Stability of the shear flow at an interface between two homogeneous fluids

by Torkild Johan Carstens

Publisher: University of California in Berkeley, Calif

Written in English
Published: Pages: 124 Downloads: 257
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  • Fluid dynamics.

Edition Notes

Statementby Torkild Johan Carstens.
The Physical Object
Paginationxv, 124 ℗ .
Number of Pages124
ID Numbers
Open LibraryOL14209008M

The flow is assumed to be inviscid and irrotational. Surface tension between the fluid layers is included, but gravity is neglected. The results show two unstable modes: one mode associated with the interface between the elastic layer and the fluid (mode 1), and the other concentrated on the interface between the two fluids (mode 2). Figure The fluid undergoes planar shear flow between two atomically flat walls. For all simulations in this study, the fluid phase consists of N f = monomers. The interaction between any two fluid monomers is modelled via the truncated Lennard-Jones (LJ) potential V . Abstract. Two problems in pipe flow are discussed in which the stability of fluid–fluid interfaces plays an important role. A stability analysis for a simplified 2-D geometry is gas–liquid pipe flow different flow regimes occur. between two uniform superposed and streaming fluids through porous medium has been investigated by Sharma and Spanos (). Khan et al. () have studied the Kelvin-Helmholtz instability arising at the interface separating two superposed, viscous, electrically conducting fluids through a porous medium in the presence of a uniform two-dimensional.

In asymptotic analysis of the hydrodynamic stability of shear flows, the viscous effects enter through the modified Tietjens Function, which is used in the graphical determination of the eigenvalues. For neutral normal modes the argument of this function is real, and values of . Instability and transition to turbulence is studied in a shear layer between two streams of different salinities and velocities. The viscous layer between the two streams is 15–18 times thicker than the diffusion layer. When the initial layer Richardson number is low, the instability organizes the shear-layer vorticity into discrete lumps as in the homogeneous case. In this work, we examine the shear-banding flow in polymer-like micellar solutions with the generalized Bautista-Manero-Puig (BMP) model. The couplings between flow, structural parameters, and diffusion naturally arise in this model, derived from the extended irreversible thermodynamics (EIT) formalism. Full tensorial expressions derived from the constitutive equations of the model, in. Shear banding occurs in the flow of complex fluids: various types of shear thinning and shear thickening micelles solutions and liquid crystals. In order to cope with the strongly inhomogeneous interface between the bands, constitutive models used in .

Ion-neutral collisions may play a relevant role for the growth rate and evolution of the KHI in solar partially ionized plasmas such as in, e.g., solar prominences. Here, we investigate the linear phase of the KHI at an interface between two partially ionized magnetized plasmas in the presence of a shear flow. The region between these two points is named the boundary layer. For all Newtonian fluids in laminar flow, the shear stress is proportional to the strain rate in the fluid, where the viscosity is the constant of proportionality. For non-Newtonian fluids, the viscosity is not constant. The shear stress is imparted onto the boundary as a result. Using the energy-conserved quantity method developed by Arnol'd (Dokl. Mat. Nauk , (); Am. Math. Soc. Trans. 19, ()) a study was made of the nonlinear stability of two inviscid fluid flows in three dimensions: (1) flow of a homogeneous fluid and (2) flow of a fluid whose energy density depends on the mass density alone (a so-called barotropic fluid).   Thus, the chapter on gas-liquid two-phase flow has been greatly extended to cover flow in the bubble regime as well as to provide an introduction to the homogeneous model and separated flow model for the other flow regimes.

Stability of the shear flow at an interface between two homogeneous fluids by Torkild Johan Carstens Download PDF EPUB FB2

The interface allows surface charges, and there exists an electrical tangential shear stress at the interface owing to the finite conductivities of the two fluids.

The long-wave linear stability analysis is performed within the generic Orr–Sommerfeld framework for both perfect and leaky by: The mechanics of two-fluid shear flows are significant in many engineering and environmental applications.

For example, the instability of two-fluid flows affects the aerodynamic lift of airfoils in the presence of deicing agents, the primary breakdown in spray combustion, the formation of sea sprays, and the heat transfer rates of annular film flows in nuclear [ ]. Shear flows in fluids tend to be unstable at high Reynolds numbers, when fluid viscosity is not strong enough to dampen out perturbations to the flow.

For example, when two layers of fluid shear against each other with relative velocity, the Kelvin–Helmholtz instability may occur. Shear instability of two immiscible fluids flow in the cell is treated in both experimentally and with the help of Kelvin–Helmholtz–Darcy theory.

The authors of that paper observe that the interface is destabilized above a critical value of the flow and that waves grow and propagate along the by: 5. The simplest problem involving instability of a shear flow is the case of a bounded homogeneous flow. This type of flow was first analyzed by Rayleigh () and is sometimes called the Rayleigh instability problem.

We consider a two-dimensional homogeneous flow with vertical boundaries at heights z 1 and z 2 such that w′ = 0 at these heights.

We then carry out a linear stability analysis, and show that there are three competing mechanisms for the destabilization: a convective instability, an absolute instability driven by surface tension and an absolute instability driven by confinement.

Hooper, A. & Boyd, W. Shear-flow instability at the interface between two. Second Newtonian flow region. Up to now, two regions of shear flow have been discussed: Newtonian flow at low shear rates and non-Newtonian flow at high shear rates.

In the first region, the viscosity is independent of the shear rate, while in the second region the viscosity decreases with increasing shear rate.

Homogeneous shear flows with an imposed mean velocity U=Syx̂ are studied in a period box of size L x ×L y ×L z, in the statistically stationary turbulent state.

