scholarly journals An Analysis of Two Fluid Layers Enclosed Between Two Non-Porous Surfaces

2022 ◽  
Vol 17 ◽  
pp. 29-33
Author(s):  
Asad Salem
Keyword(s):  
Thin Sheet ◽  
Phase Interface ◽  
Complete Analysis ◽  
Hydrodynamic Models ◽  
Two Phase ◽  
Linearized Stability ◽  
Fluid Layers ◽  
The Stability ◽  
Droplet Size Distributions ◽  
Two Fluid

The stability of a two-phase interface is a crucial occurrence that involves the design of many engineering applications. It correlates the spatial and droplet size-distributions of many fluid spraying applications and has a great effect on the estimations of the critical heat flux of systems that involves phase change or evaporation. However, the existing hydrodynamic models are only able to predict the stability of a plane fluid sheet, surrounded by an infinite pool of liquid. The case of a thin sheet of liquid surrounding a vapor sheet and enclosed between two walls has not been studied yet. The present paper solves this problem using a linearized stability analysis. Velocity potentials satisfying these conditions are introduced and a complete analysis is presented.

Nanofluidic transport and formation of nano-emulsions

2008 ◽  
Vol 2 (1) ◽  
Author(s):  
P.A. Chando ◽  
S.S. Ray ◽  
A.L. Yarin
Keyword(s):  
Stokes Equations ◽  
Theoretical Calculations ◽  
Ccd Camera ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Flow Rates ◽  
Fluid Layers ◽  
Pressure Driven Flow ◽  
Two Fluid

The focus of this research is to study fluidic transport through carbon nanotubes. The nanotubes studied were formed by electrospinning Polycaplrolactone (PCL) nanofibers and then using them as channel templates in colyacrylamide blocks which were carbonized. A pressure driven flow is initiated through the nanochannels and the rate of emulsion formation is recorded with a CCD camera. Theoretical calculations are conducted for nanochannels because in many experiments, the nanochannels studied have two-phase flows, which make direct application of Poiseuille law impossible. The model used for the calculations is a slit with two fluid layers in between. In particular, in many experiments, decane-air system is of interest. The calculations are carried out using the Navier-Stokes equations. The results of the model are used to evaluate experimental volumetric flow rates and find the distribution of air and decane in the nanochannels.

Thermal Stability of Two Fluid Layers Separated by a Solid Interlayer of Finite Thickness and Thermal Conductivity

1984 ◽  
Vol 106 (3) ◽  
pp. 605-612 ◽  
Author(s):  
I. Catton ◽  
J. H. Lienhard
Keyword(s):  
Thermal Conductivity ◽  
Fluid Layer ◽  
Heated Surface ◽  
Finite Thickness ◽  
Fluid Layers ◽  
The Stability ◽  
Stability Limits ◽  
Range Of Values ◽  
Two Fluid ◽  
Thermal Stability Of

Stability limits of two horizontal fluid layers separated by an interlayer of finite thermal conductivity are determined. The upper cooled surface and the lower heated surface are taken to be perfectly conducting. The stability limits are found to depend on the ratio of fluid layer thicknesses, the ratio of interlayer thickness to total fluid layer thickness, and the ratio of fluid thermal conductivity to interlayer thermal conductivity. Results are given for a range of values of each of the governing parameters.

A Nonlinear Stability Analysis for Difference Equations Using Semi-Implicit Mobility

1977 ◽  
Vol 17 (01) ◽  
pp. 79-91 ◽  
Author(s):  
D.W. Peaceman
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Finite Difference ◽  
Nonlinear Stability ◽  
Difference Equations ◽  
Nonlinear Stability Analysis ◽  
Time Step ◽  
Two Phase ◽  
Linearized Stability ◽  
The Stability

