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