EXAMPLE 17.3 OVERALL RATE FOR A LINEAR PROCESS Dilute A diffuses through a stagnant liquid film onto a plane surface consisting of B,reacts there to produce R which diffuses back into the mainstream.Develop the overall rate expression for the L/S reaction A()+B(S)→R() which takes place on this flat surface,see Fig.E17.3. CAL Plane surface of solid B Main body Solid A of liquid I Liquid film Equilibrium concentration △x of A on surface,CA2=0 Figure E17.3. 6
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SOLUTION By diffusion,the flux of A to the surface is 4-a0=-是cw-c小=C-C rm=s di () Reaction is first order with respect to A,so based on unit surface 1dNA=k"CA rhe=S di (的 At steady state the flow rate to the surface is equal to the reaction rate at the surface (steps in series).So rAI=TA2 and from Eqs.(i)and (ii) k,(CA-CA)=k”CAs 7
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from which k CCM () Replacing Eq.(iii)into either Eq.(i)or Eq.(ii)then eliminates CAs which cannot be measured,giving 1 mol rA1=r=rA=-1 -CAl=-koverall CAl, m2.s k,k” Comment This result shows that 1/k and 1/k"are additive resistances.It so happens that the addition of resistances to obtain on overall resistance is permissi- ble only when the rate is a linear function of the driving force and when the processes occur in series. 8
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E17.4 OVERALL RATE FOR A NONLINEAR PROCESS Repeat Example 17.3 with just one change:let the reaction step be second order with respect to A,or rh2=-k"Ch SOLUTION Combining the reaction steps to eliminate CAs,as was done in Example 17.3,is now not so simple,and gives -店=-r=元=会2rC+-网+xC, m2.s 9
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Contacting Patterns for Two-Phase Systems There are many ways that two phases can be contacted,and for each the design equation will be unique. When real flow deviates considerably from ideal flow patterns,we can do one of the two things:we may develop models to mirror actual flow closely,or we may calculate performance with ideal patterns which bracket actual flow. Five flow patterns: 10
10 • Contacting Patterns for Two-Phase Systems There are many ways that two phases can be contacted,and for each the design equation will be unique. • When real flow deviates considerably from ideal flow patterns, we can do one of the two things: we may develop models to mirror actual flow closely, or we may calculate performance with ideal patterns which bracket actual flow. • Five flow patterns: