Dyadics resistance

The dyadic resistance coefficients derive from the quasi-steady Stokes equations as follows Let be the intrinsic solutions of the dyadic... 

Available results pertinent to the hydrodynamics of fractal suspensions are sparse thus far, encompassing only three physical situations. Gilbert and Adler (1986) determined the Stokes rotation-resistance dyadic for spheres arranged in a Leibniz packing [Fig. 7(a)], With the gap between any two spheres assumed small compared with their radii, lubrication-type approximations suffice. In this analysis, the inner spheres are assumed to rotate freely, whereas external torques T( (i = 1, 2, 3) are applied to the three other spheres. For Stokes flow, these torques are linearly related to the sphere angular velocities by the expression... 

Matsuoka, M., Endou, K., Kobayasi, H., Inoue, M., and Nakajima, Y. (1997). A dyadic plasmid that shows MLS and PMS resistance in Staphylococcus aureus. FEMS Microbiol. Lett. 148, 91-96. 

The dimensionless K dyadics are intensive properties of the body. They might aptly be called specific resistance dyadics, for they are independent of the size of the body—depending only upon its shape. 

The values of the various resistance dyadics for a spherical particle of radius a are... 

There are no other simple particle shapes for which the three resistance dyadics are wholly known, though some artificial bodies have been devised (B18, B22) to demonstrate that (i) the center of reaction is not generally... 

If the shape of the particle is similarly related to each of the three mutually perpendicular planes, the resistance dyadics adopt the isotropic forms... 

If a body possesses two distinct axes of helicoidal symmetry they must intersect. The point of intersection is then the center of reaction of the body. The three resistance dyadics are then isotropic at R ... 

There exist a variety of three-dimensional bodies whose resistance dyadics are known only in part. Foremost among these are axially symmetric bodies... 

There exist few particle-boundary combinations for which the particleboundary resistance dyadics in Eqs. (38) and (39) are known for all physically possible particle-to-wall dimensions. They are known, for example, for the trivial case of a spherical particle at the center of a concentric spherical boundary, the space between them being filled with fluid.The translation and rotation dyadics for this case are clearly isotropic, white the coupling dyadic obviously vanishes at this common center. 

The sphere-plane wall configuration represents one of the few nontrivial cases for which the particle-boundary resistance dyadics in Eqs. (38) and (39) are completely known. If e, is a unit vector normal to the plane then the translation and rotation dyadics are given by equations of the form (123) and... 

Each constant K,j resistance dyadic is an intrinsic geometric property of the instantaneous configuration of the entire particle system, dependent upon the sizes, shapes, mode of arrangement, and relative orientations of all the... 

Insight into the internal structure of the multiparticle resistance dyadics may be obtained from the two-sphere example discussed by Brenner (B22). Let fli and be the radii of the spheres Ci2 is a unit vector drawn from the center of sphere 1 to the center O2 of sphere 2, and 2h is the center-to-center distance. The resistance dyadics are then, to terms of the lowest orders in ajh,... 

Expressed in terms of the individual resistance and diffusion dyadics, Eq. (350) may be written as... 

K Coupling, rotation, and translation dyadics (38), (39) Dyadic, triadic and tetradic, resistance coefficients, respectively, for a porous medium (footnote 19)... 

Ki, K2 Resistance dyadics for particles 1 and 2, respectively, in an unbounded fluid (166)... 

---