Potential flow of viscous fluids: Historical notes

Joseph, Daniel D.

doi:10.1016/j.ijmultiphaseflow.2005.09.004

Cited by 87 publications

(56 citation statements)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 At leading order the standard spherical radius damping term is recovered. 4,2 The higher order terms involving the shape modes are new. As expected, each term contains a contribution involving either the radial velocity, the bubble translational velocity, or a shape mode velocity.…”

Section: A Dissipation Functionmentioning

confidence: 99%

The stability of a bubble in a weakly viscous liquid subject to an acoustic traveling wave

Shaw¹

2009

Physics of Fluids

View full text Add to dashboard Cite

The volume oscillations, translation, and axisymmetric deformation of a bubble in an acoustic traveling wave are considered. Assuming the bubble translation and deformation is small, but placing no restriction on the volume oscillations, a combination of the Rayleigh dissipation function and perturbation analysis is employed to account for the effects of viscosity in the absence of vorticity to third order in the small interaction terms. Contributions from the acoustic field are also determined to this order, while the free oscillation terms are drawn from a previously derived model correct to the same order of analysis. To permit the study of large amplitude acoustic forcing, appropriate compressibility terms are phenomenologically added to the volume pulsation equation. Stability maps of driving pressure versus driving frequency and driving pressure versus the equilibrium bubble radius are presented. A predominant number of results are for micron-sized bubbles driven in the ultrasonic regime, but the behavior of larger bubbles driven at frequencies in the kilohertz range is also considered. In all cases, bubbles driven above the natural frequency of their respective volume oscillations are markedly more stable with regard to the acoustic driving amplitude, consistent with previous observations. Below these respective natural frequency values, the stability/instability fronts display a much more complex structure. Accounting for shape mode viscous damping causes a general increase in bubble stability, together with a reduction in the stability/instability front complexity. In the case of micron-sized bubbles this stabilization is markedly more significant for bubbles driven above the natural frequency of the respective volume mode oscillations; for larger bubbles driven in the kilohertz range, the influence of shape mode damping is less significant.

show abstract

Section: A Dissipation Functionmentioning

confidence: 99%

The stability of a bubble in a weakly viscous liquid subject to an acoustic traveling wave

Shaw¹

2009

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…Viscous potential flow theory has played an important role in the study of various stability problems [13,14]. In viscous potential flow, the viscous term in the Navier-Stokes equation is identically zero when the vorticity is zero, but the viscous stresses are not zero.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

et al. 2014

View full text Add to dashboard Cite

The nonlinear electrohydrodynamic Kelvin-Helmholtz instability of two superposed viscoelastic Walters B= dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg-Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of twodimensional disturbances. While in the nonlinear analysis, for both two-and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.Résumé : La méthode d'analyse du potentiel d'écoulement nous permet d'étudier l'instabilité électrodynamique non linéaire de type Kelvin-Helmholtz, de deux fluides diélectriques viscoélastiques de type Walter B= superposés, en présence d'un champ électrique tangentiel. Nous utilisons la méthode à échelles multiples pour obtenir la relation de dispersion du problème linéaire, alors que l'équation non linéaire de Ginzburg-Landau avec coefficients complexes pour le problème non linéaire. Nous obtenons et discutons les conditions de stabilité pour les cas linéaire et non linéaire, analytiquement et numériquement. Dans l'analyse de stabilité linéaire, nous trouvons que les vitesses de fluide et les viscosités cinématiques ont des effets déstabilisants, alors que le champ électrique, les viscoélasticités cinématiques et la tension superficielle sont stabilisants. Le système est plus stable contre les perturbations tridimensionnelles que contre les perturbations bidimensionnelles. Dans le cas non linéaire, pour des perturbations en deux et trois dimensions, nous trouvons que les vitesses de fluide, la tension superficielle et les viscosités cinématiques sont déstabilisants, alors que le champ électrique, les viscoélasticités cinématiques sont stabilisants. De plus, le système est plus instable dans son comportement sous perturbations en trois dimensions qu'en deux dimensions pour la plupart des paramètres physiques, sauf les viscosités cinématiques. [Traduit par la Rédaction]

show abstract

“…In section 6 we include the results of a few numerical experiments, which illustrate the plausibility of this assumption. For the extended discussion of the plausibility of the vorticity-free approximation for the oscillating viscous droplet problem we refer to [28,38]. In the next section, we shall see that for the vorticity-free approximation, the energy balance (16) yields the existence of a finite cessation time T f .…”

Section: Energy Balancementioning

confidence: 98%

“…First we perform a series of experiments for the Newtonian oscillating droplet. Although the numerical method was previously verified on a number of benchmark problems for Newtonian and viscoplastic fluids flows, the purpose of this experiment is to assess the accuracy of the numerical method and to study the convergence of flow statistics in this case to those given by the analysis in [31,33] and recovered in (25) and (28). Thus, a droplet of the ideal fluid (K = 0, τ s = 0) oscillates infinitely with constant amplitude.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Finite stopping times for freely oscillating drop of a yield stress fluid

Cheng

Olshanskii

2017

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

The paper addresses the question if there exists a finite stopping time for an unforced motion of a yield stress fluid with free surface. A variational inequality formulation is deduced for the problem of yield stress fluid dynamics with a free surface. The free surface is assumed to evolve with a normal velocity of the flow. We also consider capillary forces acting along the free surface. Based on the variational inequality formulation an energy equality is obtained, where kinetic and free energy rate of change is in a balance with the internal energy viscoplastic dissipation and the work of external forces. Further, the paper considers free small-amplitude oscillations of a droplet of Herschel-Bulkley fluid under the action of surface tension forces. Under certain assumptions it is shown that the finite stopping time T f of oscillations exists once the yield stress parameter is positive and the flow index α satisfies α ≥ 1. Results of several numerical experiments illustrate the analysis, reveal the dependence of T f on problem parameters and suggest an instantaneous transition of the whole drop from yielding state to the rigid one.

show abstract

Potential flow of viscous fluids: Historical notes

Cited by 87 publications

References 44 publications

The stability of a bubble in a weakly viscous liquid subject to an acoustic traveling wave

The stability of a bubble in a weakly viscous liquid subject to an acoustic traveling wave

Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

Finite stopping times for freely oscillating drop of a yield stress fluid

Contact Info

Product

Resources

About