702 research outputs found
Thermal convection in a nonlinear non-Newtonian magnetic fluid
We report theoretical and numerical results on thermal convection of a magnetic fluid in a viscoelastic carrier liquid. The viscoelastic properties are described by a general nonlinear viscoelastic model that contains as special cases the standard phenomenological constitutive equations for the stress tensor. In order to explore numerically the system we perform a truncated Galerkin expansion obtaining a generalized Lorenz system with ten modes. We find numerically that the system has stationary, periodic and chaotic regimes. We establish phase diagrams to identify the different dynamical regimes as a function of the Rayleigh number and the viscoelastic material parameters
General Nonlinear 2-Fluid Hydrodynamics of Complex Fluids and Soft Matter
We discuss general 2-fluid hydrodynamic equations for complex fluids, where
one kind is a simple Newtonian fluid, while the other is either
liquid-crystalline or polymeric/elastomeric, thus being applicable to lyotropic
liquid crystals, polymer solutions, and swollen elastomers. The procedure can
easily be generalized to other complex fluid solutions. Special emphasis is
laid on such nonlinearities that originate from the 2-fluid description, like
the transport part of the total time derivatives. It is shown that the proper
velocities, with which the hydrodynamic quantities are convected, cannot be
chosen at will, since there are subtle relations among them. Within allowed
combinations the convective velocities are generally material dependent. The
so-called stress division problem, i.e. how the nematic or elastic stresses are
distributed between the two fluids, is shown to depend partially on the choice
of the convected velocities, but is otherwise also material dependent. A set of
reasonably simplified equations is given as well as a linearized version of an
effective concentration dynamics that may be used for comparison with
experiments
Nonlinear Fluid Dynamics Description of non-Newtonian Fluids
Nonlinear hydrodynamic equations for visco-elastic media are discussed. We
start from the recently derived fully hydrodynamic nonlinear description of
permanent elasticity that utilizes the (Eulerian) strain tensor. The reversible
quadratic nonlinearities in the strain tensor dynamics are of the 'lower
convected' type, unambiguously. Replacing the (often neglected) strain
diffusion by a relaxation of the strain as a minimal ingredient, a generalized
hydrodynamic description of viscoelasticity is obtained. This can be used to
get a nonlinear dynamic equation for the stress tensor (sometimes called
constitutive equation) in terms of a power series in the variables. The form of
this equation and in particular the form of the nonlinear convective term is
not universal but depends on various material parameters. A comparison with
existing phenomenological models is given. In particular we discuss how these
ad-hoc models fit into the hydrodynamic description and where the various
non-Newtonian contributions are coming from.Comment: Acta Rheologic
Nonlinear Effects in the TGB_A Phase
We study the nonlinear interactions in the TGB_A phase by using a
rotationally invariant elastic free energy. By deforming a single grain
boundary so that the smectic layers undergo their rotation within a finite
interval, we construct a consistent three-dimensional structure. With this
structure we study the energetics and predict the ratio between the intragrain
and intergrain defect spacing, and compare our results with those from linear
elasticity and experiment.Comment: 4 pages, RevTeX, 2 included eps figure
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