Revisiting the linear stability analysis and absolute–convective transition of two fluid core annular flow

2019 ◽  
Vol 865 ◽  
pp. 743-761 ◽  
Author(s):  
D. Salin ◽  
L. Talon
Keyword(s):  
Linear Stability ◽  
Explicit Solution ◽  
Cylindrical Tube ◽  
Flow Equation ◽  
Immiscible Fluids ◽  
Creeping Flow ◽  
Complex Eigenvalue ◽  
Miscible Fluids ◽  
Two Fluids ◽  
Fluid Core

Numerous experimental, numerical and theoretical studies have shown that core annular flows can be unstable. This instability can be convective or absolute in different situations: miscible fluids with matched density but different viscosities, creeping flow of two immiscible fluids or buoyant flow along a fibre. The analysis of the linear stability of the flow equation of two fluids injected in a co-current and concentric manner into a cylindrical tube leads to a rather complex eigenvalue problem. Until now, all analytical solution to this problem has involved strong assumptions (e.g. lack of inertia) or approximations (e.g. developments at long or short wavelengths) even for axisymmetric disturbances. However, in this latter case, following C. Pekeris, who obtained, almost seventy years ago, an elegant explicit solution for the dispersion relationship of the flow of a single fluid, we derive an explicit solution for the more general case of two immiscible fluids of different viscosity, density and inertia separated by a straight interface. This formulation is well adapted to commercial software. First, we review the creeping flow limit (zero Reynolds number) of two immiscible fluids as it is used in microfluidics. Secondly, we consider the case of two fluids of different viscosities but of the same density in the absence of surface tension and also without diffusion (i.e. miscible fluids with infinite Schmidt number). In both cases, we study the transition from convective to absolute instability according to the different control parameters.

1. On the Pressure Cavities in Topaz, Beryl, and Diamond, and their bearing on Geological Theories

1862 ◽  
Vol 4 ◽  
pp. 548-549
Author(s):  
David Brewster
Keyword(s):  
Immiscible Fluids ◽  
Two Fluids ◽  
Primitive Forms

In this paper the author gave a brief account of the various phenomena of fluid and gaseous cavities which he had discovered in diamond, topaz, beryl, and other minerals. He described—1. Cavities with two immiscible fluids, the most expansible of which has received the name of Brewstolyne, and the most dense that of Cryptolyne, from the American and French mineralogists.2. Cavities containing only one of these fluids.3. Cavities containing the two fluids, and also crystals of various primitive forms, some of which melt by heat and recrystallise in cooling.4. Cavities containing gas and vapour.

Analysis of general creeping motion of a sphere inside a cylinder

2009 ◽  
Vol 642 ◽  
pp. 295-328 ◽  
Author(s):  
SUKALYAN BHATTACHARYA ◽  
COLUMBIA MISHRA ◽  
SONAL BHATTACHARYA
Keyword(s):  
Vector Field ◽  
Spherical Particle ◽  
Asymptotic Methods ◽  
Flow Equation ◽  
Creeping Flow ◽  
Separable Form ◽  
Angular Velocities ◽  
Moving Particle ◽  
Parabolic Flow ◽  
Quiescent Fluid

In this paper, we develop an efficient procedure to solve for the Stokesian fields around a spherical particle in viscous fluid bounded by a cylindrical confinement. We use our method to comprehensively simulate the general creeping flow involving the particle-conduit system. The calculations are based on the expansion of a vector field in terms of basis functions with separable form. The separable form can be applied to obtain general reflection relations for a vector field at simple surfaces. Such reflection relations enable us to solve the flow equation with specified conditions at different disconnected bodies like the sphere and the cylinder. The main focus of this article is to provide a complete description of the dynamics of a spherical particle in a cylindrical vessel. For this purpose, we consider the motion of a sphere in both quiescent fluid and pressure-driven parabolic flow. Firstly, we determine the force and torque on a translating-rotating particle in quiescent fluid in terms of general friction coefficients. Then we assume an impending parabolic flow, and calculate the force and torque on a fixed sphere as well as the linear and angular velocities of a freely moving particle. The results are presented for different radial positions of the particle and different ratios between the sphere and the cylinder radius. Because of the generality of the procedure, there is no restriction in relative dimensions, particle positions and directions of motion. For the limiting cases of geometric parameters, our results agree with the ones obtained by past researchers using different asymptotic methods.

scholarly journals Films over topography: from creeping flow to linear stability, theory and experiments, a review

