Structural precursor to freezing: An integral equation study

Brader, Joseph M.

doi:10.1063/1.2889926

Cited by 22 publications

(22 citation statements)

References 58 publications

(44 reference statements)

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“…Although the majority of integral equation theories focus on the pair correlations, triplet correlations can also be handled within the same framework [154]. In addition to providing a higher level of resolution, the development of triplet-level integral equations is motivated by the desire for an improved description of the pair correlations.…”

Section: Equilibrium Integral Equationsmentioning

confidence: 99%

“…the Kirkwood superposition approximation) in order to arrive at a closed equation. In recent years, accurate approximations for the equilibrium triplet correlations of certain model systems have been developed [153,154]. Less is known regarding the nature of the triplet correlations in nonequilibrium situations.…”

Section: Pair Smoluchowski Equationmentioning

confidence: 99%

“…Verlet [179][180][181][182][183], Wertheim [184], Baxter [185], Stell [186]), all of which showed considerable promise. However, the complexity of solving the equations has hindered progress along this route and somewhat simpler, numerically tractable, theories now seem preferable [154,187,188].…”

Section: Equilibrium Integral Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear rheology of colloidal dispersions

Brader¹

2010

J. Phys.: Condens. Matter

128

156

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Colloidal dispersions are commonly encountered in everyday life and represent an important class of complex fluid. Of particular significance for many commercial products and industrial processes is the ability to control and manipulate the macroscopic flow response of a dispersion by tuning the microscopic interactions between the constituents. An important step towards attaining this goal is the development of robust theoretical methods for predicting from first-principles the rheology and nonequilibrium microstructure of well defined model systems subject to external flow. In this review we give an overview of some promising theoretical approaches and the phenomena they seek to describe, focusing, for simplicity, on systems for which the colloidal particles interact via strongly repulsive, spherically symmetric interactions. In presenting the various theories, we will consider first low volume fraction systems, for which a number of exact results may be derived, before moving on to consider the intermediate and high volume fraction states which present both the most interesting physics and the most demanding technical challenges. In the high volume fraction regime particular emphasis will be given to the rheology of dynamically arrested states.

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Section: Equilibrium Integral Equationsmentioning

confidence: 99%

Section: Pair Smoluchowski Equationmentioning

confidence: 99%

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Nonlinear rheology of colloidal dispersions

Brader¹

2010

J. Phys.: Condens. Matter

128

156

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“…It has been shown [4] for low and intermediate rates that supplementing the expression (4) by a volume fraction dependent high frequency viscosity can account for the measured macroscopic viscosity of hard sphere suspensions 1 . In order to close the theory we first note that the triplet distribution of the considered homogeneous system may be related to an inhomogeneous pair density [27] …”

mentioning

confidence: 99%

Density functional approach to nonlinear rheology

Reinhardt¹,

Weysser²,

Brader³

2013

EPL

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-We present a density functional based closure of the pair Smoluchowski equation for Brownian particles under shear flow. Given an equilibrium free energy functional as input the theory provides first-principles predictions for the flow-distorted pair correlation function and associated rheological quantities over a wide range of volume fractions and flow rates. Taking twodimensional hard-disks under shear flow as an illustrative model we calculate the pair correlation function, viscosity and normal stress difference under both steady and start-up shear.Introduction. -The addition of colloidal particles to a Newtonian liquid gives rise to a nonlinear rheological response, characterized by a rate dependent viscosity, finite normal stress differences and nontrivial transient dynamics [1]. Understanding the interplay between particle interactions and external stress or strain fields remains a major theoretical challenge and much effort has been invested in the search for tractable closure relations which capture the essential physics of systems driven out-of-equilibrium [2]. Realistic models for which the competing effects of Brownian motion, potential and hydrodynamic interactions are simultaneously active pose particular difficulties [3].

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“…There are, however, situations that require a (semi-)analytical statistical mechanical approach as an alternative to computer simulations. In such cases, there is a choice of various liquid integral equations that are based on the Ornstein-Zernike equation, and that have often been proven to predict pair correlations accurately and efficiently [1,2,[7][8][9][10][11][12][13]. The large body of complementary experiments, simulations and analytical theory have resulted in a good understanding of pair correlations in the fluid or liquid state by now.…”

Section: Introductionmentioning

confidence: 99%

Liquid pair correlations in four spatial dimensions: theory versus simulation

2015

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Using liquid integral equation theory, we calculate the pair correlations of particles that interact via a smooth repulsive pair potential in d = 4 spatial dimensions. We discuss the performance of different closures for the Ornstein-Zernike equation, by comparing the results to computer simulation data. Our results are of relevance to understand crystal and glass formation in high-dimensional systems.

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Structural precursor to freezing: An integral equation study

Cited by 22 publications

References 58 publications

Nonlinear rheology of colloidal dispersions

Nonlinear rheology of colloidal dispersions

Density functional approach to nonlinear rheology

Liquid pair correlations in four spatial dimensions: theory versus simulation

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