547 research outputs found
Phase Separation of Rigid-Rod Suspensions in Shear Flow
We analyze the behavior of a suspension of rigid rod-like particles in shear
flow using a modified version of the Doi model, and construct diagrams for
phase coexistence under conditions of constant imposed stress and constant
imposed strain rate, among paranematic, flow-aligning nematic, and log-rolling
nematic states. We calculate the effective constitutive relations that would be
measured through the regime of phase separation into shear bands. We calculate
phase coexistence by examining the stability of interfacial steady states and
find a wide range of possible ``phase'' behaviors.Comment: 23 pages 19 figures, revised version to be published in Physical
Review
Phase Coexistence of Complex Fluids in Shear Flow
We present some results of recent calculations of rigid rod-like particles in
shear flow, based on the Doi model. This is an ideal model system for
exhibiting the generic behavior of shear-thinning fluids (polymer solutions,
wormlike micelles, surfactant solutions, liquid crystals) in shear flow. We
present calculations of phase coexistence under shear among weakly-aligned
(paranematic) and strongly-aligned phases, including alignment in the shear
plane and in the vorticity direction (log-rolling). Phase coexistence is
possible, in principle, under conditions of both common shear stress and common
strain rate, corresponding to different orientations of the interface between
phases. We discuss arguments for resolving this degeneracy. Calculation of
phase coexistence relies on the presence of inhomogeneous terms in the
dynamical equations of motion, which select the appropriate pair of coexisting
states. We cast this condition in terms of an equivalent dynamical system, and
explore some aspects of how this differs from equilibrium phase coexistence.Comment: 16 pages, 10 figures, submitted to Faraday Discussion
Continuum theory of partially fluidized granular flows
A continuum theory of partially fluidized granular flows is developed. The
theory is based on a combination of the equations for the flow velocity and
shear stresses coupled with the order parameter equation which describes the
transition between flowing and static components of the granular system. We
apply this theory to several important granular problems: avalanche flow in
deep and shallow inclined layers, rotating drums and shear granular flows
between two plates. We carry out quantitative comparisons between the theory
and experiment.Comment: 28 pages, 23 figures, submitted to Phys. Rev.
An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification
Using state-of-the-art numerical techniques, such as mesh adaptivity, implicit time-stepping and a non-linear multi-grid solver, the phase-field equations for the non-isothermal solidification of a dilute binary alloy have been solved. Using the quantitative, thin-interface formulation of the problem we have found that at high Lewis number a minimum in the dendrite tip radius is predicted with increasing undercooling, as predicted by marginal stability theory. Over the dimensionless undercooling range 0.2–0.8 the radius selection parameter, σ*, was observed to vary by over a factor of 2 and in a non-monotonic fashion, despite the anisotropy strength being constant
Nonlinear dynamics of sand banks and sand waves
Sand banks and sand waves are two types of sand structures that are commonly observed on an off-shore sea bed. We describe the formation of these features using the equations of the fluid motion coupled with the mass conservation law for the sediment transport. The bottom features are a result of an instability due to tide–bottom interactions. There are at least two mechanisms responsible for the growth of sand banks and sand waves. One is linear instability, and the other is nonlinear coupling between long sand banks and short sand waves. One novel feature of this work is the suggestion that the latter is more important for the generation of sand banks. We derive nonlinear amplitude equations governing the coupled dynamics of sand waves and sand banks. Based on these equations, we estimate characteristic features for sand banks and find that the estimates are consistent with measurements
Flat Nonholonomic Matching
In this paper we extend the matching technique to a
class of nonholonomic systems with symmetries. Assuming
that the momentum equation defines an integrable
distribution, we introduce a family of reduced
systems. The method of controlled Lagrangians is then
applied to these systems resulting in a smooth stabilizing
controller
Dynamical Models of Extreme Rolling of Vessels in Head Waves
Rolling of a ship is a swinging motion around its length axis. In particular vessels transporting containers may show large amplitude roll when sailing in seas with large head waves. The dynamics of the ship is such that rolling interacts with heave being the motion of the mass point of the ship in vertical direction. Due to the shape of the hull of the vessel its heave is influenced considerably by the phase of the wave as it passes the ship. The interaction of heave and roll can be modeled by a mass-spring-pendulum system. The effect of waves is then included in the system by a periodic forcing term. In first instance the damping of the spring can be taken infinitely large making the system a pendulum with an in vertical direction periodically moving suspension. For a small angular deflection the roll motion is then described by the Mathieu equation containing a periodic forcing. If the period of the solution of the equation without forcing is about twice the period of the forcing then the oscillation gets unstable and the amplitude starts to grow. After describing this model we turn to situation that the ship is not anymore statically fixed at the fluctuating water level. It may move up and down showing a motion
modeled by a damped spring. One step further we also allow for pitch, a swinging motion around a horizontal axis perpendicular to the ship. It is recommended to investigate the way waves may directly drive this mode and to determine the amount of energy that flows along this path towards the roll mode. Since at sea waves are a superposition of waves with different wavelengths, we also pay attention to the properties of such a type of forcing containing stochastic elements. It is recommended that as a measure for the
occurrence of large deflections of the roll angle one should take the expected time for which a given large deflection may occur instead of the mean amplitude of the deflection
Quantification of mesh induced anisotropy effects in the phase-field method.
Phase-field modelling is one of the most powerful techniques currently available for the simulation from first principles the time dependant evolution of complex solidification microstructures. However, unless care is taken the computational mesh used to solve the set of partial differential equations that result from the phase-field formulation of the solidification problem may introduce a stray, or implicit, anisotropy, which would be highly undesirable in quantitative calculations. In this paper we quantify this effect as a function of various computational parameters and subsequently suggest techniques for mitigating the effect of this stray anisotropy
- …