19B.7 Time for a droplet to evaporate. A droplet of pure A of initial radius R is suspended in a large body of motionless gas B. The concentration of A in the infinite distance from the droplet. gas...

Extracted text: 19B.7 Time for a droplet to evaporate. A droplet of pure A of initial radius R is suspended in a large body of motionless gas B. The concentration of A in the infinite distance from the droplet. gas phase is x, AR at r = R and zero at an (a) Assuming that R is constant, show that at steady state AB 2 dx dr R²NArlr=R (19B.7-1) XA where Nl-R is the molar flux in the r direction at the droplet surface, c is the total molar concentration in the gas phase, and DAR is the diffusivity in the gas phase. Assume constant temperature and pressure throughout. Show that integration of Eq. 19B.7-1 from the droplet surface to infinity gives АВ RNArlr=R = = -cD АВ In(1 - XAR) (19B.7-2) (b) We now let the droplet radius R be a function of time, and treat the problem as a quasi-steady one. Then the rate of decrease of moles of A within the drop can be equated to the instantaneous rate of loss of mass across the liquid-gas interface d -TR°C) = 47R°N olar = -4rRcDg In(1 – XXAR) (L) AR°C' In(1 - Х AR) (19B.7-3) Ar lr=R АВ dt where c is the molar density of pure liquid A. Show that when this equation is integrated from t = 0 to t = to (the time for complete evaporation of the droplet), one gets to = 2cD AB In[1/(1 – xAR)] (19B.7-4) Does this result look physically reasonable?