Oscillatory Marangoni flows with inertia

2016 ◽  
Vol 803 ◽  
pp. 94-118
Author(s):  
Orest Shardt ◽  
Hassan Masoud ◽  
Howard A. Stone
Keyword(s):  
Surface Tension ◽  
Uniform Distribution ◽  
Average Concentration ◽  
Late Time ◽  
Initial Amplitude ◽  
Oscillatory Behaviour ◽  
Coupled Flow ◽  
Spreading Dynamics ◽  
Unsteady Stokes Flow ◽  
Surfactant Transport

When the surface of a liquid has a non-uniform distribution of a surfactant that lowers surface tension, the resulting variation in surface tension drives a flow that spreads the surfactant towards a uniform distribution. We study the spreading dynamics of an insoluble and non-diffusing surfactant on an initially motionless liquid. We derive solutions for the evolution over time of sinusoidal variations in surfactant concentration with a small initial amplitude relative to the average concentration. In this limit, the coupled flow and surfactant transport equations are linear. In contrast to exponential decay when the inertia of the flow is negligible, the solution for unsteady Stokes flow exhibits oscillations when inertia is sufficient to spread the surfactant beyond a uniform distribution. This oscillatory behaviour exhibits two properties that distinguish it from that of a simple harmonic oscillator: the amplitude changes sign at most three times, and the decay at late times follows a power law with an exponent of $-3/2$. As the surface oscillates, the structure of the subsurface flow alternates between one and two rows of counter-rotating vortices, starting with one row and ending with two during the late-time monotonic decay. We also examine numerically the evolution of the surfactant distribution when the system is nonlinear due to a large initial amplitude.

A Microfluidic Tensiometer

2004 ◽  
Author(s):  
Hans C. Mayer ◽  
Shelley L. Anna
Keyword(s):  
Surface Tension ◽  
Transport Mechanism ◽  
Microfluidic Devices ◽  
Dynamic Surface Tension ◽  
Two Phase ◽  
Surface Tension Data ◽  
Dynamic Surface ◽  
Theoretical Predictions ◽  
Surfactant Transport ◽  
Interface Curvature

Recent theoretical predictions indicate that a shift in surfactant transport mechanism from diffusion controlled to kinetically controlled occurs at highly curved interfaces where the length scale is on the same order as feature sizes in microfluidic devices. At present, experimental evidence of this shift in transport mechanism is lacking and this is due to the limitations on degree of interface curvature imposed by traditional methods of surface tension measurement. We show that the measurement of dynamic surface tension is possible at highly curved interfaces using a microfluidic tensiometer that utilizes glass micropipettes to control curvature dimension. Comparison of dynamic surface tension data from our microfluidic tensiometer with data obtained from traditional techniques will validate the theoretical arguments reported, and will improve understanding of two phase flows in microfluidic devices.

scholarly journals Thermophysical Properties of Pipe Steel in the Liquid State

Metals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 1099
Author(s):  
Vladimir S. Tsepelev ◽  
Yuri N. Starodubtsev ◽  
Nadezhda P. Tsepeleva
Keyword(s):  
Surface Tension ◽  
Thermal Decomposition ◽  
High Temperature ◽  
Uniform Distribution ◽  
Transition Zone ◽  
Thermophysical Properties ◽  
Pipe Steel ◽  
Cluster Structure ◽  
Vacuum Degassing ◽  
Temperature Dependences

The temperature dependences of the kinematic viscosity and surface tension of liquid pipe steel with different modes of melt preparation were investigated. A transition zone was found on the temperature dependences of the thermophysical properties, which separates the regions with different activation energies of viscous flow and surface tension. At the heating stage in the transition zone, the thermal decomposition of clusters based on cementite Fe3C occurs. As a result of the decomposition, free carbon atoms appear which tend to give a uniform distribution in liquid iron with increasing temperature. At a low content of alloying elements and impurities, a high-temperature melt should have a large-scale cluster structure, which provides a more uniform distribution of chemical elements. The melt after vacuum degassing has a narrow transition zone near 1920 K, in contrast to the wide transition zone of the melt without vacuum degassing. The wider transition zone is shifted to high-temperature and this shift is associated with the thermal decomposition of carbides and oxides. Studies have shown that heating liquid pipe steel above the temperature of the liquid–liquid structural transition makes it possible to obtain a more homogeneous structure with a more uniform distribution of alloying and impurity elements in the melt. The sharp drop in surface tension at temperatures above 1920 K in the melt without vacuum degassing is associated with the diffusion of free S and O atoms, which are released after thermal decomposition of sulfides and oxides.