Abstract The usual linearized stability analysis of the finite-difference solution for two-phase flow in porous media is not delicate enough to distinguish porous media is not delicate enough to distinguish between the stability of equations using semi-implicit mobility and those using completely implicit mobility. A nonlinear stability analysis is developed and applied to finite-difference equations using an upstream mobility that is explicit, completely implicit, or semi-implicit. The nonlinear analysis yields a sufficient (though not necessary) condition for stability. The results for explicit and completely implicit mobilities agree with those obtained by the standard linearized analysis; in particular, use of completely implicit mobility particular, use of completely implicit mobility results in unconditional stability. For semi-implicit mobility, the analysis shows a mild restriction that generally will not be violated in practical reservoir simulations. Some numerical results that support the theoretical conclusions are presented. Introduction Early finite-difference, Multiphase reservoir simulators using explicit mobility were found to require exceedingly small time steps to solve certain types of problems, particularly coning and gas percolation. Both these problems are characterized percolation. Both these problems are characterized by regions of high flow velocity. Coats developed an ad hoc technique for dealing with gas percolation, but a more general and highly successful approach for dealing with high-velocity problems has been the use of implicit mobility. Blair and Weinaug developed a simulator using completely implicit mobility that greatly relaxed the time-step restriction. Their simulator involved iterative solution of nonlinear difference equations, which considerably increased the computational work per time step. Three more recent papers introduced the use of semi-implicit mobility, which proved to be greatly superior to the fully implicit method with respect to computational effort, ease of use, and maximum permissible time-step size. As a result, semi-implicit mobility has achieved wide use throughout the industry. However, this success has been pragmatic, with little or no theoretical work to justify its use. In this paper, we attempt to place the use of semi-implicit mobility on a sounder theoretical foundation by examining the stability of semi-implicit difference equations. The usual linearized stability analysis is not delicate enough to distinguish between the semi-implicit and completely implicit difference equation. A nonlinear stability analysis is developed that permits the detection of some differences between the stability of difference equations using implicit mobility and those using semi-implicit mobility. DIFFERENTIAL EQUATIONS The ideas to be developed may be adequately presented using the following simplified system: presented using the following simplified system: horizontal, one-dimensional, two-phase, incompressible flow in homogeneous porous media, with zero capillary pressure. A variable cross-section is included so that a variable flow velocity may be considered. The basic differential equations are (1) (2) The total volumetric flow rate is given by (3) Addition of Eqs. 1 and 2 yields =O SPEJ P. 79

Capillary Instability of Viscoelastic Liquid Film With Heat and Mass Transfer

2019 ◽  
Vol 142 (2) ◽  
Author(s):  
Mukesh Kumar Awasthi
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Viscoelastic Liquid ◽  
Capillary Instability ◽  
Viscous Potential Flow ◽  
Viscous Gas ◽  
Coaxial Cylinders ◽  
Fluid Layers ◽  
The Stability ◽  
Two Fluid

Abstract This paper examines the effect of transfer of heat and mass on the capillary instability between a viscoelastic liquid and a viscous gas. The viscoelastic liquid obeys the Oldroyd B-model. These two fluid layers considered in coaxial cylinders and viscoelastic–viscous potential flow theory are used for investigation. To study the stability of the interface, the normal-mode procedure is employed and a cubic dispersion equation in terms of growth rate has been obtained. We observe that the viscoelastic liquid–viscous gas interface is more unstable than the viscous liquid–viscous gas interface. Additionally, we show that the unstable axisymmetric wave modes are stabilized by allowing heat transfer at the interface.

Stability Analysis of Chaotic Wavy Stratified Fluid-Fluid Flow With the 1D Fixed-Flux Two-Fluid Model

2016 ◽  
Author(s):  
Avinash Vaidheeswaran ◽  
William D. Fullmer ◽  
Krishna Chetty ◽  
Raul G. Marino ◽  
Martin Lopez de Bertodano
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Two Phase Flow ◽  
Chaotic Behavior ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Two Fluid Model ◽  
The Stability ◽  
Two Fluid

The one-dimensional fixed-flux two-fluid model (TFM) is used to analyze the stability of the wavy interface in a slightly inclined pipe geometry. The model is reduced from the complete 1-D TFM, assuming a constant total volumetric flux, which resembles the equations of shallow water theory (SWT). From the point of view of two-phase flow physics, the Kelvin-Helmholtz instability, resulting from the relative motion between the phases, is still preserved after the simplification. Hence, the numerical fixed-flux TFM proves to be an effective tool to analyze local features of two-phase flow, in particular the chaotic behavior of the interface. Experiments on smooth- and wavy-stratified flows with water and gasoline were performed to understand the interface dynamics. The mathematical behavior concerning the well-posedness and stability of the fixed-flux TFM is first addressed using linear stability theory. The findings from the linear stability analysis are also important in developing the eigenvalue based donoring flux-limiter scheme used in the numerical simulations. The stability analysis is extended past the linear theory using nonlinear simulations to estimate the Largest Lyapunov Exponent which confirms the non-linear boundedness of the fixed-flux TFM. Furthermore, the numerical model is shown to be convergent using the power spectra in Fourier space. The nonlinear results are validated with the experimental data. The chaotic behavior of the interface from the numerical predictions is similar to the results from the experiments.

