Screened Oseen tensor

In a semi-dilute solution the pair correlation function is given by equation (11) and the velocity correlation function is given by the screened Oseen tensor... 

A model that can take these findings into account is based on the idea that the screening of hydrodynamic interactions is incomplete and that a residual part is still active on distances r > H(c) [40,117]. As a consequence the solvent viscosity r s in the Oseen tensor is replaced by an effective... 

It is sometimes hypothesized that hydrodynamic interactions in polymer solutions are screened, i.e., the interactions fall off with distance not as the /R of the Oseen tensor but instead decrease exponentially, e.g., as exp(—KR)/R. Analogies are sometimes drawn with another long-range potential, namely the Coulomb potential, which in electroneutral solutions and as a result of electroneutrality decreases not as 1// but instead as exp(—KR)/R. Corresponding analogies are not drawn between hydrodynamics and the Newtonian gravitational potential, because gravity is not screened. 

Equation (78) describes a screening of the Oseen tensor. In the presence of the polymer chains the Oseen tensor T r) should be replaced by a screened tensor G(r), which for small distances is approximately equal to... 

We have now examined three phenomenological behaviors, namely two-bead microrheology, leading-order concentration dependences of transport coefficients, and -dependent chain internal modes. These three lines of evidence converge to the same conclusion. Hydrodynamic interactions in polymer and colloid solutions are described by the Oseen and Kynch tensors they are not screened. 

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