Starting Poiseuille Flow in a Circular Tube With Two Immiscible Fluids

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Chiu-On Ng ◽  
C. Y. Wang
Keyword(s):  
Circular Tube ◽  
Slip Length ◽  
Finite Thickness ◽  
Applied Pressure ◽  
Immiscible Fluids ◽  
Circular Duct ◽  
Two Fluids ◽  
Plasma Skimming ◽  
Start Up ◽  
Starting Flow

Starting flow due to a suddenly applied pressure gradient in a circular tube containing two immiscible fluids is solved using eigenfunction expansions. The orthogonality of the eigenfunctions is developed for the first time for circular composite regions. The problem, which is pertinent to flow lubricated by a less viscous near-wall fluid, depends on the ratio of the radius of the core region to that of the tube, and the ratios of dynamic and kinematic viscosities of the two fluids. In general, a higher lubricating effect will lead to a longer time for the starting transient to die out. The time development of velocity profile and slip length are examined for the starting flows of whole blood enveloped by plasma and water enveloped by air in a circular duct. Owing to a sharp contrast in viscosity, the starting transient duration for water/air flow can be ten times longer than that of blood/plasma flow. Also, the slip length exhibits a singularity in the course of the start-up. For blood with a thin plasma skimming layer, the singularity occurs very early, and hence for the most part of the start-up, the slip length is nearly a constant. For water lubricated by air of finite thickness, the singularity may occur at a time that is comparable to the transient duration of the start-up, and hence, an unsteady slip length has to be considered in this case.

Core–annular flow in a periodically constricted circular tube. Part 2. Nonlinear dynamics

2002 ◽  
Vol 470 ◽  
pp. 181-222 ◽  
Author(s):  
CHARALAMPOS KOURIS ◽  
JOHN TSAMOPOULOS
Keyword(s):  
Nonlinear Dynamics ◽  
Flow Rate ◽  
Annular Flow ◽  
Circular Tube ◽  
Applied Pressure ◽  
Immiscible Fluids ◽  
Variable Cross ◽  
Computational Domain ◽  
Experimental Conditions ◽  
Time Periodic

Nonlinear dynamics of the concentric, two-phase flow of two immiscible fluids in a circular tube of variable cross-section is studied for parameter values where the steady core–annular flow (CAF) is linearly unstable. The simulations are based on a pseudo-spectral numerical method. They are carried out assuming axial symmetry, that the total flow rate remains constant and that all dependent variables are periodic in the axial direction, which includes the minimum necessary number of repeated units so that the obtained solution is independent of this number. The time integration originates with the numerically computed steady CAF or the steady CAF seeded with either the most unstable mode or random small disturbances. Only a limited number of the most interesting cases are presented. For the most part, the values of the majority of the dimensionless parameters are such that oil flows in the centre of the tube driven by an applied pressure gradient against gravity, whereas water is flowing in the annulus. It is shown that, whereas the steady (unstable) solution may indicate that the heavier water flows countercurrently with respect to the oil, the time periodic (observable) solution may indicate the same, albeit at a much smaller core flow rate or that concurrent flow occurs. This is due to the water being trapped between the large-amplitude interfacial waves that are generated and being convected by the oil. It is also shown that increasing the inverse Weber number increases the wave amplitude to the point that the flow of the core fluid may become discontinuous with a mechanism that depends on the viscosity ratio between the two fluids. Increasing the amplitude of the sinusoidal variation of the tube leads to a combination of travelling and standing waves, which interact to produce a time periodic solution with a long period associated with the time it takes the travelling wave to travel through the computational domain and a second much shorter period that is related to their interaction time. Qualitative agreement has been obtained upon comparing our numerical simulations with limited experimental reports, even though the experimental conditions were not identical to those in our model.

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.

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.

Two-Dimensional Analysis of an Elastic Layer Coupled to a Viscous Fluid

2004 ◽  
Vol 71 (2) ◽  
pp. 162-167 ◽  
Author(s):  
Jongwon Seok ◽  
Andrew T. Kim ◽  
Timothy S. Cale ◽  
John A. Tichy
Keyword(s):  
Viscous Fluid ◽  
Critical Thickness ◽  
Chemical Mechanical Planarization ◽  
Finite Thickness ◽  
Applied Pressure ◽  
Direct Application ◽  
Two Dimensional ◽  
Soft Layer ◽  
Additive Property ◽  
Linear Elasticity Theory

