Thermocapillary Fingering of a Gravity-Driven Self-Rewetting Fluid Film Flowing Down a Vertical Slippery Wall

2021 ◽  
Author(s):  
Chicheng Ma ◽  
Jianlin Liu
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Stability Analysis ◽  
Film Theory ◽  
Vertical Plane ◽  
Wall Slip ◽  
Fluid Film ◽  
Numerical Verification ◽  
Gravity Driven ◽  
Interfacial Temperature

Abstract The surface tension of a self-rewetting fluid (SRF) has a parabolic shape with the increase of temperature, implying potential applications in many industrial fields. In this paper, flow patterns and stability analysis are numerically performed for a gravity driven self-rewetting fluid film flowing down a heated vertical plane with wall slip. Using the thin film theory, the evolution equation for the interfacial thickness is derived. The discussion is given considering two cases in the review of the temperature difference between the interfacial temperature and the temperature corresponding to the minimum surface tension. The base state of the two-dimensional flow is firstly obtained and the influence of the Marangoni effect and slippery effect is analyzed. Then linear stability analysis and related numerical verification are displayed, showing good consistency with each other. For a low interfacial temperature, the Marangoni promotes the fingering instability and for a high interfacial temperature, the inverse Marangoni impedes the surface instability. The wall slip is found to influence the free surface in a complex way because it can either destabilize or stabilize the flow of the free surface.

Stability of Hadley Circulations in a Viscoelastic Fluid With Deformable Free Surface

2003 ◽  
Author(s):  
P. N. Kaloni ◽  
J. X. Lou
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Stability Analysis ◽  
Eigenvalue Problem ◽  
Viscoelastic Fluid ◽  
Lower Surface ◽  
Horizontal Layer ◽  
Convective Stability ◽  
Rigid Plate ◽  
Temperature Dependent

This paper deals with liner convective stability analysis of Oldroyd B fluid in a thin horizontal layer with a deformable free surface. The lower surface of the layer is in contact with an adiabatic rigid plate and the upper deformable surface is subject to a temperature dependent surface tension. The eigenvalue problem is solved by the Chebyshev Tau-QZ method and the results for various different forms of upper surfaces are presented.

Stability analysis of gravity driven shear flows with free surface for power-law fluids

1998 ◽  
Vol 68 (3-4) ◽  
pp. 169-178 ◽  
Author(s):  
Y. A. Berezin ◽  
K. Hutter ◽  
L. A. Spodareva
Keyword(s):  
Free Surface ◽  
Stability Analysis ◽  
Power Law ◽  
Shear Flows ◽  
Power Law Fluids ◽  
Gravity Driven

Steady and Unsteady Simulations for Annular Internal Condensing Flows in a Channel

2014 ◽  
Author(s):  
Ranjeeth Naik ◽  
Amitabh Narain ◽  
Soumya Mitra
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Method Of Characteristics ◽  
Governing Equations ◽  
The Method Of Characteristics ◽  
Wave Simulation ◽  
Condensing Flows ◽  
Gravity Driven ◽  
Annular Regime ◽  
Internal Condensing Flows

This paper highlights: (i) numerical methods developed to solve annular/stratified internal condensing flow problems, and (ii) the assessed effects of transverse gravity and surface tension on shear driven (horizontal channels) and gravity driven (inclined channels) internal condensing flows. A comparative study of the flow physics is presented with the help of steady and unsteady computational results obtained from the numerical solutions of the full two-dimensional governing equations for annular internal condensing flows. These simulations directly apply to recently-demonstrated innovative condenser operations which make the flow regime annular over the entire length of the condenser. The simulation algorithm is based on an active integration of our own codes developed on MATLAB with the standard single-phase CFD simulation codes available on COMSOL. The approach allows for an accurate wave simulation technique for the highly sensitive shear driven annular condensing flows. This simulation approach employs a sharp-interface model and uses a moving grid technique to accurately locate the dynamic interface by the solution of the interface tracking equation (employing the method of characteristics) along with the rest of the governing equations. The 4th order time-step accuracy in the method of characteristics has enabled, for the first time, the ability to track time-varying interface locations associated with wave phenomena and accurate satisfaction of all the interface conditions — including the more difficult to satisfy interfacial mass-flux equalities. A combination of steady and unsteady simulation results are also used to identify the effects of transverse gravity, axial gravity, and surface tension on the growth of waves. The results presented bring out the differences within different types of shear driven flows and differences between shear driven and gravity driven flows. The unsteady wave simulation capability has been used here to do the stability analysis for annular shear-driven steady flows. In stability analysis, an assessment of the dynamic response of the steady solutions to arbitrary instantaneous initial disturbance are obtained. The results mark the location beyond which the annular regime transitions to a non-annular regime (experimentally known to be a plug-slug regimes). The computational prediction of heat-flux values agree with the experimentally measured values (at measurement locations) obtained from relevant runs of our in-house experiments. Also, a comparison between the computationally predicted and experimentally measured values regarding the length of the annular regime is possible, and will be presented elsewhere.

scholarly journals The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin liquid drop

2005 ◽  
Vol 2005 (6) ◽  
pp. 703-715
Author(s):  
E. Momoniat
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Viscous Liquid ◽  
Liquid Drop ◽  
Nonlinear Partial Differential Equation ◽  
Group Method ◽  
Lie Group Method ◽  
Nonuniform Surface ◽  
Equation Modelling ◽  
Gravity Driven

The effects of nonuniform surface tension on the axisymmetric gravity-driven spreading of a thin viscous liquid drop are investigated. A second-order nonlinear partial differential equation modelling the evolution of the free surface of a thin viscous liquid drop is derived. The nonuniform surface tension is represented by a functionΣ(r). The Lie group method is used to determineΣ(r)such that exact and approximate invariant solutions admitted by the free surface equation can be determined. It is shown that the nonuniform surface tension can be represented as a power law inr. The effect of this nonuniformity is to reduce the surface tension at the centre of the drop and increase it at the foot of the drop. This results in a deflection away from the solution for spreading under gravity only and the formation of a capillary ridge.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

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