Tham khảo tài liệu 'the mems handbook introduction & fundamentals (2nd ed) - m. gad el hak part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Physics of Thin Liquid Films 12-35 Change of Phase Evaporation and Condensation Interfacial Conditions We now consider the case of an evaporating condensing thin film of a simple liquid lying on a heated cooled plane surface held at constant temperature 0 which is higher lower than the saturation temperature at the given vapor pressure. It is assumed that the speed of vapor particles is sufficiently low so that the vapor can be considered an incompressible fluid. The boundary conditions appropriate for phase transformation at the film interface z h are now formulated. The mass conservation equation at the interface is given by the balance between the liquid and vapor fluxes through the interface j Pv Vv - Vi n Pf vf - Vi n where j is the mass flux due to evaporation Pu and Pf are respectively the densities of the vapor and the liquid Vu and Vf are the vapor and liquid velocities at z h and V is the velocity of the interface. Equation provides the relationship between the normal components of the vapor and liquid velocities at the interface. The tangential components of both of the velocity fields are equal at the interface Vf - Vv tm 0 m 1 2. The boundary condition that expresses the stress balance and extends Equation to the case of phase transformation reads Delhaye 1974 Burelbach et al. 1988 j Vf - Vv - T - Tu n 2Hơ n - Vsơ where T is the stress tensor in the vapor phase and temperature dependence of surface tension is accounted for. The energy balance at z h is given by Delhaye 1974 Burelbach et al. 1988 l L tfun - u2f nj kthV - kth vVứv n 2p ef n f - 2Pv eu n Vu r 0 where L is the latent heat of vaporization per unit mass kthu LI. u are respectively the thermal conductivity viscosity and the temperature of the vapor Vvr Vu Vi Vfr Vf Vi are the vapor and liquid velocities relative to the interface respectively uun Vur n Vf n Vfr n are the normal components of the latter and ef eu are the rate-of-deformation .
