- 7 (Pav + 32 ) = - R . 12 = Km ( WQ- Way!) at As. soild 3 liquid pure B. CA 1- ert 2 Initially. Ho A - Bideal CA O STDABt / liquid A, B amp; C...
a). Write the simplified species A continuity equation for Ca(x1,t) in the liquid. Identify terms for convection. Diffusion reaction
- 7 (Pav + 32 ) = - R . 12 = Km ( WQ- Way!) at As.soild3 liquidpure B.CA 1- ert2Initially. HoA - BidealCA OSTDABt / liquid A, B & Cmixturegular coordinatestoC. IKNAZO = CAO)DABconst f. DAB.HH .AX ,solid Aevalid pseudo - binaryJuliquidonlyFIG. 2: Schematic of solid layer A dissolving in semi-infinite liquid and undergoing homogeneous reaction.A solid layer having thickness H comprised of species A is in contact with a semi-infinite liquid as shown schemat-MAGIC RUBically above. Initially, the layer has thickness Ho and the liquid is pure species B. For t > 0, species A dissolvesin the liquid forming an ideal mixture and undergoes a first-order, homogeneous reaction A + B - C with rateconstant k. Species A is only slightly soluble in A so that both the liquid density p and diffusivity DAB are constant,and the pseudo-binary approximation is valid. The solid density p ~ p. The concentration of A at the solid-liquidinterface (X1 = H) is CAeq. In your analysis, assume one-dimensional diffusion in the x1-direction: gA = CA($1, t) and1 = v1 (x1, t).1. 10 pts Write the simplified species A continuity equation for CA (1, t) in the liquid. Identify terms forconvection, diffusion and reaction.2. 10 pts Use the continuity equation and jump mass balance at $1 = H to show v1 (x1, t) = 0.AtB-JC3. 10 pts Write the initial and boundary conditions for CA (21, t).
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