scholarly journals Surface-tension- and injection-driven spreading of a thin viscous film

2018 ◽  
Vol 861 ◽  
pp. 765-795 ◽  
Author(s):  
K. B. Kiradjiev ◽  
C. J. W. Breward ◽  
I. M. Griffiths
Keyword(s):  
Surface Tension ◽  
Film Thickness ◽  
Power Law ◽  
Contact Line ◽  
Numerical Solutions ◽  
Injection Rate ◽  
Late Time ◽  
Spatially Varying ◽  
Limiting Case ◽  
Film Profile

We consider the spreading of a thin viscous droplet, injected through a finite region of a substrate, under the influence of surface tension. We neglect gravity and assume that there is a precursor layer covering the whole substrate and that the rate of injection is constant. We analyse the evolution of the film profile for early and late time, and obtain power-law dependencies for the maximum film thickness at the centre of the injection region and the position of an apparent contact line, which compare well with numerical solutions of the full problem. We relax the conditions on the injection rate to consider more general time-dependent and spatially varying forms. In the case of power-law injection of the form$t^{k}$, we observe a switch in the behaviour of the evolution of the film thickness for late time from increasing to decreasing at a critical value of$k$. We show that point-source injection can be treated as a limiting case of a finite-injection slot and the solutions exhibit identical behaviours for late time. Finally, we formulate the problem with thickness-dependent injection rate, discuss the behaviour of the maximum film thickness and the position of the apparent contact line and give power-law dependencies for these.

scholarly journals Gravitational Collapse of Massless Fields in an Expanding Universe

2018 ◽  
Vol 168 ◽  
pp. 02002 ◽  
Author(s):  
Chul-Moon Yoo
Keyword(s):  
Boundary Condition ◽  
Scalar Field ◽  
Gravitational Collapse ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Integrability Condition ◽  
Massless Scalar ◽  
Late Time ◽  
Massless Scalar Field ◽  
Initial Amplitude

Gravitational collapse of a massless scalar field with the periodic boundary condition in a cubic box is reported. This system can be regarded as a lattice universe model. The initial data is constructed for a Gaussian like profile of the scalar field taking the integrability condition associated with the periodic boundary condition into account. For a large initial amplitude, a black hole is formed after a certain period of time. While the scalar field spreads out in the whole region for a small initial amplitude. The difference of the late time expansion law of the lattice universe depending on the final fate of the gravitational collapse is discussed.

Statics and Dynamics of Soft Wetting

2020 ◽  
Vol 52 (1) ◽  
pp. 285-308 ◽  
Author(s):  
Bruno Andreotti ◽  
Jacco H. Snoeijer
Keyword(s):  
Surface Tension ◽  
Solid Surface ◽  
Contact Line ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Theoretical Progress ◽  
Spreading Dynamics ◽  
Statics And Dynamics ◽  
Solid Surface Tension ◽  
Rigid Surfaces

The laws of wetting are well known for drops on rigid surfaces but change dramatically when the substrate is soft and deformable. The combination of wetting and the intricacies of soft polymeric interfaces have provided many rich examples of fluid–structure interactions, both in terms of phenomenology and from a fundamental perspective. In this review we discuss experimental and theoretical progress on the statics and dynamics of soft wetting. In this context we critically revisit the foundations of capillarity, such as the nature of solid surface tension, the microscopic mechanics near the contact line, and the dissipative mechanisms that lead to unexpected spreading dynamics.

