E Resistance Coefficient of a Particle in Non-Local Fluid

To extend result (D.5) to non-linear cases, it is convenient to begin with equation (D.6). The derivative with respect to time ought to be replaced by the Yaumann derivative (see, Section 8.4), so that, in the simplest case, the covariant equation for the resistance force has the form 

Indeed, the last equation can be differentiated with respect to time to obtain equation (D.7) consequently 

At low velocity gradients, expression (D.9) can be expanded in a series in powers of the antisymmetrical gradient uj13. The first term of the series has the form of (D.5). 

The motion of a spherical particle in a non-local fluid was considered by Pokrovskii and Pyshnograi (1988). We reproduce the calculation of the resistant coefficient here. 

We consider the viscous liquid to be incompressible and the motion of the particle to be slow. It means that the Reynolds number of the problem is 

---