The Newtonian Viscosity of a Moderately Dense Suspension

Wajnryb, Eligiusz; Dahler, John S.

doi:10.1002/9780470141618.ch4

Cited by 11 publications

(12 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…which agrees very well with previous calculations of these coefficients first done by Batchelor & Green (1972) and Batchelor (1976) and then with higher precision due to inclusion of hydrodynamic interactions at higher orders by , Jones (1988), Wajnryb & Dahler (1997), Cichocki et al (1999), Cichocki et al (2002) and Cichocki et al (2003). It is also worth pointing out that, since the absolute values of the coefficients D qq , K qq and G increase quickly with , the validity of the asymptotic expansion in the volume fraction φ may break down for large values of ; in other words for 1 the two-particle corrections are no longer much smaller than unity.…”

supporting

confidence: 87%

Short-time self-diffusion, collective diffusion and effective viscosity of dilute hard sphere magnetic suspensions

Mizerski

Wajnryb

2016

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

The virial corrections to short-time self-and collective diffusion coefficients as well as the effective viscosity are calculated for suspensions of hard spheres with the same radii and constant (blocked within the particle) magnetization modelled by a point dipole. Analytic, integral formulae derived from basic principles of statistical mechanics are provided for both cases -in the absence and in the presence of an external magnetic field. In the former case the diffusion and viscosity coefficients are evaluated numerically as a function of the strength of magnetic interactions between the particles and it is reported that the translational collective diffusion coefficient is significantly greater than all the other coefficients. In the presence of an external magnetic field the coefficients become anisotropic and are evaluated in the asymptotic regime of weak interparticle magnetic interactions.

show abstract

supporting

confidence: 87%

Short-time self-diffusion, collective diffusion and effective viscosity of dilute hard sphere magnetic suspensions

Mizerski

Wajnryb

2016

J. Fluid Mech.

Self Cite

View full text Add to dashboard Cite

show abstract

“…When there is no finite critical point, but the critical behaviour happens at infinity, then we have to consider the large-variable asymptotic forms for the root approximants, with the substitution (21). The first-order approximant gives…”

Section: Methods Of Defining Critical Indicesmentioning

confidence: 99%

Critical indices from self-similar root approximants

Gluzman

Yukalov

2017

Eur. Phys. J. Plus

View full text Add to dashboard Cite

The method of self-similar root approximants has earlier been shown to provide accurate interpolating formulas for functions for which small-variable expansions are given and the behaviour of the functions at large variables is known. Now this method is generalized for the purpose of extrapolating small-variable expansions to the region of finite and large variables, where the sought function exhibits critical behaviour. The procedure of calculating critical indices is formulated and illustrated by a variety of physical problems.a Corresponding author: V.I. Yukalov

show abstract

“…for the effective viscosity of a suspension [44]. The higher order coefficients depend on the location of particles.…”

Section: Effective Viscosity Of Passive Suspensionsmentioning

confidence: 99%

Optimized Factor Approximants and Critical Index

Gluzman¹

2021

Symmetry

View full text Add to dashboard Cite

Based on expansions with only two coefficients and known critical points, we consider a minimal model of critical phenomena. The method of analysis is both based on and inspired with the symmetry properties of functional self-similarity relation between the consecutive functional approximations. Factor approximants are applied together with various natural optimization conditions of non-perturbative nature. The role of control parameter is played by the critical index by itself. The minimal derivative condition imposed on critical amplitude appears to bring the most reasonable, uniquely defined results. The minimal difference condition also imposed on amplitudes produces upper and lower bound on the critical index. While one of the bounds is close to the result from the minimal difference condition, the second bound is determined by the non-optimized factor approximant. One would expect that for the minimal derivative condition to work well, the bounds determined by the minimal difference condition should be not too wide. In this sense the technique of optimization presented above is self-consistent, since it automatically supplies the solution and the bounds. In the case of effective viscosity of passive suspensions the bounds could be found that are too wide to make any sense from either of the solutions. Other optimization conditions imposed on the factor approximants, lead to better estimates for the critical index for the effective viscosity. The optimization is based on equating two explicit expressions following from two different definitions of the critical index, while optimization parameter is introduced as the trial third-order coefficient in the expansion.

show abstract

The Newtonian Viscosity of a Moderately Dense Suspension

Cited by 11 publications

References 22 publications

Short-time self-diffusion, collective diffusion and effective viscosity of dilute hard sphere magnetic suspensions

Short-time self-diffusion, collective diffusion and effective viscosity of dilute hard sphere magnetic suspensions

Critical indices from self-similar root approximants

Optimized Factor Approximants and Critical Index

Contact Info

Product

Resources

About