In contrast with unbounded shear flows, the finite size of the system constrains the large‐scale dynamics. The Reynolds number, defined by Re≡SL 2 y /ν varies in the range ⩽Re⩽ The total kinetic energy and. In this work, we study the nonlinear travelling waves in density stratified fluids with piecewise-linear shear currents.

Beginning with the formulation of the water-wave problem due to Ablowitz et al. Fluid Mech., vol.pp. –), we extend the work of Ashton & Fokas (J. Fluid Mech., vol.pp. –) and Haut & Ablowitz (J.

Fluid Mech., vol.pp. A wave interaction approach to studying non-modal homogeneous and stratified shear instabilities - Volume - Anirban Guha, Gregory A. Lawrence. The global linear stability of incompressible, two-dimensional shear flows is investigated under the assumptions that far-field pressure feedback between distant points in the flow field is negligible and that the basic flow is only weakly non-parallel, i.e.

that its streamwise development is slow on the scale of a typical instability wavelength. For that purpose we study the linear stability response to very long waves of a three-layer phase Poiseuille flow with an inner thin layer which represents the interphase. Although this fact is an approximation, it nevertheless takes into account the.

Keywords: Electrohydrodynamic stability, Shear flow, Surface tension, Electric field AMS classification: 76 I. Introduction We consider the parallel flow of two fluids separated by a plane interface and stressed by perpendicular electric fields. On each side of the interface there is an unbounded Coquette flow.

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure.

such as the interface between two homogeneous fluids, The viscosity of a fluid is a measure of its resistance to deformation at a given rate. Using a perturbation method up to the second order, the equation for long waves at the interface between two viscous fluids is derived for plane Couette–Poiseuille flow.

Drag Reduction in a Homogeneous Flow. Flow Between Two Coaxial Cylinders. Fig. A–C illustrates the flow conditions of several test fluids in the gap. The time for the flow to become the influence of the viscoelastic behavior in the shear-induced structure on the stability of the forming process of Taylor cells is relatively.

The linear stability of co-extrusion flow of two upper convected Maxwell fluids through a pipe at low Reynolds numbers is studied for arbitrary wavelength disturbances. The fluids interface can. Shear instability of two-fluid parallel flow in a Hele-Shaw cell Article (PDF Available) in Physics of Fluids 9(11) November with Reads How we measure 'reads'.

Renardy, “ Instability at the interface between two shearing fluids in a channel,” Phys. Flu (). Google Scholar Scitation; A. Hooper, “ Long-wave instability at the interface between two viscous fluids: Thin layer effects,” Phys.

Flu (). Google Scholar Scitation. We consider a stratified two-layer flow of two immiscible incompressible fluids in a horizontal channel. The flow is assumed to be isothermal and is driven by an imposed pressure gradient. The flow configuration is sketched in Figure 1.

The interface between the fluids, labeled as j=1,2 (1 – lower phase, 2 – upper phase), is assumed to be. The present investigation is concerned with the effects of viscosity on the stability of a bounded stratified shear flow with Prandtl number Pr ≫1.

Theoretical results obtained from the solution of the Orr–Sommerfeld equation extended to stratified fluids are compared with experiments performed in a tilting tube filled with water and brine.

The investigation concerns the stability of an interface between two inviscid fluids of different densities which flow parallel to each other in an oscillatory manner. The development of three-dimensional patterns in the wake of two-dimensional objects is examined from the point of view of hydrodynamic stability.

It is first shown that for parallel shear flows, which are homogeneous along their span, the time-asymptotic state of the instability is always two-dimensional.

The motion of deformable drops suspended in a linear shear flow at nonzero Reynolds numbers is studied by numerical simulations in two dimensions. It is found that a deformable dr. The current thinking is that this behaviour, in which regions of two different shear rates are seen simultaneously in flow of a single fluid, arises from a non-monotonicity in the underlying constitutive relation between the shear stress and shear rate for homogeneous flow (Spenley et al.

; Makhloufi et al. ; Mair & Callaghan). Two problems in pipe flow are discussed in which the stability of fluid-fluid interfaces plays an important role. A stability analysis for a simplified 2-D geometry is presented. In gas-liquid pipe flow different flow regimes occur. This is known to be related to the stability properties of the flow.

We shall present a linear stability analysis of plane two-phase Poiseuille flow. Linear stability of the stratified gas-liquid and liquid-liquid plane-parallel flows in the inclined channels is studied with respect to all wavenumber perturbations.

The main objective is to predi. This is a study of turbulence which results from Kelvin—Helmholtz instability at the interface between two miscible fluids in a two-dimensional shear flow in the laboratory.

We simulate the spatial and temporal evolution of inhomogeneous flow fields in viscometric devices such as cylindrical Couette cells. The computations focus on a class of two species elastic network models which are prototypes for a model which can capture, in a self-consistent manner, the creation and destruction of elastically active network segments as well as diffusive coupling between the.

The water-mud flow interface is modeled by a two layer flow with continuous interface. Vertical profiles are based on the erf function near the interface, in an empirical way, to qualitatively model a simple shear. To model vertical profiles, we consider the group of functions F(, Z) defined by: (1).

The linear stability characteristics of pressure-driven two-layer channel flow are considered, wherein a Newtonian fluid layer overlies a layer of .for a shear flow for which only stationary waves are possible in the homogeneous case.

Stratification can also alter qualitatively the character of instability of shear flows, as clearly put in evidence by Holmboe6 for a piecewise linear shear current as the three-layer configuration is modified to the two .Two-state shear diagrams for complex fluids in shear flow while in the latter case a mechanical condition on interface stability is required.

Complete phase diagrams have been calculated for a model system of rigid rod p. d. olmsted: complex fluids in shear flow