Transient shear stresses on a suspension cell in turbulence

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Abstract
A model flow field representative of Kolmogorov eddies in turbulence is proposed, and its two parameters are expressed in terms of the known bioreactor variables ε, the rate of turbulent power dissipation, and ν, the fluid kinematic viscosity. The trajectory through this flow field of a small sphere representing a cell is determined, and from that the time‐varying local shear rate can be found. This allows calculation of the shear stress at any point on the sphere's surface as it rotates in and moves through the model eddy. The maximum shear stress imposed on the cell by the surrounding turbulence has a range of 0.5–5 dyn/cm2, and can be estimated by 5.33ρ(εν)1/2. The shear stress has two major frequency components with ranges of 1–4 and 20–80 s−1; the higher frequency component is estimated by 0.678(ε/ν)1/2. The rotation of the direction of the shear stress vector at each point on the cell's surface is also discussed. Two ways in which external stresses might affect cell growth are proposed.