Bioreactor design. a bioreactor is loaded with spherical support particles of radius a each of which contains a uniform dispersion of acrobic cells. the cells have been genetically modified to produce antivenin, which is used to treat rattlesnake bites and is often in short supply during the summer in tucson. the oxygen concentration on the surface of the particles is ca. the oxygen concentration in the middle of the particles is finite. the oxygen concentration profile in the particles is needed in the design of this reactor to ensure that cells near the center have enough oxygen to live. experimental measurements show that the respiration rate of the cells is first-order in the oxygen concentration. a. draw a schematic of the problem to solve. b. develop an equation and boundary conditions to model the oxygen concentration profile in the particles. c. solve the equation to obtain the oxygen concentration profile as a fiunction of particle radius c(r). relationships: (g) species (oxygen) conservation in a porous medium (no convection) 려 where daf is the effective diffusivity of oxygen in the spherical support particles and r is the rate of oxygen consumption by the acrobic organisms (note that, here, r is taken to be positive when oxygen is consumed). (ii) the laplacian operator in spherical coordinates: