Question

Estimation of Flow Rate for Centrifugation of Yeast Cells A maximum flow rate of 50 liters/min was achieved for the centrifugation of bacteria cells in a tubular centrifuge. The cells were 2.0 μm in diameter and had a density of 1.08 g/cm3. The medium had a density of 1.01 g/cm3 and viscosity of 1.2 cp. It is desired to centrifuge yeast cells in this same centrifuge. The yeast cells have a diameter of 5.0 μm and a density of 1.10 g/cm3. The medium has a density of 1.02 g/cm3 and a viscosity of 1.3 cp. Estimate the maximum flow rate that can be used to centrifuge the yeast cells.

Answer 1

$\fn_phv flow rate= v*\sum$

v= velocity under gravity

$\fn_phv \sum$= factor for centrifuge

1) for bacterial cells:

maximum flow rate= 50 L/min

density of cells= 1.08g/cm³

dameter of cells=2 micrometer

density of medium=1.01g/cm³

viscosity=1.2 cp

2) to calculate maximum flow rate of yeast cells with

density of cells = 1.1 g/cm³

dameter of cells = 5 micrometer

density of medium = 1.02 g/cm³

viscosity = 1.3 cp

maximum flow rate of yeast cells= v_g2 ( velocity under gravity for yeast cells)/ v_g1 (velocity undr gravity for bacterial cells) * given max flow rate of bacterial cells

v_g2/v_g1 = $\inline \fn_phv \frac{2 a_{2}^2 (\rho_{2} -\rho_{2} ')/9\mu_{2}}{2 a_{1}^2 (\rho_{1} -\rho_{1} ')/9\mu_{1}}$   =  $\inline \fn_phv \frac{2(2.5)(1.1-1.02)/9(1.3)}{2(1)(1.08-1.01)/9(1.2)}$

max flow rate of yeast cells = v_g2/v_g1 * max flow rate of bacterial cells

= 0.24/.091 * 50 l/min

max flow rate of yeast cells = 131.86 l/min