To find the flux of A at the vapor-liquid interface, we can use the following expression for the radial flux (Jr):

Jr_interface = -D_A * C_A/r |_(r=r_interface)

the convective-diffusive transport equation for species A in the liquid wedge using cylindrical coordinates (r, , z)is (1/r) * (/) * C_A/r + (/r) * C_A/ = D_A(C_A/r + (1/r) * C_A/r + (1/r) * C_A/).

At the vapor-liquid interface, the concentration of A should be in equilibrium with the gas phase: C_A(r, ) = C_A^sat () for r = r_interface

Far from the interface, there should be no gradients in the concentration of A: C_A/r 0 and C_A/ 0 for r

Since A is sparingly soluble, we assume that there is no accumulation of A at the solid-liquid interface, leading to a no-flux boundary condition: C_A/r = 0 for r = r_solid

To solve for the flux of A at the vapor-liquid interface, one would need to solve the above transport equation along with the given boundary conditions. This may require numerical methods, such as finite-difference or finite-element methods, to obtain a solution for the concentration profile C_A(r, ). Once the concentration profile is known, it can be used to determine the flux of A at the vapor-liquid interface.