Statistical Microhydrodynamics

Sinaiski, Emmanuil G.; Zaichik, L. I.

doi:10.1002/9783527621804

Cited by 5 publications

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“…Since the aim is to resolve the turbulence fluctuations, the temporal time step ∆t is chosen to be of the order of the fastest eddy turnover times in the turbulent fluid. Now, due to small polymer-bead (and colloid) diameters and polymer thickness, it is expected that the microflow around polymer chains is always going to be a creeping flow that can be described by Stokesian Dynamics [33]. Since, due to its diffusive nature, a creeping flow establishes itself essentially instantaneously with respect to the much slower inertial turbulence fluctuations [13], the hydrodynamic interactions and the accompanying viscous drag on polymer chains correspond to Stokes flow modes superposed on large scale turbulence.…”

Section: Creeping Microflow and Polymer Motionmentioning

confidence: 99%

“…Therefore, no explicit computation of µ takes place, and this is problematic in the context of calculating Brownian motion effects, where knowledge of this matrix is required [33]. Hence, one needs to employ Fixman's method [39,40] for solving stochastic differential equations, since the latter is a "matrix-free" method, requiring only matrix-vector products, not the µ matrix itself.…”

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A method for the computation of turbulent polymeric liquids including hydrodynamic interactions and chain entanglements

Kivotides

2017

Physics Letters A

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An asymptotically exact method for the direct computation of turbulent polymeric liquids that includes (a) fully resolved, creeping microflow fields due to hydrodynamic interactions between chains, (b) exact account of (subfilter) residual stresses, (c) polymer Brownian motion, and (d) direct calculation of chain entanglements, is formulated. Although developed in the context of polymeric fluids, the method is equally applicable to turbulent colloidal dispersions and aerosols.a On visit to Department of Aerospace, California Institute of Technology (GALCIT) 1 PROLOGUE Traditionally, the study of polymeric liquids [1,2] (and similarly of colloidal dispersions [3,4]) involves two major strains of thought. On the one hand, there is the viscoelastic fluid dynamics approach [5][6][7], that models complex fluids as continuum field theories, by employing a suitable constitutive law. Due to its relative simplicity and affinity with standard fluid dynamical investigations, this approach is particularly suitable for the analysis of complicated flow phenomena including instabilities and turbulence [8][9][10]. However, such studies are usually limited to dilute polymer systems, since dense polymer flows necessarily involve entanglements between polymer chains, and the effects of the latter on elastic stresses levels are difficult to accurately capture with standard constitutive laws [11,12]. Another, equally important, limitation of the classical field theoretic approach is that the employed constitutive laws originate in rheological flows that are either simple elongational/shear flows, or involve periodic unsteady effects (see particularly lucid discussions of these in [11,13]). The applicability of rheological constitutive laws to fully developed turbulent fluctuation fields is not straightfoward, since the latter are non-Gaussian and highly intermittent [14][15][16], hence the polymer chains find themselves interacting with velocity fields of a much higher degree of unstructured unsteadiness than usually is the case in rheology [17,18].The need for a constitutive law is bypassed via mesoscopic modeling of polymeric liquids [19]. In this formulation, the solvent is described via the Navier-Stokes equation, and is coupled with the polymer chains that are modeled by some version of the bead-spring model [12,20,21]. Due to the mesoscopic character of the modeling, the polymer chains interact via effective intermolecular potentials, and undergo Brownian motion. Such hybrid fluid-chains formulation has many advantages over the aforementioned fully continuum approach: (a) there is no need for a constitutive law, since elastic effects in the flow are taken into account from first principles via chain elasticity, and the explicit coupling of the chains with the flow field. It is important to note that, in order for this statement to be valid in non-dilute systems, one needs to employ a version of the bead-spring model that allows the formation of entanglements between chains and the calculation of their implication...

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Section: Creeping Microflow and Polymer Motionmentioning

confidence: 99%

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A method for the computation of turbulent polymeric liquids including hydrodynamic interactions and chain entanglements

Kivotides

2017

Physics Letters A

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“…Lata 1905-1906 przyniosły artykuły: Einsteina pod tytułem O ruchu cząstek zawiesiny, postulowanym przez molekularno-kinetyczną teorię ciepła 91 , opublikowanego przez niego w czasopiśmie "Annalen der Physik" 92 (1905 r.); i Smoluchowskiego zatytułowany Zarys teorii kinetycznej ruchów Browna i roztworów mętnych (1906 r.), wydany jako rozprawa Wydziału Matematyczno-Przyrodniczego Akademii Umiejętności w Krakowie 93 , ale także w "Annalen der Physik" 94 . Prace te traktowały o ruchach Browna, czyli o zjawisku polegającym na chaotycznym ruchu zawieszonych w płynie mikrocząsteczek o rozmiarach rzędu od 1 nm do 1μm 95 . Ich mechanizm był dla nauki przez długi czas prawdziwą zagadką 96 .…”

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Profesor Marian Smoluchowski (1872–1917) – zapomniany rektor Uniwersytetu Jagiellońskiego

Słowik¹

2020

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Professor Marian Smoluchowski (1872–1917): The Forgotten Rector of the Jagiellonian University The article presents the figure of the great Polish physicist Professor Marian Smoluchowski who lived at the turn of the 19th and 20th centuries. It presents his most important achievements as a scientist, a physicist of the Nobel Prize dimension, and in other fields:: didactic, organizational, as well as personal (related to his greatest passion – mountaineering). The study specifies the three most important periods of Smoluchowski’s life and scientific activity: the Vienna, Lviv and Krakow periods, and describes his cooperation with other scholars, mostly of the world-wide renown, such as Albert Einstein. The Viennese period included childhood, education at the Collegium Theresianum, physical studies at the University of Vienna, PhD and habilitation. In Lviv, Smoluchowski spent fourteen years employed at Jan Kazimierz University. There, he developed, among others, the theory of Brownian motion. He spent the last four years of his life in Krakow as a professor at the Jagiellonian University, where he mainly dealt with experimental physics. In 1917 he was elected rector of the University, but in the same year, at the age of 45, he died prematurely of dysentery before taking over this office. He managed to prepare the inaugural lecture “On the uniformity of natural laws.”

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2008

Particles in Turbulent Flows

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Statistical Microhydrodynamics

Cited by 5 publications

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A method for the computation of turbulent polymeric liquids including hydrodynamic interactions and chain entanglements

A method for the computation of turbulent polymeric liquids including hydrodynamic interactions and chain entanglements

Profesor Marian Smoluchowski (1872–1917) – zapomniany rektor Uniwersytetu Jagiellońskiego

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