2018 ◽  
Vol 229 (4) ◽  
pp. 1451-1451
Author(s):  
H. Irschik ◽  
M. Krommer ◽  
C. Marchioli ◽  
G. J. Weng ◽  
M. Ostoja-Starzewski
Keyword(s):  
Linear Stability ◽  
Stability Theory ◽  
Creeping Flow ◽  
Linear Stability Theory ◽  
Theory And Experiments

Fabrication of Plastic Micro-Channels for Microfluidics Solvent Extraction

2015 ◽  
Author(s):  
Tatjana Dankovic ◽  
Gareth Hatch ◽  
Alan Feinerman
Keyword(s):  
Solvent Extraction ◽  
Close Contact ◽  
Middle Layer ◽  
Extraction Process ◽  
Immiscible Fluids ◽  
Immiscible Fluid ◽  
Intimate Contact ◽  
Two Fluids ◽  
Massively Parallel Systems ◽  
Micro Channels

In this work plastic micro channel systems were investigated as a potential device for micro solvent extraction of rare earth elements. The proposed microfluidic structures are made by laser welding of three layers of inexpensive thermoplastic films which form separate paths (top and bottom channels) for each of the immiscible fluids. The middle layer is perforated in order to provide contact between two fluids and to enable the extraction process. Experiments were performed to show that two different immiscible fluids (water and 1-octanol) can flow through the fabricated device and exit at separate outlets without mixing even when those fluids get into close contact within the main channel. Experimental results for single devices show that immiscible fluids can be brought into intimate contact and then separated with compliant polymeric microfluidic devices. The transfer of a compound from one immiscible fluid to the other was verified by dye exchange between the immiscible fluids. The same fabrication method is a promising technique for fabrication of massively parallel systems with larger throughput.

The linear stability of a core–annular flow in an asymptotically corrugated tube

2002 ◽  
Vol 466 ◽  
pp. 113-147 ◽  
Author(s):  
HSIEN-HUNG WEI ◽  
DAVID S. RUMSCHITZKI
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Linear Stability ◽  
Annular Flow ◽  
Immiscible Fluids ◽  
Base Flow ◽  
Leading Order ◽  
Partial Differential ◽  
The Mean ◽  
Liquid Displacement

This paper examines the core–annular flow of two immiscible fluids in a straight circular tube with a small corrugation, in the limit where the ratio ε of the mean undisturbed annulus thickness to the mean core radius and the corrugation (characterized by the parameter σ) are both asymptotically small and where the surface tension is small. It is motivated by the problems of liquid–liquid displacement in irregular rock pores such as occur in secondary oil recovery and in the evolution of the liquid film lining the bronchii in the lungs whose diameters vary over different generations of branching. We investigate the asymptotic base flow in this limit and consider the linear stability of its leading order (in the corrugation parameter) solution. For the chosen scalings of the non-dimensional parameters the core's base flow slaves that of the annulus. The equation governing the leading-order interfacial position for a given wall corrugation function shows a competition between shear and capillarity. The former tends to align the interface shape with that of the wall and the latter tends to introduce a phase shift, which can be of either sign depending on whether the circumferential or the longitudinal component of capillarity dominates. The asymptotic linear stability of this leading-order base flow reduces to a single partial differential equation with non-constant coefficients deriving from the non-uniform base flow for the time evolution of an interfacial disturbance. Examination of a single mode k wall function allows the use of Floquet theory to analyse this equation. Direct numerical solutions of the above partial differential equation agree with the predictions of the Floquet analysis. The resulting spectrum is periodic in α- space, α being the disturbance wavenumber space. The presence of a small corrugation not only modifies (at order σ2) the primary eigenvalue of the system. In addition, short-wave order-one disturbances that would be stabilized flowing to capillarity in the absence of corrugation can, in the presence of corrugation and over time scales of order ln(1/σ), excite higher wall harmonics (α±nk) leading to the growth of unstable long waves. Similar results obtain for more complicated wall shape functions. The main result is that a small corrugation makes a core–annular flow unstable to far more disturbances than would destabilize the same uncorrugated flow system. A companion paper examines that competition between this added destabilization due to pore corrugation with the wave steepening and stabilization in the weakly nonlinear regime.

