Recently, Rajagopal [1] has considered an unsteady shearing flow of the incompressible second-order fluid with the constitutive equation for the extra stress S given by S = juAj 4axA2 + «2^i(1) In (1), ju, aj, a2 are constants, with jn > 0; \1 and A2 are the first two Rivlin-Ericksen tensors [2]. Rajagopal [1] showed that the time-dependent plane flow x = u(y,t), y = 0, in {x, y, t) e (-oo, oo)...

1 SUMMARY This paper is concerned with the application of radial basis function networks (RBFNs) for solving non-Newtonian fluid flow problems. Indirect RBFNs, which are based on an integration process, are employed to represent the solution variables; the governing differential equations are discretized by means of point collocation. To enhance numerical stability, stress-splitting techniques ...

This paper reviews the derivation of equations for slow dynamical processes in a variety of systems, including rotating rigid rotors, crystalline solids, isotropic and nematic elastomers, gels in an isotropic fluid background, and nematic liquid crystals. It presents a recent derivation of the Leslie–Ericksen equations for the dynamics of nematic liquid crystals that clarifies the nature of the...

We present explicit expressions of the helicity conservation in nematic liquid-crystal flows, for both the Ericksen–Leslie and Landau–de Gennes theories. This is done by using a minimal coupling argument that leads to an Euler-like equation for a modified vorticity involving both velocity and structure fields (e.g. director and alignment tensor). This equation for the modified vorticity shares ...

The alignment properties and distribution of flow speed during Poiseuille flow through a microchannel of a nematic liquid crystal in a cell with homeotropic surface alignment has been measured using a combination of conoscopy, fluorescence confocal polarizing microscopy, and time-lapse imaging. Two topologically distinct director profiles, with associated fluid velocity fields, are found to exi...

In this paper, we propose a finite-element scheme for solving numerically the equations of a transient two dimensional grade-two fluid non-Newtonian Rivlin-Ericksen fluid model. This system of equations is considered an appropriate model for the motion of a water solution of polymers. As expected, the difficulties of this problem arise from the transport equation. As one of our aims is to deriv...

During the processing of nematic soft solids through process flow elements (pipe bends, elbows, etc.), constitutive behavior makes its presence felt via (with rheology driven effects increasing pressure drop) and final product microstructure. This paper explores microstructure configurations liquid crystals in a 90° pipe bends with different types wall anchoring. The governing equations Leslie–...