Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow

Bellout, Hamid; Bloom, Frederick

doi:10.1007/978-3-319-00891-2

Cited by 16 publications

(13 citation statements)

References 82 publications

(201 reference statements)

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“…where the higher-order derivatives ∇ 2n ≡ (∇ 2 ) n , n ≥ 2 account for non-Newtonian effects [56] (SI Model Justification). Such higher-order stresses arise naturally from diagrammatic expansions [57].…”

Section: Resultsmentioning

confidence: 99%

Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids

Słomka

Dunkel

2017

Proc. Natl. Acad. Sci. U.S.A.

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Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain symmetry-breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present analytical and numerical evidence for the existence of an inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break mirror symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Our simulations further demonstrate how active scale selection controls mirror-symmetry breaking and the emergence of a 3D inverse cascade.

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Section: Resultsmentioning

confidence: 99%

Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids

Słomka

Dunkel

2017

Proc. Natl. Acad. Sci. U.S.A.

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“…where the higher-order derivatives ∇ 2n ≡ (∇ 2 ) n , n ≥ 2 account for non-Newtonian effects [35]. The one-dimensional version of Eqs.…”

Section: Theorymentioning

confidence: 99%

Geometry-dependent viscosity reduction in sheared active fluids

Słomka

Dunkel

2017

Phys. Rev. Fluids

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We investigate flow pattern formation and viscosity reduction mechanisms in active fluids by studying a generalized Navier-Stokes model that captures the experimentally observed bulk vortex dynamics in microbial suspensions. We present exact analytical solutions including stress-free vortex lattices and introduce a computational framework that allows the efficient treatment of previously intractable higher-order shear boundary conditions. Large-scale parameter scans identify the conditions for spontaneous flow symmetry breaking, geometry-dependent viscosity reduction and negative-viscosity states amenable to energy harvesting in confined suspensions. The theory uses only generic assumptions about the symmetries and long-wavelength structure of active stress tensors, suggesting that inviscid phases may be achievable in a broad class of non-equilibrium fluids by tuning confinement geometry and pattern scale selection.Self-driven vortical flows in microbial [1] and synthesized active liquids [2-4] often exhibit a dominant length scale [5][6][7][8], distinctly different from the scale-free spectra of conventional turbulence [9]. Experimentally observed vortices in dense bacterial suspensions typically have diameters Λ ∼ 50 − 100 µm [5,8,10] and decay within a few seconds in a bulk fluid [10]. However, when the suspension is enclosed by a small container of dimensions comparable to Λ, individual vortices become stabilized for several minutes [11,12] and can be coupled together to form magnetically ordered vortex lattices [13]. Another form of confinement-induced symmetry breaking was observed recently in a microfluidic realization of bacterial 'racetracks' [14]. For sufficiently narrow tracks of diameter Λ, bacteria spontaneously aligned their swimming directions to form persistent unidirectional currents. These examples illustrate the importance of confinement geometry for flow-pattern formation in non-equilibrium liquids. Conversely, biologically or chemically powered fluids may profoundly affect the dynamics of moving boundaries as active components can significantly alter the effective viscosity of the surrounding solvent fluid [15][16][17]. In particular, recent shear experiments suggest that Escherichia coli bacteria can create effectively inviscid flow if their concentration and activity are sufficiently large to support coherent collective swimming [18]. From a theory perspective, it is desirable to formulate a minimal hydrodynamic model that is analytically tractable and can account for all the aforementioned experimental observations without overfitting.Previous theoretical work [19][20][21][22][23][24] identified potential viscosity reduction mechanisms [15,18] in certain classes of active suspensions, but the complexity and specific nature of the underlying multi-field models have made analytical insight, time-resolved dynamical studies and comparison with experiment challenging. To better understand the general conditions under which active fluids can develop spontaneous symmetry-breaking and quasi-invis...

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“…It is a direct consequence of the principle of virtual work. We refer to [3,4,5,7,25,30,32] and the references therein for detailed physical background.…”

Section: Guowei Liu and Rui Xuementioning

confidence: 99%

“…For instance, molten plastics, polymer solutions and paints tend to be non-Newtonian fluids. One can refer to [3,4,5,7,25,30,32] and the references therein for detailed physical significance. Factually, equations (1)- (3) were firstly formulated by Ladyzhenskaya as a modification to the Navier-Stokes equations when the gradient |∇u| of the velocity is relatively large ( [25]).…”

Section: Guowei Liu and Rui Xuementioning

confidence: 99%

“…Due to the wide applications in the real world, there is a large literature on the mathematical theory of the non-Newtonian fluid (see [3,4,5,7,13,14,24,25,28,29,30,32,36,37,38,39,40,41], etc). For example, [32] proved the well-posedness of solutions to the Cauchy problem, [13,14] studied the decay rate of solutions to the Cauchy problem.…”

Section: Guowei Liu and Rui Xuementioning

confidence: 99%

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Pullback dynamic behavior for a non-autonomous incompressible non-Newtonian fluid

Liu¹,

Xue²

2018

Discrete &Amp; Continuous Dynamical Systems - B

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This paper studies the pullback asymptotic behavior of solutions for a non-autonomous incompressible non-Newtonian fluid on 2D bounded domains. We show existence of the pullback exponential attractor introduced by Langa, Miranville and Real [27], moreover, give existence of the global pullback attractor with finite fractal dimension and reveal the relationship between the global pullback attractor and the pullback exponential attractor. These results improve our previous associated results in papers [29, 40] for the non-Newtonian fluid. 2 i,j=1 |e ij (u)| 2 , and µ 0 , µ 1 , α, η are parameters associated to the fluid which generally depend on the temperature and pressure. In this paper we assume that µ 0 , µ 1 , η are positive constants and 0 < α < 1.

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Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow

Cited by 16 publications

References 82 publications

Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids

Spontaneous mirror-symmetry breaking induces inverse energy cascade in 3D active fluids

Geometry-dependent viscosity reduction in sheared active fluids

Pullback dynamic behavior for a non-autonomous incompressible non-Newtonian fluid

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