What is the einstein equation of viscosity?
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The Einstein equation of viscosity, μ = (1 + αfϕ)μ0, relates the viscosity of a dispersion/suspension to the liquid viscosity (μ0), solid volume fraction (ϕ), and a coefficient (αf) . Einstein derived an explicit first-order expansion for the effective viscosity of a Stokes fluid with a random suspension of small rigid particles at low density, based on scale separation and non-interacting particles assumptions . A rigorous derivation of Einstein's formula for the effective viscosity of dilute suspensions of rigid balls was provided, emphasizing the importance of correctly modeling fluid elasticity for predicting suspension rheology . This equation is crucial for understanding and predicting the behavior of nanofluid lubricants and dilute suspensions in various flow conditions.
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| The Einstein viscosity equation is corrected for fluid elasticity in dilute suspensions, accounting for shear-thickening due to elastic stretching near particles, crucial for accurate suspension rheology prediction. | |
33 Citations | The Einstein viscosity equation for nanolubricated friction is μ = (1 + αfϕ)μ0, where μ0 is liquid viscosity, ϕ is solid volume fraction, and αf is a coefficient. |
25 Citations | The Einstein formula for effective viscosity of dilute suspensions of rigid balls in a volume is derived rigorously for n ≫ 1 particles, providing a basis for viscosity calculations in such systems. |
Open access•Posted Content | Einstein's effective viscosity formula provides a first-order expansion for the effective viscosity of a Stokes fluid with a random suspension of small rigid particles at low density. |
Open access•Journal Article | The paper discusses the correction to suspension viscosity due to fluid elasticity, emphasizing the importance of modeling extensional rheology for accurate shear rheology predictions. |
Related Questions
What is the generalised einstein equation of viscosity?5 answersThe generalized Einstein equation for viscosity, as presented in the research papers, describes the viscosity of a dispersion/suspension in terms of the liquid viscosity, solid volume fraction, and a coefficient. This equation, μ = (1 + αfϕ)μ0, where μ0 is the liquid viscosity, ϕ is the solid volume fraction, and αf is a coefficient, is applied to nanofluid lubricants, providing insights into the coefficient of friction with nanofluid lubrication. Furthermore, the generalization of Navier-Stokes theory to relativity in the context of general-relativistic viscous phenomena in neutron star mergers also contributes to the understanding of viscosity in relativistic fluids, incorporating properties like stability, dissipative contributions, and entropy production.
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Step 3: The viscosity and elasticity of thyroid neoplasms were assessed using various ultrasound techniques in the studies. The viscosity values were measured using Viscosity Plane-wave UltraSound (Vi PLUS) and shear wave elastography techniques, while the elasticity was evaluated through quantitative elastography and shear wave velocity measurements. The results showed that the viscosity and elasticity values varied between benign and malignant thyroid nodules, with differences observed in the mean, maximum, and minimum elasticity values. Additionally, factors such as tissue type, composition, size, and localization were found to influence the stiffness of thyroid nodules, impacting the differentiation between benign and malignant pathologies.
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