Question

Microcarrier beads 120 μm in diameter are used to culture recombinant CHO cells for production of growth hormone. It is proposed to use a 6-cm turbine impeller to mix the culture in a 3.5-1itre stirred tank. Air and carbon dioxide are supplied by flow through the reactor headspace. The microcarrier suspension has a density of approximately 1010 kg m^-3 and a viscosity of 1.3 x 10^-3 Pa s. Estimate the kinematic viscosity.

(a) 1.30 × 10^-6 m^2s^-1

(b) 1.29 × 10^-6 m^2s^-1

(c) 1.50 × 10^-6 m^2s^-1

(d) 1.49 × 10^-6 m^2s^-1

I had been asked this question in an interview for internship.

I want to ask this question from Role of Shear in Stirred Fermenters topic in chapter Fluid Flow and Mixing of Bioprocess Engineering

Answer 1

To estimate the kinematic viscosity ($\nu$), we can use the relationship between dynamic viscosity ($\mu$) and density ($\rho$):

ν=μρ\nu = \frac{\mu}{\rho}ν=ρμ​

Given Data:

• Dynamic viscosity ($\mu$): 1.3×10−31.3 \times 10^{-3}1.3×10−3 Pa·s.
• Density ($\rho$): 1010 kg/m31010 \, \text{kg/m}^31010kg/m3.

Step-by-Step Calculation:

1. Convert the units: The dynamic viscosity is in Pa·s, and density is in kg/m³. To ensure the correct units for kinematic viscosity (m²/s), we can directly use the formula with the given units.

2. Apply the formula:

ν=1.3×10−3 Pa\cdotps1010 kg/m3\nu = \frac{1.3 \times 10^{-3} \, \text{Pa·s}}{1010 \, \text{kg/m}^3}ν=1010kg/m31.3×10−3Pa\cdotps​

Since 1 Pa·s = 1 kg/(m·s), we can simplify the units:

ν=1.3×10−31010\nu = \frac{1.3 \times 10^{-3}}{1010}ν=10101.3×10−3​ ν=1.29×10−6 m2/s\nu = 1.29 \times 10^{-6} \, \text{m}^2/\text{s}ν=1.29×10−6m2/s

Answer:

(b) 1.29 × 10⁻⁶ m²/s

This is the correct value for the kinematic viscosity of the microcarrier suspension.