Characteristic Time to Achieve Equilibrium in the Gas-Particle Interface

2 Characteristic Time to Achieve Equilibrium in the Gas-Particle Interface 

At the liquid surface, molecules are arriving from the gas, molecules are leaving the surface back to the gas, and molecules are diffusing into the liquid phase. Let us call these fluxes / , R, and / /, respectively. Since the surface is presumed to have no thickness Rg = Rg - - Ri. The flux of molecules from the gas to the interface is given by the kinetic theory of gases. 

The rate of evaporation R of A from the liquid depends on the surface concentration of A, C Rp,t). The evaporation process does not know whether equilibrium has been reached it simply expels molecules at a rate dependent on C0- If the two phases were at equilibrium, then R — where R is given by (11.51). If the two phases are not in equilibrium, we replace po by the corresponding ps(t), where ps(t) is the gas-phase partial pressure of A just above the surface of the droplet at any time t. In so doing. 

This amounts to saying that the rate of evaporation from the droplet at any time can be calculated from the equilibrium rate corresponding to the instantaneous partial pressure of A just above the surface of the drop. From Henry s law, C Rp, t) = H psit), and therefore we can rewrite (11.52) using C(Rp, t), the concentration of A at the droplet surface as 

The net flux across the interface toward the liquid phase is 

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