Question

A suspension of yeast cells is to be filtered at a constant filtration rate of 50 L/min.
The suspension has a solid content of 70 kg/m3 of suspension and the yeast cells
have a bulk density of 800 kg/m3. Laboratory tests indicate that the specific cake
resistance is 40 m/kg and the viscosity of the filtrate is 2.9x10-3 kg/m.s. The filter has
an area of 0.1 m2 and the medium offers negligible resistance. How long can the
filtration rate be maintained before the pressure drop exceeds 1 N/m2? What volume
of cake and filtrate are collected during this time? Note that ρ0 is expressed in mass
of solids per volume of filtrate and NOT total volume of suspension.

Answer 1

We are given,

Density$=800kg/m^3$

Specific cake resistance $=40m/kg$

Viscosity of the filtrate $=2.9\ *10^{-3}kg/m.s$

Area$=0.1m^2$

Pressure$=1N/m^2$

$\alpha$ $=70kg/m^3$

Formula used.

$t\ =\dfrac{\mu\alpha\rho_0}{2\Delta P}(\dfrac{V}{A})^2$

$R$ _c$=\alpha\rho_0(\dfrac{V}{A})$

$40\ *0.1\ =70\ *800\ *V\newline 4\ =56000V\newline V=7.14\ *10^{-5}$

$t\ =\dfrac{2.9*10^{-3} \ \ *70\ \ *800}{2\ *1}\ (\dfrac{7.14*10^{-5}}{0.1})^2$

$=81.2\ \ *(5.1 *10^{-7})$

$=4.1\ *10^{-5}$