Applicability conditions of the Stokes formula

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.