A droplet of pure A of initial radius R is suspended in a large body of...
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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 gas phase is xAR at r = R and zero at an infinite distance from the droplet. (a) Assuming that R is constant, show that at steady state CDAB 2 dxA 1- XA (19B.7-1) dr where NAl-R is the molar flux in the r direction at the droplet surface, c is the total molar concentration in the gas phase, and DAB 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 RNA,lr=R = -cD AB In(1 – xAR) (19B.7-2) %3D (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 (R°C) = 4nR*N,lrak = -4rR¢D g In(1 – xar) (19B.7-3) dt where c is the molar density of pure liquid A. Show that when this equation is integrated from t = 0 to t = t, (the time for complete evaporation of the droplet), one gets R? (19B.7-4) 2cD AB In[1/(1 – xX AR)] Does this result look physically reasonable? 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 gas phase is xAR at r = R and zero at an infinite distance from the droplet. (a) Assuming that R is constant, show that at steady state CDAB 2 dxA 1- XA (19B.7-1) dr where NAl-R is the molar flux in the r direction at the droplet surface, c is the total molar concentration in the gas phase, and DAB 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 RNA,lr=R = -cD AB In(1 – xAR) (19B.7-2) %3D (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 (R°C) = 4nR*N,lrak = -4rR¢D g In(1 – xar) (19B.7-3) dt where c is the molar density of pure liquid A. Show that when this equation is integrated from t = 0 to t = t, (the time for complete evaporation of the droplet), one gets R? (19B.7-4) 2cD AB In[1/(1 – xX AR)] Does this result look physically reasonable?
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Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
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