An Improved Bounded Gradient Maximization Method for Interface-Capturing VOF Simulations

2009 ◽  
Author(s):  
Brandon Witbeck ◽  
D. Keith Walters
Keyword(s):  
High Resolution ◽  
Phase Interface ◽  
Time Dependent ◽  
Test Cases ◽  
Discretization Scheme ◽  
Spatial Discretization ◽  
Two Phase ◽  
Initial Development ◽  
Interface Capturing ◽  
The Stability

A new high-resolution spatial discretization scheme is presented for the volume-of-fluid (VOF) method. This scheme is an adaptation of the previously published bounded gradient maximization (BGM) scheme [1]. This scheme resolves the phase interface without any explicit geometrical reconstruction of the interface. A net upwind bias in each cell ensures the stability of the scheme, and face limiting satisfies the boundedness criteria at the cell faces to prevent variable overshoot. In contrast to most existing methods, no method using “switching” between upwind-biased and downwind-biased discretization is employed to gain method stability. This paper presents the initial development and implementation of a time-dependent version of the method. Test cases are performed for a number of 2-D and 3-D two-phase flows on both structured and unstructured meshes. Results indicate that the method performs well in maintaining the resolution of the phase interface.

scholarly journals THEORETICAL STUDY OF THE STABILITY OF TWO-FLUID LAYERS

1974 ◽  
Vol 7 (2) ◽  
pp. 81-87 ◽  
Author(s):  
NOBUYUKI IMAISHI ◽  
KATSUHIKO FUJIKAWA
Keyword(s):  
Theoretical Study ◽  
Fluid Layers ◽  
The Stability ◽  
Two Fluid

Using surfactants to stabilize two-phase pipe flows of core–annular type

2012 ◽  
Vol 704 ◽  
pp. 333-359 ◽  
Author(s):  
Andrew P. Bassom ◽  
M. G. Blyth ◽  
D. T. Papageorgiou
Keyword(s):  
Reynolds Number ◽  
Outer Layer ◽  
Evolution Equations ◽  
Fluid Motion ◽  
Base Flow ◽  
Two Phase ◽  
Interface Position ◽  
Axial Pressure Gradient ◽  
Fluid Layers ◽  
Two Fluid

AbstractThe stability of a core–annular fluid arrangement consisting of two concentric fluid layers surrounding a solid cylindrical rod on the axis of a circular pipe is examined when the interface between the two fluid layers is covered with an insoluble surfactant. The motion is driven either by an imposed axial pressure gradient or by the movement of the rod at a prescribed constant velocity. In the basic state the fluid motion is unidirectional and the interface between the two fluids is cylindrical. A linear stability analysis is performed for arbitrary layer thicknesses and arbitrary Reynolds number. The results show that the flow can be fully stabilized, even at zero Reynolds number, if the base flow shear rate at the interface is set appropriately. This result is confirmed by an asymptotic analysis valid when either of the two fluid layers is thin in comparison to the gap between the pipe wall and the rod. It is found that for a thin inner layer the flow can be stabilized if the inner fluid is more viscous than the outer fluid, and the opposite holds true for a thin outer layer. It is also demonstrated that traditional core–annular flow, for which the rod is absent, may be stabilized at zero Reynolds number if the annular layer is sufficiently thin. Finally, weakly nonlinear simulations of a coupled set of partial differential evolution equations for the interface position and surfactant concentration are conducted with the rod present in the limit of a thin inner layer or a thin outer layer. The ensuing dynamics are found to be sensitive to the size of the curvature of the undisturbed interface.

scholarly journals The Effect of Slightly Upward and Downward Inclined Pipes on the Stability of Gas-Oil Two-Phase Flow

2014 ◽  
Vol 14 (1) ◽  
pp. 13
Author(s):  
Peyman Sabzi ◽  
Saheb Noroozi
Keyword(s):  
Two Phase Flow ◽  
Flow Instability ◽  
Fluid Model ◽  
Phase Flow ◽  
Momentum Exchange ◽  
Two Phase ◽  
Two Fluid Model ◽  
The Stability ◽  
Inclined Pipes ◽  
Two Fluid

Pipeline inclination has an important effect on the stability of two-phase flow and flow assurance in the pipeline. This inclination may be intentional; it may be inevitable in pipeline installation; or it may be due to an error in pipeline installation. In this situation, even the slight inclination of the pipe plays an important role in the growth or elimination of the instability of the two-phase flow. In this study using a code designed for the analysis of pipelines’ two-phase flow, the stability of the two-phase flow for Kerosene oil flow along with methane gas has been compared in downward inclined pipes, upward inclined pipes, and horizontal pipes. Using the mentioned computer code, it has been proved that the pipe’s upward inclination results in the increase of two-phase flow instability, while the pipe’s downward inclination is helpful in two-phase flow stability. In order to model two-phase flow in the pipe, two-fluid model has been used. This model considers each phase separately and the equations of mass conservation and momentum are written for each phase. The momentum exchange between the two phases and between each phase and the pipe wall has been considered. Conservation equations have been solved using SIMPLE algorithm in a numerical form with finite volume method.Keywords: Pipes, Two-Phase Flow, Inclined Stability, Two-Fluid Model

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