Macroporous adsorbent materials are frequently used in the form of spherical pellets in many different applications. Consider a case where the adsorption of a solute A is very favorable (i.e., A is strongly bound). In this case, when A is adsorbed from a dilute solution on a high-capacity adsorbent, an adsorption front develops within the particle separating a clean core from a saturated layer as shown in Fig. P.11.8. A diffuses through the saturated layer and binds at the adsorption front. Over time, the adsorption front moves toward the center of the particle until the entire particle is fully saturated. Define q_m as the binding capacity in mg per cm³

of particle volume, C_A,s as the concentration of A in the fluid at the particle surface in mg per cm³ of fluid, and D_e as the effective pore diffusivity of A in the saturated layer. All three are assumed to be constant. Assuming pseudo-steady-state and that q_m>>CA,s :

(a) Develop an expression to describe the rate mass transfer of A through the saturated layer when the adsorption front is at a radial distance R_e. Note that C_A = 0 at the adsorption front.

(b) Write an expression for the amount of A adsorbed when the adsorption front is at a radial distance R_e.

(c) Use your expressions in (a)

and

(b) to find an expression for the position of the adsorption front as a function of time by equating the rate of mass transfer to the rate of change of the amount of A adsorbed.

FIGURE P.11.8:

Transcribed Image Text:

Expanding solute saturated area R CA=0_ Re(t) CA.S Shrinking solute-free core