Applicability conditions of the Stokes formula

Jean-Louis Bretonnet; Jean-François Wax; Jean-Louis Bretonnet; Jean-François Wax

doi:10.3934/matersci.2021049

AIMS Materials Science

2021, Volume 8, Issue 5: 809-822. doi: 10.3934/matersci.2021049

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Applicability conditions of the Stokes formula

Université de Lorraine, LCP-A2MC EA 3469, 1 Bd. F. Arago, Metz, France

Received: 16 July 2021 Accepted: 18 October 2021 Published: 11 November 2021

In our research work on the microscopic properties of liquids in relation to biotechnical applications, we were led to use the Stokes formula to calculate the force exerted by a fluid on colloidal suspensions, and to look in the bibliography for the demonstration of this formula. The proofs that we have found are often partial and the applicability conditions not always explicit, which led us to resort to the initial demonstration made by Stokes ^[1] in 1850 with the mathematical formalism used in that time. Here we give the detailed demonstration by means of the vector analysis specific to this type of problem. We end the article with a brief discussion of low Reynolds number flows dominated by viscosity and where inertial effects are neglected.
- Stockes formula,
- rheology of colloidal suspensions
Citation: Jean-Louis Bretonnet, Jean-François Wax. Applicability conditions of the Stokes formula[J]. AIMS Materials Science, 2021, 8(5): 809-822. doi: 10.3934/matersci.2021049

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Abstract

In our research work on the microscopic properties of liquids in relation to biotechnical applications, we were led to use the Stokes formula to calculate the force exerted by a fluid on colloidal suspensions, and to look in the bibliography for the demonstration of this formula. The proofs that we have found are often partial and the applicability conditions not always explicit, which led us to resort to the initial demonstration made by Stokes ^[1] in 1850 with the mathematical formalism used in that time. Here we give the detailed demonstration by means of the vector analysis specific to this type of problem. We end the article with a brief discussion of low Reynolds number flows dominated by viscosity and where inertial effects are neglected.

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