The capillary instability of vertical liquid jets of different viscosities have been examined by imposing audio-frequency disturbances. Real time sequences of photographs allow a direct measurement of growth rates of disturbances of various wavelengths. Results show that in general non-linear effects dominate the growth processes. This is in agreement with Yuen's analysis. The growth rate of the difference between the neck and the swell, however, agrees well with the linearized analysis of Rayleigh and Chandrasekhar. The non-linear effect causes a liquid jet to disintegrate into drops with ligaments in between. The sizes of the ligaments decrease with increasing wave-number. The subsequent roll up of the ligament into droplet, the eventual coalescing of the droplet with the main drop and drop oscillation have also been studied.

A third-order theory has been developed to study capillary instability of a liquid jet. The result shows that the asymmetrical development of an initially sinusoidal wave is a non-linear effect with generation of higher harmonics as well as feedback into the fundamental. The growth of the surface wave is found to depend explicitly on the dimensionless initial amplitude of the disturbance and the dimensionless wave-number k of the wave. For the same initial disturbance, the wave is found to have a maximum growth rate at k = 0·7 in agreement with the linearized theory. For the same wave-number, the growth is proportional to the initial amplitude of the disturbance. The cut-off wave-number and the fundamental frequency (or growth rate for the unstable case) of the wave for a given k are found to be different from the linearized theory. Furthermore, at the cut-off wave-number, the present theory shows the disturbance experiences a growth which is proportional to t2. The excellent agreement between Donnelly & Glaberson's experiment and Rayleigh's linearized theory is found to be due to their method of measurement.

Drag data of water, methanol, heptane and benzene droplets are reported here. This data together with the data of Eisenklam et al. cover the entire range of Reynolds numbers from 1 to 2000 and mass transfer numbers from 0 to 3. The present study shows that the drag coefficients as a function of Reynolds numbers correlate well with the "standard drag" curve provided the characteristic density is the free stream density and the characteristic viscosity coefficient is n r {T T ). The basis for the choice of these two characteristic properties is discussed. The present correlation is insensitive to the mass transfer number. This suggests that mass efflux has little effect on drag of evaporating droplets.Present study indicates that for the determination of the drag coefficient of any evaporative droplet at quasisteady state, one needs only to know the wet bulb temperature as a function of free stream temperature. This information is sufficient to calculate y-r {T r ). The "standard drag" curve can then be applied to determine the drag coefficient. NOMENCLATURE A -area a = acceleration C m (T s -Ta) L 4 PiiTa) mass transfer number [g-a]h/U 2 drag coefficient 3 P a (T s ) = drag coefficient of incompressible flow Cf = friction drag coefficient C m = specific heat of surrounding at arithmetic mean of droplet vapor at Ta and air at T s D = total drag d = maximum horizontal diameter of droplet g = gravitational constant h = maximum vertical diameter of droplet L = latent heat of vaporization of droplet at Ta in = total mass M = molecular weight Re = Reynolds number Pa{T s )Ud Re r = Pa(T s )Ud Re s = -T = temperature in °C U = velocity of droplet relative to free stream velocity u = radial velocity x = mass fraction Greek Symbols P = density Ta-T s T = T s /t = viscosity coefficient Subscripts a d I m r s V = air = droplet = liquid = mean = reference condition according to 1/3 rule = free stream = vapor 147 Downloaded by [New York University] at 04:

Heat transfer rates to simulated and freely suspended liquid droplets were measured in an atmospheric hot air tunnel. The experiments were limited to water, methanol, and heptane droplets in a Reynolds number range of 25 to 2000, and a mass transfer number range of 0.07 to 2.79. The present experimental data together with data by others can best be correlated by Nuf(1+Bf).7 = 2 + 0.57 ReM1/2 Prf1/3, where properties are evaluated at film conditions except for the density in the Reynolds number which is the free-stream density. Thus the data shows that at higher temperatures, evaporation reduces heat transfer rates directly by a factor of (1 + Bf).7. Indirectly, evaporation affects heat transfer rates through the changes in both the composition and temperature of the surrounding gaseous medium.

Numerical solutions for high-temperature air flowing past water and methanol droplets and solid spheres, and superheated steam flowing past water droplets were obtained in the Reynolds number range of 10 to 100. The coupled momentum, energy, and specie continuity equations of variable thermophysical properties were solved using finite difference techniques. The numerical results of heat transfer and total drag agree well with existing experimental data. Mass transfer decreases friction drag significantly but at the same time increases pressure drag by almost an equal amount. The net effect is that the standard drag curve for solid spheres can be used for evaporating droplets provided the density is the free stream density and the viscosity of the vapor mixture is evaluated at an appropriate reference temperature and concentration. Both the mass efflux and variable properties decrease heat transfer rates to the droplets.