Fungal pellets can become hollow by oxygen limitation leading to cell lysis in the middle of...

  

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Fungal pellets can become hollow by oxygen limitation leading to cell lysis in the middle of the pellet. It can be assumed that there are no external mass transfer limitations, that mass transfer is limited by diffusion, and that the consumption of oxygen can be described by zeroth order kinetics. In such as situation the distribution of the concentration of oxygen СA across a pellet can be described by: CA = CAS + koR² (r² 6D R² - 2R3 rR² 1+- - 2R3 R3 CA is the oxygen concentration at radius r from the centre. CAs is the oxygen concentration at the surface (r=R) ko is the zeroth order rate constant of oxygen consumption D is the diffusion coefficient Ro is the radius from the centre at which oxygen becomes depleted. The oxygen concentration at 0 < r < Ro will therefore be zero. At Ro <r <R the oxygen concentration will not be zero, and oxygen will be consumed at a rate ko. (a) Make a sketch of a hollow pellet. (b) Very small pellets will not have a centre in which oxygen depletion occurs, i.e. CA remains > 0 everywhere. Show that the concentration distribution in such particles can be described by: CA = CAS + ko (p²2- 6D (1 mark) - (r² - R²) (2 marks) (c) Show that there is a maximum particles radius Rmax at which oxygen is depleted just at the centre point which can be described by: Rmax = 6DCAS ko (d) It has been found that at an oxygen concentration at the surface CAs of 4 ppm the value of Rmax is 1.5 mm. Calculate Rmax at oxygen concentrations at the surface of 6 ppm and 8 ppm. Fungal pellets can become hollow by oxygen limitation leading to cell lysis in the middle of the pellet. It can be assumed that there are no external mass transfer limitations, that mass transfer is limited by diffusion, and that the consumption of oxygen can be described by zeroth order kinetics. In such as situation the distribution of the concentration of oxygen СA across a pellet can be described by: CA = CAS + koR² (r² 6D R² - 2R3 rR² 1+- - 2R3 R3 CA is the oxygen concentration at radius r from the centre. CAs is the oxygen concentration at the surface (r=R) ko is the zeroth order rate constant of oxygen consumption D is the diffusion coefficient Ro is the radius from the centre at which oxygen becomes depleted. The oxygen concentration at 0 < r < Ro will therefore be zero. At Ro <r <R the oxygen concentration will not be zero, and oxygen will be consumed at a rate ko. (a) Make a sketch of a hollow pellet. (b) Very small pellets will not have a centre in which oxygen depletion occurs, i.e. CA remains > 0 everywhere. Show that the concentration distribution in such particles can be described by: CA = CAS + ko (p²2- 6D (1 mark) - (r² - R²) (2 marks) (c) Show that there is a maximum particles radius Rmax at which oxygen is depleted just at the centre point which can be described by: Rmax = 6DCAS ko (d) It has been found that at an oxygen concentration at the surface CAs of 4 ppm the value of Rmax is 1.5 mm. Calculate Rmax at oxygen concentrations at the surface of 6 ppm and 8 ppm.

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To answer the provided questions we need to proceed one by one a To make a sketch of a hollow pellet you would draw a sphere with an empty circle in t... View the full answer