thermohydrodynamic characteristics of capillary flow with evaporative meniscus allows one to elucidate the mechanism of heat and mass transfer in porous media, to evaluate the efficiency of cooling system of electronic devices with high power density, as well as to optimize MEMS. 

We now describe the conditions that correspond to the interface surface. Eor stationary capillarity flow, these conditions can be expressed by the equations of continuity of mass, thermal fluxes on the interface surface and the equilibrium of all acting forces (Landau and Lifshitz 1959). Eor a capillary with evaporative meniscus the balance equations have the following form ... 

Morris SJS (2003) The evaporating meniscus in the channel. J Fluid Mech 494 297-317 Peles YP, Yarin LP, Hetsroni G (2000) Thermohydrodynamic characteristics of two-phase flow in a heated capillary. Int J Multiphase Flow 26 1063-1093 Peles YP, Yarin LP, Hetsroni G (2001) Steady and unsteady flow in a heated capfllary. Int J Multiphase Flow 27 577-598... 

Peles et al. (1998) and Khrustalev and Faghri (1996) considered two-phase laminar flow in a heated micro-channel with distinct evaporating meniscus in the frame of quasi-one-dimensional and two-dimensional models. 

Chapter 9 consists of the following in Sect. 9.2 the physical model of two-phase flow with evaporating meniscus is described. The calculation of the parameters distribution along the micro-channel is presented in Sect. 9.3. The stationary flow regimes are considered in Sect. 9.4. The data from the experimental facility and results related to two-phase flow in a heated capillary are described in Sect. 9.5. 

The subject of the present chapter is the analysis of possible states of capillary flow with distinct evaporative meniscus. The system of quasi-one-dimensional mass, momentum and energy equations are applied to classify the operating parameters corresponding to various types of flow. The domains of steady and unsteady states are also outlined. 

Two-phase flows in micro-channels with an evaporating meniscus, which separates the liquid and vapor regions, have been considered by Khrustalev and Faghri (1996) and Peles et al. (1998, 2000). In the latter a quasi-one-dimensional model was used to analyze the thermohydrodynamic characteristics of the flow in a heated capillary, with a distinct interface. This model takes into account the multi-stage character of the process, as well as the effect of capillary, friction and gravity forces on the flow development. The theoretical and experimental studies of the steady forced flow in a micro-channel with evaporating meniscus were carried out by Peles et al. (2001). These studies revealed the effect of a number of dimensionless parameters such as the Peclet and Jacob numbers, dimensionless heat transfer flux, etc., on the velocity, temperature and pressure distributions in the liquid and vapor regions. The structure of flow in heated micro-channels is determined by a number of factors the physical properties of fluid, its velocity, heat flux on... 

To calculate the flow fields outside the evaporating meniscus we use the onedimensional model, developed by Peles et al. (1998, 2000, 2001). Assuming that the compressibility and the energy dissipation are negligible (a flow with moderate velocities), the thermal conductivity and viscosity are independent of the pressure and temperature, we arrive at the following system of equations ... 

Fig. 10.17a-d Vapor flow over the evaporating Liquid flow in the evaporating meniscus (c) Khrustalev and Faghri (1996) with permission... 

The capillary flow with distinct evaporative meniscus is described in the frame of the quasi-dimensional model. The effect of heat flux and capillary pressure oscillations on the stability of laminar flow at small and moderate Peclet number is estimated. It is shown that the stable stationary flow with fixed meniscus position occurs at low wall heat fluxes (Pe -Cl), whereas at high wall heat fluxes Pe > 1, the exponential increase of small disturbances takes place. The latter leads to the transition from stable stationary to an unstable regime of flow with oscillating meniscus. 

Buffone, C., Sefiane, K., Christy, J.R.E. Experimental investigation of self-induced thermocapillary convection for an evaporating meniscus in capillary tubes using microparticle image velocimetry. Phys. Fluids 17, 052104 (2005)... 

Temperature Measurement, Methods, Fig. 4 (a) Schematic of the liquid-vapor interface characteristic of an evaporating meniscus, (b) Temperature profile along the surface beneath the evaporating meniscus measured with TLCs (Adapted from [6])... 

To study the effect of surfactants, rates of evaporation of a nonionic surfactant solution from single quartz capillaries with radii from 10 to 20 pm were measured [15]. The results obtained for evaporation of pure water (curve 1) and 0.25% solution of syntamide-5 (curve 2) from capillaries of equal radii, r = 8.2 pm, are shown in Fig. 12. Here L is the distance of evaporating meniscus from the open capillary end and t is the time. The capillaries filled with water and with surfactant solutions, respectively, were placed in an evacuated chamber [16] near each other. Curves 1 and 2 refer to evaporation in vacuum (p/ps = 0) at A = 5 x 10 " cm /s, where K is the coefficient characterizing the rate of evaporation. The coefficient K = L j4t depends on external conditions of evaporation and is proportional to the difference between vapor pressure over meniscus, p , and in surrounding media, po-At first, the curves 1 and 2 practically coincide, but later on evaporation from the capillary filled with the surfactant solution gradually slows down. This can be explained by the concentration of surfactant molecules near the evaporating meniscus surface. 

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