Nonlinear Instability of an Evaporating Capillary Jet

The temporal instability of an evaporating liquid jet is investigated numerically. Effects of liquid Reynolds number, disturbance wave number, and the surface evaporation rate on the growth rate of the instability are studied. The results are compared with that of the linear analytical solution. For a high evaporation rate the propagation of the disturbance is no longer linear; thus, the linear analysis cannot predict the growth accurately. A modi ed growth rate for the instability of an evaporating jet is de ned. The breakup mechanism of viscous liquid jets and the formation of satellite drops are described. The results show that the satellite size decreases with decreasing Reynolds number and increasing wave number and evaporation rate. For large evaporation rates the satellite drops become very small, or even completely eliminated. The effect of the evaporationrate on the breakup time is also studied. Nomenclature cp = speci c heat h = height function k = wave number kt = thermal conductivity L = latent heat Ni = shape function Pr = Prandtl number, 1cp=kt p = pressure Q = evaporation rate per unit length R = radius of jet Re = Reynolds number. r0=/1=2.1=º/ rn = radius of neck rs = radius of swell r0 = undisturbed jet radius Ts = saturation temperature T1 = gas temperature tb = numerical break-up time tc = characteristic time.r 30 =/ 1=2 t cb = breakup time caused by capillarity t eb = breakup time caused by evaporation U = characteristicvelocity u = velocity vector.u; v/ We = Weber number, U 2r0= z = jet axis ¯ = dimensionless evaporation rate, Q=