26.32 Recall from example 3. Chapter 25, that the differential model for the radial concentration profile of dissolved oxygen within cylindrical engineered tissue bundle (Figure 25.8) is one DAB 0 de 1 dcx Rmax CA d12 Kata with boundary conditions r=R, dea dr 0, r=R, CA = CAR PA H Often, K, is very small relative to c, so that the homogeneous reaction term approaches a zero-order process that is not depen- dent on concentration: Ra mixed RA R KACA CA so that DAB do 1 de dr2 m = 0 r di where m is the metabolic respiration rate of the tissue. In the present process, m=0.25 mole/m.h at 25C, and R, and R, are equal to 0.25 cm and 0.75 cm, respectively. Pure O2 gas ar 1.0 atm flows through the tube of length 15 cm. The muss- transfer resistance due to the thin-walled tube is neglected, and the Henry's law constant for dissolution of O, in the tissue is 0.78 atm-m /mole at 25C. The diffusion coefficient of oxygen in water is 2.1. 108 cm/s at 25C, which approximates the diffusivity of oxygen dissolved in the tissue, a. Develop a model, in final integrated form, to predict the concentration profile cr), and then plot out the concentra- tion profile. Note that for diffusion with zero-order bomo geneous chemical reaction, there will be a critical radius, R., where the dissolved oxygen concentration goes to zero. Therefore, if R.