Steady flows of nonlinear bipolar viscous fluids between rotating cylinders

Abstract

Abstract. The boundary-value problem governing the steady Couette flow of a nonlinear bipolar viscous fluid is formulated and solved for particular, degenerate, values of the constitutive parameters; for the general situation, in which the relevant constitutive parameters are positive, we establish existence and uniqueness of solutions to the boundary-value problems. Continuous dependence of solutions, in appropriate norms, is also established with respect to the parameters governing the nonlinearity and multipolarity of the model as these constitutive parameters converge to zero.

Some Remarks on Applying Homogenization Theory to Modeling the Constitutive Response of Carbon Nanotubes

“…In such case, a set of high(er)-order elastic constants that belongs to the framework of multipolar theory needs to be determined'. Examples of multipolar effects in continua may be found, for example, in [35][36][37][38]. Thus, even if one could justify modeling the graphitic sheet as an isotropic elastic continuum (and we have already indicated that, contrary to current consensus opinion on this point, the response is probably not isotropic) one can not carry such isotropic response over to the nanotube surface as a consequence of the relevant mapping somehow being conformal1 it is not.…”

Inertial manifolds of incompressible, nonlinear bipolar viscous fluids

“…Finally, we note that special examples of flows of incompressible bipolar viscous fluids have been examined in detail in [5] as well as in the recent series of papers by Bellout and Bloom on plane Poiseuille flows ( [21]- [23]) and the study by Bloom and Hao [24] of Couette flow between rotating cylinders.…”

Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow

“…3 we turn to a study of a variety of incompressible bipolar flows in special geometries and types of domains. Building on the work in [BH2], we formulate the classical problem of flow between rotating concentric cylinders for an incompressible, nonlinear, bipolar fluid in Sect. 3.2 and prove results concerning the existence, uniqueness, and continuous dependence (on constitutive parameters) for such flows.…”