A two-dimensional elastohydrodynamic analysis is performed on a system consisting of a viscous fluid flowing between a sliding soft layer of finite thickness and a tilted flat plate. The behavior of a soft layer subject to a distributed contact pressure is described in detail. Green’s functions are obtained for each Fourier coefficient of the distributed applied pressure, utilizing the additive property of linear elasticity theory. The resulting equations are numerically evaluated for some typical cases. As a function of the contact dimension, calculations are performed for the critical thickness of the layer beyond which the deformed shape essentially resembles that of the layer having an infinite thickness, in the case of a uniformly applied pressure. We also investigate the effect of layer thickness on the hydrodynamics, which illustrates that conditions in which the infinite half-space assumptions can be justified are highly limited. The findings of this paper have direct application to the modeling of chemical mechanical planarization (CMP).

scholarly journals Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state

2014 ◽  
Vol 740 ◽  
pp. 168-195 ◽  
Author(s):  
Clarissa Schönecker ◽  
Tobias Baier ◽  
Steffen Hardt
Keyword(s):  
Flow Field ◽  
Slip Length ◽  
Two Fluids ◽  
Cassie State ◽  
Effective Slip Length ◽  
Primary Fluid ◽  
Effective Slip ◽  
Local Slip ◽  
Analytical Expressions ◽  
Secondary Fluid

AbstractAnalytical expressions for the flow field as well as for the effective slip length of a shear flow over a surface with periodic rectangular grooves are derived. The primary fluid is in the Cassie state with the grooves being filled with a secondary immiscible fluid. The coupling of the two fluids is reflected in a locally varying slip distribution along the fluid–fluid interface, which models the effect of the secondary fluid on the outer flow. The obtained closed-form analytical expressions for the flow field and effective slip length of the primary fluid explicitly contain the influence of the viscosities of the two fluids as well as the magnitude of the local slip, which is a function of the surface geometry. They agree well with results from numerical computations of the full geometry. The analytical expressions allow an investigation of the influence of the viscous stresses inside the secondary fluid for arbitrary geometries of the rectangular grooves. For classic superhydrophobic surfaces, the deviations in the effective slip length compared to the case of inviscid gas flow are pointed out. Another important finding with respect to an accurate modelling of flow over microstructured surfaces is that not only the effective slip length, but also the local slip length of a grooved surface, is anisotropic.

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.

Thermal Effects of Two Immiscible Fluids in a Circular Tube with Nano Particles

2017 ◽  
Vol 6 (1) ◽  
pp. 105-119 ◽  
Author(s):  
K. Maruthi Prasad ◽  
N. Subadra ◽  
M. A. S. Srinivas
Keyword(s):  
Thermal Effects ◽  
Circular Tube ◽  
Immiscible Fluids ◽  
Nano Particles

A Useful Solution for Estimating Contact Pressure Between a Plate and Foundation

1999 ◽  
Vol 122 (4) ◽  
pp. 781-789
Author(s):  
L. B. Shulkin ◽  
D. A. Mendelsohn ◽  
G. L. Kinzel ◽  
T. Altan
Keyword(s):  
Finite Element ◽  
Pressure Distribution ◽  
Contact Pressure ◽  
Finite Thickness ◽  
Applied Pressure ◽  
Three Dimensional ◽  
Sensitivity Study ◽  
Winkler Foundation ◽  
Contact Pressure Distribution ◽  
Design Variables

Many manufacturing situations involve a finite thickness plate or layer of material which is pressed against a much thicker foundation of the same or different material. One key example is a blank holder (plate) pressed against a die (foundation) in a sheet metal forming operation. In designing such a plate/foundation system the design objective often involves the contact stress distribution between the plate and foundation and the design variables are typically the thickness and modulus of the plate, the stiffness of the foundation and the applied pressure distribution on the noncontacting side of the plate. In general the problem relating the variables to the contact pressure distribution is three-dimensional and requires a complex finite element or boundary element solution. However, if the applied pressure distribution consists of sufficiently localized patches, which is often the case in applications, then an approximate 3D solution can be constructed by superposition. Specifically, the paper provides a convenient calculation procedure for the contact pressure due to a single circular patch of applied pressure on an infinite, isotropic, elastic layer which rests on a Winkler foundation. The procedure is validated by using known analytical solutions and the finite element method (FEM). Next a sensitivity study is presented for ascertaining the validity of the solution’s use in constructing solutions to practical problems involving multiple patches of loading. This is accomplished through a parametric study of the effects of loading radius, layer thickness, layer elastic properties, foundation stiffness and the form of the applied pressure distribution on the magnitude and extent of the contact pressure distribution. Finally, a procedure for determining an appropriate Winkler stiffness parameter for a foundation is presented. [S1087-1357(00)00603-1]

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