Boundary Integral Analysis of the Creeping Flow of Long Bubbles in Capillaries

1989 ◽  
Vol 56 (1) ◽  
pp. 211-217 ◽  
Author(s):  
M. J. Martinez ◽  
K. S. Udell
Keyword(s):  
Surface Tension ◽  
Tube Wall ◽  
Boundary Integral ◽  
Creeping Flow ◽  
Experimental Measurements ◽  
Integral Analysis ◽  
Interfacial Surface ◽  
Liquid Bubble ◽  
Creeping Motion

A boundary integral analysis of the creeping motion of a long inviscid bubble in a liquid filled tube is presented. The effects of interfacial surface tension are included in the stress balance across the liquid-bubble interface. Velocities, stresses, and the bubble profile are obtained as a function of the capillary number. Computed values of the thickness of the liquid film between the bubble and tube wall are in excellent agreement with published experimental measurements. The results are of interest in exposing the role of surface tension in multiphase flow in capillary tubes and porous materials.

Instability of two-layer creeping flow in a channel with parallel-sided walls

1997 ◽  
Vol 351 ◽  
pp. 139-165 ◽  
Author(s):  
C. POZRIKIDIS
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Stokes Flow ◽  
Capillary Number ◽  
Travelling Waves ◽  
Boundary Integral ◽  
Creeping Flow ◽  
Two Dimensional ◽  
Two Fluids ◽  
Axial Pressure Gradient

The evolution of the interface between two viscous fluid layers in a two-dimensional horizontal channel confined between two parallel walls is considered in the limit of Stokes flow. The motion is generated either by the translation of the walls, in a shear-driven or plane-Couette mode, or by an axial pressure gradient, in a plane-Poiseuille mode. Linear stability analysis for infinitesimal perturbations and fluids with matched densities shows that when the viscosities of the fluids are different and the Reynolds number is sufficiently high, the flow is unstable. At vanishing Reynolds number, the flow is stable when the surface tension has a non-zero value, and neutrally stable when the surface tension vanishes. We investigate the behaviour of the interface subject to finite-amplitude two-dimensional perturbations by solving the equations of Stokes flow using a boundary-integral method. Integral equations for the interfacial velocity are formulated for the three modular cases of shear-driven, pressure-driven, and gravity-driven flow, and numerical computations are performed for the first two modes. The results show that disturbances of sufficiently large amplitude may cause permanent interfacial deformation in which the interface folds, develops elongated fingers, or supports slowly evolving travelling waves. Smaller amplitude disturbances decay, sometimes after a transient period of interfacial folding. The ratio of the viscosities of the two fluids plays an important role in determining the morphology of the emerging interfacial patterns, but the parabolicity of the unperturbed velocity profile does not affect the character of the motion. Increasing the contrast in the viscosities of the two fluids, while keeping the channel capillary number fixed, destabilizes the interfaces; re-examining the flow in terms of an alternative capillary number that is defined with respect to the velocity drop across the more-viscous layer shows that this is a reasonable behaviour. Comparing the numerical results with the predictions of a lubrication-flow model shows that, in the absence of inertia, the simplified approach can only describe a limited range of motions, and that the physical relevance of the steadily travelling waves predicted by long-wave theories must be accepted with a certain degree of reservation.

The flow of a liquid film along a periodic wall

1988 ◽  
Vol 188 ◽  
pp. 275-300 ◽  
Author(s):  
C. Pozrikidis
Keyword(s):  
Surface Tension ◽  
Liquid Film ◽  
Numerical Procedure ◽  
Surface Profile ◽  
Rotating Disk ◽  
Boundary Integral ◽  
Creeping Flow ◽  
Boundary Integral Method ◽  
Free Surface Profile ◽  
Gravity Driven Flow

The creeping flow of a liquid film along an inclined periodic wall of arbitrary geometry is considered. The problem is formulated using the boundary-integral method for Stokes flow. This method is extended to two-dimensional flows involving free surfaces, and is implemented in an iterative numerical procedure. Detailed calculations for flow along a sinusoidal wall are perfomed. The free-surface profile is studied as a function of flow rate, inclination angle, wave amplitude, and surface tension, and is compared with previous asymptotic solutions. The results include streamline patterns, velocity profiles and wall-shear-stress distributions, and establish criteria for flow reversal. For specified wall geometry, the asymptotic behaviour for very small flow rates is shown to be a strong function of surface tension. It is demonstrated that these results are valid in a qualitative sense for general wall geometries. The analogy between gravity-driven flow and the flow of a liquid layer on a rotating disk (spin coating) is also discussed.

