Special cases of the equation of continuity 1. Equation for constant c and D AB,
Equation of Continuity Special cases of the equation of continuity 2. Equimolar counterdiffusion of gases, At constant P, with no reaction, c = constant, v M = 0, D AB = constant and R A =0 Fick’s 2 nd Law of diffusion
Equation of Continuity Special cases of the equation of continuity 3. For constant ρ and D AB (liquids), Starting with the vector notation of the mass balance
Equation of Continuity Example 1. Estimate the effect of chemical reaction on the rate of gas absorption in an agitated tank. Consider a system in which the dissolved gas A undergoes an irreversible first order reaction with the liquid B; that is A disappears within the liquid phase at a rate proportional to the local concentration of A. What assumptions can be made?
Equation of Continuity 1.Gas A dissolves in liquid B and diffuses into the liquid phase 2.An irreversible 1 st order homogeneous reaction takes place A + B AB Assumption: AB is negligible in the solution (pseudobinary assumption)
Equation of Continuity Expanding the equation and taking c inside the space derivative, Assuming steady-state, Assuming concentration of A is small, then total c is almost constant and
Equation of Continuity Assuming that diffusion is along the z-direction only,
Equation of Continuity Rearranging, Looks familiar? How to solve this ODE?
Equation of Continuity A hollow sphere with permeable solid walls has its inner and outer surfaces maintained at a constant concentration C A1 and C A0 respectively. Develop the expression for the concentration profile for a component A in the wall at steady-state conditions. What is the flux at each surface? Example 2.