scholarly journals The role of surfactants on the mechanism of the long-wave instability in liquid film flows

2014 ◽  
Vol 741 ◽  
pp. 139-155 ◽  
Author(s):  
George Karapetsas ◽  
Vasilis Bontozoglou
Keyword(s):  
Liquid Film ◽  
Concentration Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Instability ◽  
Navier Stokes Equations ◽  
Flow Perturbation ◽  
Long Wave ◽  
Insoluble Surfactant ◽  
Interfacial Concentration

AbstractThe analysis for the physical mechanism of the long-wave instability in liquid film flow is extended to take into account the presence of a surfactant of arbitrary solubility. The Navier–Stokes equations are supplemented by mass balances for the concentrations at the interface and in the bulk, by a Langmuir model for adsorption kinetics at the interface, and are expanded in the limit of long-wave disturbances. The longitudinal flow perturbation, known to result from the perturbation shear stress which develops along the deformed interface, is shown to contribute a convective flux that triggers an interfacial concentration gradient. This gradient is, at leading order, in phase with the interfacial deformation, and as a result produces Marangoni stresses that stabilize the flow. The strength of the interfacial concentration gradient is shown to be maximum for an insoluble surfactant and to decrease with increasing surfactant solubility. The decrease is explained in terms of the spatial phase of mass transfer between interface and bulk, which mitigates the interfacial flux by the flow perturbation and leads to the attenuation of Marangoni stresses. Higher-order terms are derived, which provide corrections for disturbances of finite wavelength.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

Experimental and Numerical Study of Vortex Induced Vibrations on a Spool Model

2018 ◽  
Author(s):  
David Gross ◽  
Yann Roux ◽  
Benjamin Rousse ◽  
François Pétrié ◽  
Ludovic Assier ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Perturbation ◽  
Industry Standards ◽  
Vortex Induced Vibrations ◽  
Recommended Practices ◽  
Decay Tests

The problem of Vortex-Induced Vibrations (VIV) on spool and jumper geometries is known to present several drawbacks when approached with conventional engineering tools used in the study of VIV on risers. Current recommended practices can lead to over-conservatism that the industry needs to quantify and minimize within notably cost reduction objectives. Within this purpose, the paper will present a brief critical review of the Industry standards and more particularly focus on both experimental and Computational Fluid Dynamic (CFD) approaches. Both qualitative and quantitative comparisons between basin tests and CFD results for a 2D ‘M-shape’ spool model will be detailed. The results presented here are part of a larger experimental and numerical campaign which considered a number of current velocities, heading and geometry configurations. The vibratory response of the model will be investigated for one of the current velocities and compared with the results obtained through recommended practices (e.g. Shear7 and DNV guidelines). The strategy used by the software K-FSI to solve the fluid-structure interaction (FSI) problem is a partitioned coupling solver between fluid solver (FINE™/Marine) and structural solvers (ARA). FINE™/Marine solves the Reynolds-Averaged Navier-Stokes Equations in a conservative way via the finite volume method and can work on structured or unstructured meshes with arbitrary polyhedrons, while ARA is a nonlinear finite element solver with a large displacement formulation. The experiments were conducted in the BGO FIRST facility located in La Seyne sur Mer, France. Particular attention was paid towards the model design, fabrication, instrumentation and characterization, to ensure an excellent agreement between the structural numerical model and the actual physical model. This included the use of a material with low structural damping, the performance of stiffness and decay tests in air and in still water, plus the rationalization of the instrumentation to be able to capture the response with the minimum flow perturbation or interaction due to instrumentation.

Evaporation of Thin Film of Polar Liquid in Presence of Soluble Surfactant

2015 ◽  
Vol 1105 ◽  
pp. 105-109 ◽  
Author(s):  
Varvara Yu. Gordeeva ◽  
Andrey V. Lyushnin
Keyword(s):  
Liquid Film ◽  
Stokes Equations ◽  
Thin Liquid Film ◽  
Specific Interaction ◽  
Surface Concentration ◽  
Double Electric Layer ◽  
Solid Substrate ◽  
Polar Liquid ◽  
Navier Stokes ◽  
Navier Stokes Equations

Evaporation of a thin layer of a polar liquid (water) having a free surface and located on a solid substrate is investigated. A surfactant is solved in the liquid film. The surface tension is a linear function of the surface concentration of the surfactant. The surface energy of the solid-liquid interface is a nonmonotonic function of the layer thickness and is the sum of the Van der Waals interaction and the specific interaction of the double electric layer on the interface. The effect of the solvable surfactant on the dynamics of the propagation of the evaporation front in the thin liquid film is analyzed in the long-wave approximation in the system of Navier-Stokes equations.