Pearling, wrinkling, and buckling of vesicles in elongational flows

2015 ◽  
Vol 777 ◽  
pp. 1-26 ◽  
Author(s):  
Vivek Narsimhan ◽  
Andrew P. Spann ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Surface Tension ◽  
Extensional Flow ◽  
Boundary Integral ◽  
Physical Models ◽  
Initial Shape ◽  
Bending Modulus ◽  
Elongational Flows ◽  
The Stability ◽  
Spherical Vesicles

Tubular vesicles in extensional flow can undergo ‘pearling’, i.e. the formation of beads in their central neck reminiscent of the Rayleigh–Plateau instability for droplets. In this paper, we perform boundary integral simulations to determine the conditions for the onset of this instability. Our simulations agree well with experiments, and we explore additional topics such as the role of the vesicle’s initial shape on the number of pearls formed. We also compare our simulations to simple physical models of pearling that have been presented in the literature, where the vesicle is approximated as an infinitely long cylinder with a constant surface tension and bending modulus. We present a complete linear stability analysis of this idealized problem, including the effects of non-axisymmetric deformations as well as surface viscosity. We demonstrate that, while such models capture the essential physics of pearling, they cannot capture the stability of these transitions accurately, since finite length effects and non-uniform surface tension effects are important. We close our paper with a brief discussion of vesicles in compressional flows. Unlike quasi-spherical vesicles, we find that tubular vesicles can transition to a wide variety of permanent, buckled states under compression. The idealized problem mentioned above gives the essential physics behind these instabilities, which to our knowledge has not been examined heretofore.

On the Role of Marangoni Effects on the Critical Heat Flux for Pool Boiling of Binary Mixtures

1996 ◽  
Vol 118 (1) ◽  
pp. 103-109 ◽  
Author(s):  
W. R. McGillis ◽  
V. P. Carey
Keyword(s):  
Surface Tension ◽  
Heat Flux ◽  
Binary Mixtures ◽  
Critical Heat Flux ◽  
Full Range ◽  
Pool Boiling ◽  
Marangoni Effect ◽  
Restoring Force ◽  
Marangoni Effects

The Marangoni effect on the critical heat flux (CHF) condition in pool boiling of binary mixtures has been identified and its effect has been quantitatively estimated with a modified model derived from hydrodynamics. The physical process of CHF in binary mixtures, and models used to describe it, are examined in the light of recent experimental evidence, accurate mixture properties, and phase equilibrium revealing a correlation to surface tension gradients and volatility. A correlation is developed from a heuristic model including the additional liquid restoring force caused by surface tension gradients. The CHF condition was determined experimentally for saturated methanol/water, 2-propanol/water, and ethylene glycol/water mixtures, over the full range of concentrations, and compared to the model. The evidence in this study demonstrates that in a mixture with large differences in surface tension, there is an additional hydrodynamic restoring force affecting the CHF condition.

scholarly journals Influence of moisture content on the contact angle and surface tension measured on birch wood surfaces

2021 ◽  
Author(s):  
Rami Benkreif ◽  
Fatima Zohra Brahmia ◽  
Csilla Csiha
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Moisture Content ◽  
Solid Wood ◽  
Contact Angles ◽  
Surface Moisture ◽  
Wood Coatings ◽  
The Relationship ◽  
Wood Surfaces

AbstractSurface tension of solid wood surfaces affects the wettability and thus the adhesion of various adhesives and wood coatings. By measuring the contact angle of the wood, the surface tension can be calculated based on the Young-Dupré equation. Several publications have reported on contact angle measured with different test liquids, under different conditions. Results can only be compared if the test conditions are similar. While the roles of the drop volume, image shooting time etc., are widely recognized, the role of the wood surface moisture content (MC) is not evaluated in detail. In this study, the effect of wood moisture content on contact angle values, measured with distilled water and diiodomethane, on sanded birch (Betula pendula) surfaces was investigated, in order to find the relationship between them. With increasing MC from approximately 6% to 30%, increasing contact angle (decreasing surface tension) values were measured according to a logarithmic function. The function makes possible the calculation of contact angles that correspond to different MCs.

scholarly journals Interactions between an Associative Amphiphilic Block Polyelectrolyte and Surfactants in Water: Effect of Charge Type on Solution Properties and Aggregation

Polymers ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1729
Author(s):  
Patrizio Raffa
Keyword(s):  
Surface Tension ◽  
Self Assembly ◽  
Interaction Model ◽  
Industrial Applications ◽  
Molecular Organization ◽  
Different Types ◽  
Solution Rheology ◽  
Interesting Class ◽  
First Time

The study of interactions between polyelectrolytes (PE) and surfactants is of great interest for both fundamental and applied research. These mixtures can represent, for example, models of self-assembly and molecular organization in biological systems, but they are also relevant in industrial applications. Amphiphilic block polyelectrolytes represent an interesting class of PE, but their interactions with surfactants have not been extensively explored so far, most studies being restricted to non-associating PE. In this work, interactions between an anionic amphiphilic triblock polyelectrolyte and different types of surfactants bearing respectively negative, positive and no charge, are investigated via surface tension and solution rheology measurements for the first time. It is evidenced that the surfactants have different effects on viscosity and surface tension, depending on their charge type. Micellization of the surfactant is affected by the presence of the polymer in all cases; shear viscosity of polymer solutions decreases in presence of the same charge or nonionic surfactants, while the opposite charge surfactant causes precipitation. This study highlights the importance of the charge type, and the role of the associating hydrophobic block in the PE structure, on the solution behavior of the mixtures. Moreover, a possible interaction model is proposed, based on the obtained data.

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.

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