Kynch tensor

Each transport coefficient depends in a different way on the Oseen and Kynch tensors and their rotational analogs. The uniform agreement between calculations and experiments indicates that at most distances these tensors accurately describe hydrodynamic interactions between colloids and segments of polymer chains. 

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. 

Here is the drag coefficient of a single colloid particle in pure solvent, I is the identity tensor, and further terms in each sum involve the relative positions of several particles. The above considerations apply equally to colloidal spheres and to segments of polymer chains. If the diffusing objects are not spheres the ijlij and the F, all depend implicitly on the orientations of the objects. For interacting spherical colloids, the case under consideration in this chapter, the extended b, and Tij are the hydrodynamic interaction tensors obtained by Kynch(32), whose lead terms are... 

---