61 research outputs found
A Minimal Model for Vorticity and Gradient Banding in Complex Fluids
A general phenomenological reaction-diffusion model for flow-induced phase
transitions in complex fluids is presented. The model consists of an equation
of motion for a nonconserved composition variable, coupled to a Newtonian
stress relations for the reactant and product species. Multivalued reaction
terms allow for different homogeneous phases to coexist with each other,
resulting in banded composition and shear rate profiles. The one-dimensional
equation of motion is evolved from a random initial state to its final
steady-state. We find that the system chooses banded states over homogeneous
states, depending on the shape of the stress constitutive curve and the
magnitude of the diffusion coefficient. Banding in the flow gradient direction
under shear rate control is observed for shear-thinning transitions, while
banding in the vorticity direction under stress control is observed for
shear-thickening transitions.Comment: 11 pages, submitted to Eur Phys J
Two-state shear diagrams for complex fluids in shear flow
The possible "phase diagrams'' for shear-induced phase transitions between two phases are collected. We consider shear-thickening and shear-thinning fluids, under conditions of both common strain rate and common stress in the two phases, and present the four fundamental shear stress vs. strain rate curves and discuss their concentration dependence. We outline how to construct more complicated phase diagrams, discuss in which class various experimental systems fall, and sketch how to reconstruct the phase diagrams from rheological measurements
Classical generalized constant coupling model for geometrically frustrated antiferromagnets
A generalized constant coupling approximation for classical geometrically
frustrated antiferromagnets is presented. Starting from a frustrated unit we
introduce the interactions with the surrounding units in terms of an internal
effective field which is fixed by a self consistency condition. Results for the
magnetic susceptibility and specific heat are compared with Monte Carlo data
for the classical Heisenberg model for the pyrochlore and kagome lattices. The
predictions for the susceptibility are found to be essentially exact, and the
corresponding predictions for the specific heat are found to be in very good
agreement with the Monte Carlo results.Comment: 4 pages, 3 figures, 2 columns. Discussion about the zero T value of
the pyrochlore specific heat correcte
Bulk and Interfacial Shear Thinning of Immiscible Polymers
Nonequilibrium molecular dynamics simulations are used to study the shear
thinning behavior of immiscible symmetric polymer blends. The phase separated
polymers are subjected to a simple shear flow imposed by moving a wall parallel
to the fluid-fluid interface. The viscosity begins to shear thin at much lower
rates in the bulk than at the interface. The entire shear rate dependence of
the interfacial viscosity is consistent with a shorter effective chain length
that also describes the width of the interface. This is independent
of chain length and is a function only of the degree of immiscibility of
the two polymers. Changes in polymer conformation are studied as a function of
position and shear rate.Shear thinning correlates more closely with a decrease
in the component of the radius of gyration along the velocity gradient than
with elongation along the flow. At the interface, this contraction of chains is
independent of and consistent with the bulk behavior for chains of length
. The distribution of conformational changes along chains is also studied.
Central regions begin to stretch at a shear rate that decreases with increasing
, while shear induced changes at the ends of chains are independent of .Comment: 8 pages, 8 figure
Shear-banding in a lyotropic lamellar phase, Part 2: Temporal fluctuations
We analyze the temporal fluctuations of the flow field associated to a
shear-induced transition in a lyotropic lamellar phase: the layering transition
of the onion texture. In the first part of this work [Salmon et al., submitted
to Phys. Rev. E], we have evidenced banded flows at the onset of this
shear-induced transition which are well accounted for by the classical picture
of shear-banding. In the present paper, we focus on the temporal fluctuations
of the flow field recorded in the coexistence domain. These striking dynamics
are very slow (100--1000s) and cannot be due to external mechanical noise.
Using velocimetry coupled to structural measurements, we show that these
fluctuations are due to a motion of the interface separating the two
differently sheared bands. Such a motion seems to be governed by the
fluctuations of , the local stress at the interface between the
two bands. Our results thus provide more evidence for the relevance of the
classical mechanical approach of shear-banding even if the mechanism leading to
the fluctuations of remains unclear
Interfaces in Diblocks: A Study of Miktoarm Star Copolymers
We study AB miktoarm star block copolymers in the strong segregation
limit, focussing on the role that the AB interface plays in determining the
phase behavior. We develop an extension of the kinked-path approach which
allows us to explore the energetic dependence on interfacial shape. We consider
a one-parameter family of interfaces to study the columnar to lamellar
transition in asymmetric stars. We compare with recent experimental results. We
discuss the stability of the A15 lattice of sphere-like micelles in the context
of interfacial energy minimization. We corroborate our theory by implementing a
numerically exact self-consistent field theory to probe the phase diagram and
the shape of the AB interface.Comment: 12 pages, 11 included figure
Shear-banding in a lyotropic lamellar phase, Part 1: Time-averaged velocity profiles
Using velocity profile measurements based on dynamic light scattering and
coupled to structural and rheological measurements in a Couette cell, we
present evidences for a shear-banding scenario in the shear flow of the onion
texture of a lyotropic lamellar phase. Time-averaged measurements clearly show
the presence of structural shear-banding in the vicinity of a shear-induced
transition, associated to the nucleation and growth of a highly sheared band in
the flow. Our experiments also reveal the presence of slip at the walls of the
Couette cell. Using a simple mechanical approach, we demonstrate that our data
confirms the classical assumption of the shear-banding picture, in which the
interface between bands lies at a given stress . We also outline
the presence of large temporal fluctuations of the flow field, which are the
subject of the second part of this paper [Salmon {\it et al.}, submitted to
Phys. Rev. E]
A phenomenological model for shear-thickening in wormlike micelle solutions
We present a simple phenomenological model to describe shear-thickening in a
wormlike
micelle solution. The solution is assumed to undergo a reaction above a
critical
shear stress, to form a gel-like phase.
There is no flow within this "gel" phase, and it is insoluble in the
solution.
The amount of gel in the system is determined
by a competition between a stress-dependent reaction rate, which creates
gel, and a
constant breakage rate, which destroys gel. We recover a re-entrant region
in the
stress-shear rate curve, which is only accessible under controlled stress
conditions.
When the apparent shear rate is fixed, the corresponding stress-shear rate
relation
is discontinuous. Our results are in qualitative agreement with the
experimental
observations of Pine et al
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