Please use this identifier to cite or link to this item: doi:10.22028/D291-30808
Title: Shear Thinning in the Prandtl Model and Its Relation to Generalized Newtonian Fluids
Author(s): Müser, Martin H.
Language: English
Title: Lubricants
Volume: 8
Issue: 4
Publisher/Platform: MDPI
Year of Publication: 2020
Free key words: friction
shear thinning
molecular dynamics
Fokker Planck equation
blood flow
DDC notations: 500 Science
600 Technology
Publikation type: Journal Article
Abstract: The Prandtl model is certainly the simplest and most generic microscopic model describing solid friction. It consists of a single, thermalized atom attached to a spring, which is dragged past a sinusoidal potential representing the surface energy corrugation of a counterface. While it was primarily introduced to rationalize how Coulomb’s friction law can arise from small-scale instabilities, Prandtl argued that his model also describes the shear thinning of liquids. Given its success regarding the interpretation of atomic-force-microscopy experiments, surprisingly little attention has been paid to the question how the Prandtl model relates to fluid rheology. Analyzing its Langevin and Brownian dynamics, we show that the Prandtl model produces friction–velocity relationships, which, converted to a dependence of effective (excess) viscosity on shear rate η(γ˙), is strikingly similar to the Carreau–Yasuda (CY) relation, which is obeyed by many non-Newtonian liquids. The two dimensionless parameters in the CY relation are found to span a broad range of values. When thermal energy is small compared to the corrugation of the sinusoidal potential, the leading-order γ˙ 2 corrections to the equilibrium viscosity only matter in the initial part of the cross-over from Stokes friction to the regime, where η obeys approximately a sublinear power law of 1/γ.
DOI of the first publication: 10.3390/lubricants8040038
Link to this record: urn:nbn:de:bsz:291--ds-308084
ISSN: 2075-4442
Date of registration: 17-Dec-2020
Faculty: NT - Naturwissenschaftlich- Technische Fakultät
Department: NT - Materialwissenschaft und Werkstofftechnik
Professorship: NT - Prof. Dr. Martin Müser
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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