Viscous flow in a cylindrical tube containing a line of spherical particles

1969 ◽  
Vol 38 (1) ◽  
pp. 75-96 ◽  
Author(s):  
Henry Wang ◽  
Richard Skalak
Keyword(s):  
Pressure Drop ◽  
Cylindrical Tube ◽  
Tube Diameter ◽  
Creeping Flow ◽  
Spherical Particles ◽  
Sphere Diameter ◽  
Wide Range ◽  
Mean Pressure ◽  
Order Of Magnitude ◽  
Flow Through

The viscous, creeping flow through a cylindrical tube of a liquid, which contains rigid, spherical particles, is investigated analytically. The spheres are located on the axis of the cylinder and are equally spaced. Solutions are derived for particles in motion and fixed, with and without fluid discharge. Numerical results are presented for the drag on each sphere and the mean pressure drop for a wide range of sizes and spacings of the spheres. The study is motivated by possible application to blood flow in capillaries, where red blood cells represent particles of the same order of magnitude as the diameter of the capillary itself. The results may also be of interest in other applications, such as sedimentation and fluidized beds. It is shown that there is little interaction between particles if the spacing is more than one tube diameter, and that the additional pressure drop over that for Poiseuille flow is less than 50% if the sphere diameter is less than 0·8 of the tube diameter.

Electrohydrodynamic linear stability of two immiscible fluids in channel flow

2006 ◽  
Vol 51 (25) ◽  
pp. 5316-5323 ◽  
Author(s):  
O. Ozen ◽  
N. Aubry ◽  
D.T. Papageorgiou ◽  
P.G. Petropoulos
Keyword(s):  
Linear Stability ◽  
Channel Flow ◽  
Immiscible Fluids

Lattice Boltzmann Simulation of Surface Tension Dominated Vortices Behaviour in Two-Phase Mixing Layer

2006 ◽  
Author(s):  
Y. Y. Yan ◽  
Y. Q. Zu
Keyword(s):  
Surface Tension ◽  
Multiphase Flow ◽  
Lattice Boltzmann ◽  
Mixing Layer ◽  
Vertical Direction ◽  
Immiscible Fluids ◽  
Interfacial Interactions ◽  
Two Phase ◽  
Phase Mixing ◽  
Two Fluids

Surface tension dominating mixings and interfacial interactions are major phenomena of multiphase flow in microchannels and a variety of micro mixers. Such phenomena are concerned with interfacial interactions not only at fluid-solid interface but also at different fluids/phases interfaces. In this paper, vortices behaviours in a mixing layer of two immiscible fluids are studied numerically. The lattice Boltzmann method (LBM) is employed to simulat surface tension dominated mixing process. As a mesoscopic numerical method, the LBM has many advantages, which include the ability of incorporating microscopic interactions, the simplicity of programming and the nature of parallel algorithm and is therefore ideal for simulating multiphase flow. In this article, the index function methodology of the LBM is employed to simulate surface tension dominated vertices behaviour in a two-dimensional immiscible two-phase mixing layer. The initial interface between two-fluids is evenly distributed around the midpoint in vertical direction. Different velocity perturbations which consist of a basic wave and a series of sub-harmonic waves are forced at the entrance of a rectangular mixing layer of the flow field. By changing the strength of surface tension and the combinations of perturbation waves, the effects of the surface tension and the velocity perturbation on vortices merging are investigated. The vortices contours and frequency spectrums are used to analyse the mechanism of vortices merging. Some interesting phenomena, which do not take place in a single-phase mixing layer, are observed and the corresponding mechanism is discussed in details.

Quasi-Static Capillary Impregnation of a Porous Fiber Bed

1999 ◽  
Author(s):  
J. He ◽  
M. C. Altan
Keyword(s):  
Fiber Volume Fraction ◽  
Volume Fraction ◽  
Capillary Forces ◽  
Bond Number ◽  
Contact Angles ◽  
Flow Equation ◽  
Creeping Flow ◽  
Experimental Result ◽  
Fiber Volume ◽  
Front Motion

Abstract The impregnation of a fiber bed by capillary forces in a gravity field is analyzed. Fiber bed is modeled as infinitely long, parallel cylinders arranged in a hexagonal pattern. Quasi-static creeping flow equation is used to obtain the fluid front location and shape during impregnation of the fiber bed. The fluid front motion during impregnation are presented for different Bond numbers, contact angles and fiber volume fractions. It is found that impregnation velocity is significantly affected by contact angle and fiber volume fraction at the initial stages of impregnation. The influence of the Bond number becomes more significant when the fluid front approaches its final position where gravity balances capillary forces. The permeability of the fiber bed is also obtained from the time-dependent motion of the fluid front. The permeability predictions agree with the published experimental result and with those obtained by using lubrication theory.

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