Potential Flows of Viscous and Viscoelastic Fluids

Joseph, Daniel D.; Funada, Toshio; Wang, Jing

doi:10.1017/cbo9780511550928

Cited by 92 publications

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“…The stability analysis gives the critical h, the wave length, and the maximum growth rate of the most unstable disturbance. Here, we introduce a method of stability analysis for the free film problem based on the dissipation method of viscous potential flow (8). Stability studies based on the Navier-Stokes equations for long waves were considered by Ruckenstein and Jain (6), Gumerman and Homsy (9), and in the nonlinear case by Williams and Davis (10) and Erneux and Davis (11).…”

Section: Thin Film | Irrotational Flow | Dissipation Methodsmentioning

confidence: 99%

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Instability of stationary liquid sheets

Ardekani

Joseph

2009

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

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The rupture of a 3D stationary free liquid film under the competing effects of surface tension and van der Waals forces is studied as a linearized stability problem in a purely irrotational analysis utilizing the dissipation method. The results of the foregoing analysis are compared with a 2D long-wave approximation that has given rise to an extensive literature on the rupture problem. The irrotational and long-wave approximations are here compared with the exact 2D solution. The exact solution and the two approximate theories give the same results for infinitely long waves. The problem considered depends on two dimensionless parameters, the Hamaker number and the Ohnesorge number. The Hamaker number is a dimensionless number defined as a measure of the ratio of van der Waals forces to surface tension. The exact solution and the two approximate solutions differ by <1% when the Hamaker number is small for all values of the Ohnesorge number. When the Ohhnesorge number is close to one, as in the case of water films separated by distance 100 Å, the long-wave approximation overestimates and the potential flow approximation underestimates the exact solution by similar small amounts. The high accuracy of the dissipation method shows that the effects of vorticity are small for small to moderate Hamaker numbers. thin film | irrotational flow | dissipation methodA stable free liquid layer in balance between stabilizing surface tension and destabilizing van der Waals molecular forces can become unstable and be driven to rupture. Molecular forces are important in thin films in the range 100-1,000 Å. Ultrathin "black films" may arise from the stabilizing effects of electric double-layer potentials discussed by Overbeek (1).The rupture of a film often occurs in many contexts, the coalescence of droplets and bubbles, in the creation of dry patches, in the problem of aerodynamic dissemination (2), and in the formation of holes in moving sheets from atomizers studied by Dombrowski and Fraser (3). Stability analysis based on the free energy of stationary films for the critical thickness at which spontaneous local thinning first occurs was given by Vrij (4) and Scheludko (5). Ruckenstein and Jain (6) introduced the fundamental analytic simplification by introducing the disjoining pressure as an "extra pressure" analogous to other prescribed body forces in potential form and constructed a dynamic analysis based on the linear theory of stability. The term "disjoining pressure" was introduced by Deryagin to designate the excess pressure in a thin layer compared with a thick one. If film thickness h is small enough, the stabilizing effects of surface tension are insufficient and the film will thin under the influence of the large disjoining pressure. For a planar film, molecular interactions are accounted for in a strict thermodynamic theory through the concept of a disjoining pressure by Ivanov and Tosev (7). The stability analysis gives the critical h, the wave length, and the maximum growth rate of the most unstable disturbance. He...

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Section: Thin Film | Irrotational Flow | Dissipation Methodsmentioning

confidence: 99%

“…In gas-liquid flows, the viscous normal stress does not vanish and it can be evaluated on the potential flow as explained by Joseph et al (8). The continuity of the shear stress is not required in viscous potential flow (VPF).…”

Section: Dissipation Methods (Viscous Correction Of Viscous Potential mentioning

confidence: 99%

Instability of stationary liquid sheets

Ardekani

Joseph

2009

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

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“…Achievement of this goal would lead to greater conformity with two-dimensional simulations without the compromise of using large aspect ratios. It may be possible to extend the results of this paper to a lubricated device without the need for small aspect ratios using the theory of Joesph [8,9].…”

Section: Introductionmentioning

confidence: 96%

Viscoelastic Hele-Shaw flow in a cross-slot geometry

Chaffin

Rees

2018

European Journal of Mechanics - B/Fluids

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a b s t r a c tIn this paper a cross-slot geometry for which the height of the channel is small compared to the other channel dimensions is considered. The normal components of the viscoelastic stresses are found analytically for a second order fluid up to numerical inversion. The validity of the theoretical analysis was corroborated by comparison with numerical simulations based on a stabilized Galerkin least squares finite element method using an Oldroyd B fluid. Close agreement was found between numerical predictions and analytical results for Weissenberg numbers up to 0.2. An explicit expression is formulated for viscoelastic parameters in terms of the variation and strength of the first normal stress difference around the stagnation point. The analysis is generalized for the case where the inlet channel width is different from the outlet channel width. For such configurations it was found that uniformity of the elongation rate was reduced.

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“…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].…”

Section: Introductionmentioning

confidence: 99%

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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Potential Flows of Viscous and Viscoelastic Fluids

Cited by 92 publications

References 0 publications

Instability of stationary liquid sheets

Instability of stationary liquid sheets

Viscoelastic Hele-Shaw flow in a cross-slot geometry

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

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