scholarly journals Study of the stability of a thin liquid layer in the Landau–Levich problem

2020 ◽  
pp. 48-55
Author(s):  
A. V. Lyushnin ◽  
◽  
K. A. Permyakova ◽  
Keyword(s):  
Liquid Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Thin Liquid Layer ◽  
Wave Approximation ◽  
Long Wave ◽  
Interphase Boundaries ◽  
The Stability ◽  
Long Wave Approximation

The stability of the liquid layer in the Landay–Levich problem is theoretically investigated. The free energy of this layer is the sum of the dispersion (van der Waals) interaction and the specific electrical interaction caused by the presence of two electric layers at both interphase boundaries. In the framework of long-wave approximation, the stability of such a system with respect to perturbations is studied in the system of Navier–Stokes equations. A stability map is provided for different layer thicknesses.

scholarly journals Effect of the evaporation action on the stability of a thin liquid layer in the Landau–Levich problem

2021 ◽  
pp. 23-29
Author(s):  
A. V. Lyushnin ◽  
Keyword(s):  
Liquid Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Dimensionless Number ◽  
Navier Stokes Equations ◽  
Wave Approximation ◽  
Long Wave ◽  
Interphase Boundaries ◽  
The Stability ◽  
Long Wave Approximation

The stability of the liquid layer in the Landau–Levich problem is theoretically investigated in the presence of the evaporation effect from the free surface. The free energy of a thin layer of an incompressible fluid is the sum of the dispersion (van der Waals) interaction and the specific electrical interaction caused by the presence of double electric layers at both interphase boundaries. The stability of such a system with respect to perturbations is studied in the framework of the long – wave approximation in the system of Navier-Stokes equations. A stability map is provided for different values of the evaporation parameter. It is established that the stability of the system increases with an increase in the dimensionless number of evaporation.

The Effect of Streamwise Tube Motion on the Unsteady Fluid Forces in a Normal Triangle Tube Array

2015 ◽  
Author(s):  
Salim El Bouzidi ◽  
Marwan Hassan
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Experimental Investigations ◽  
Arbitrary Lagrangian Eulerian ◽  
Streamwise Direction ◽  
Navier Stokes Equations ◽  
Critical Flow Velocity ◽  
Flow Perturbation ◽  
Short Period ◽  
Fluidelastic Instability

Fluidelastic instability is generally regarded as the most severe type of flow excitation mechanism. When this mechanism prevails, it could cause serious damage to tube arrays in a very short period of time. This mechanism is characterized by a critical flow velocity beyond which the tubes undergo unstable oscillations. Recently, a number of experimental investigations showed that it is possible to have instability in the streamwise direction; previously, it was believed that fluidelastic instability was only a concern in the direction transverse to the flow. The purpose of this study is to characterize the flow in the channels surrounding a vibrating tube in a normal triangular bundle with P/d = 1.5. The tube is oscillating in the streamwise direction with a constant amplitude. Numerical simulations were conducted by solving the unsteady Reynolds Averaged Navier-Stokes equations (uRANS) cast in Arbitrary Lagrangian-Eulerian (ALE) form. The unsteady flow perturbation is estimated along the flow channel. The pressure perturbation is used to compute the streamwise unsteady force coefficients in the context of Chen’s model. The perturbation phase and decay are extracted and utilized in the framework of the Lever & Weaver model to study the stability of tube bundles due to tube motion in the streamwise direction.

scholarly journals CALCULATIONS OF WAVES FORMED FROM SURFACE CAVITIES

1976 ◽  
Vol 1 (15) ◽  
pp. 63 ◽  
Author(s):  
Charles L. Mader
Keyword(s):  
Water Waves ◽  
Wave Motion ◽  
Stokes Equations ◽  
Water Model ◽  
Navier Stokes ◽  
Critical Depth ◽  
Shallow Water Model ◽  
Navier Stokes Equations ◽  
Tsunami Waves ◽  
Long Wave

The wave motion resulting from cavities in the ocean surface was investigated using both the long wave, shallow water model and the incompressible Navier-Stokes equations. The fluid flow resulting from the calculated collapse of the cavities is significantly different for the two models. The experimentally observed flow resulting from explosively formed cavities is in better agreement with the flow calculated using the incompressible Navier-Stokes model. The resulting wave motions decay rapidly to deep water waves. Large cavities located under the surface of the ocean will be more likely to result in Tsunami waves than cavities on the surface. This is contrary to what has been suggested by the upper critical depth phenomenon.

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