Numerical studies of surface-tension effects in nonlinear Kelvin–Helmholtz and Rayleigh–Taylor instability

1982 ◽  
Vol 119 ◽  
pp. 507-532 ◽  
Author(s):  
D. I. Pullin
Keyword(s):  
Surface Tension ◽  
Interfacial Tension ◽  
Vortex Sheet ◽  
Taylor Instability ◽  
Late Time ◽  
Initial Value ◽  
Linearized Stability ◽  
Highly Nonlinear ◽  
Rayleigh Taylor Instability ◽  
Tension Term

We consider the behaviour of an interface between two immiscible inviscid incompressible fluids of different density moving under the action of gravity, inertial and interfacial tension forces. A vortex-sheet model of the exact nonlinear two-dimensional motion of this interface is formulated which includes expressions for an appropriate set of integral invariants. A numerical method for solving the vortex-sheet initial-value equations is developed, and is used to study the nonlinear growth of finite-amplitude normal modes for both Kelvin-Helmholtz and Rayleigh-Taylor instability. In the absence of an interfacial or surface-tension term in the integral-differential equation that describes the evolution of the circulation distribution on the vortex sheet, it is found that chaotic motion of, or the appearance of curvature singularities in, the discretized interface profiles prevent the simulations from proceeding to the late-time highly nonlinear phase of the motion. This unphysical behaviour is interpreted as a numerical manifestation of possible ill-posedness in the initial-value equations equivalent to the infinite growth rate of infinitesimal-wavelength disturbances in the linearized stability theory. The inclusion of an interfacial tension term in the circulation equation (which stabilizes linearized short-wavelength perturbations) was found to smooth profile irregularities but only for finite times. While coherent interfacial motion could then be followed well into the nonlinear regime for both the Kelvin-Helmholtz and Rayleigh-Taylor modes, locally irregular behaviour eventually reappeared and resisted subsequent attempts at numerical smoothing or suppression. Although several numerical and/or physical mechanisms are discussed that might produce irregular behaviour of the discretized interface in the presence of an interfacial-tension term, the basic cause of this instability remains unknown. The final description of the nonlinear interface motion thus awaits further research.

Surface Tension Driven Film Flow due to Condensation With a Vapor Borne Surfactant

2000 ◽  
Author(s):  
R. Qiao ◽  
Z. Yuan ◽  
K. E. Herold
Keyword(s):  
Mass Transfer ◽  
Surface Tension ◽  
Heat And Mass Transfer ◽  
Liquid Surface ◽  
Surface Concentration ◽  
Marangoni Flow ◽  
Absorption Chillers ◽  
Mass Transfer Processes ◽  
Surfactant Transport ◽  
Bottom Side

Abstract In absorption chillers, it is well known that the presence of small amounts of alcohol can enhance the absorber heat and mass transfer significantly. Similar enhancement is also observed in the condenser. Among the theories to explain such phenomena, the recently described Vapor Surfactant theory provides the most comprehensive explanation of the available data. According to this theory, the surfactant arrives at the liquid surface primarily from the vapor. As the water vapor flows toward eventual absorption/condensation, it carries the vapor borne surfactant toward the surface. Once the surfactant arrives at the surface, it tends to concentrate there due to its low solubility and low diffusivity in the liquid as well as the natural affinity of a surfactant for the surface. Non-uniform surface concentration of the surfactant leads to surface tension forces in the liquid surface layer that drive the surface flows often observed. These Marangoni flows are what enhance the heat and mass transfer processes. Although it was often theorized that Marangoni flow plays a role in enhancement, the important role of the vapor has not been well understood. A number of previous attempts have been made to compute Marangoni flow but all such attempts have assumed that the surfactant transport in the liquid is the key. This paper presents calculations of liquid film flows driven by the surfactant as it arrives at the surface from the vapor. This completely new model involves several very interesting features. A two-dimension numerical simulation of such a flow is reported here. The geometry is a thin film (3mm × 10cm) of liquid water with a small patch of cooling centered on the bottom side. The upper surface is exposed to steam+surfactant vapor so that condensation will occur. The model computes the surface concentration of surfactant and relates that to the surface tension. Calculations show that the condensation rate is much higher when Marangoni convection is occurring, even if the surfactant concentration in the vapor is very small (120ppm). This is in accordance with observations in absorption chillers. The result helps to clarify understanding of surfactant-induced enhancement of heat and mass transfer in absorption chillers.

scholarly journals Experimental Investigation on the Effects of Ethanol-Enhanced Steam Injection Remediation in Nitrobenzene-Contaminated Heterogeneous Aquifers

2021 ◽  
Vol 11 (24) ◽  
pp. 12029
Author(s):  
Ruxue Liu ◽  
Xinru Yang ◽  
Jiayin Xie ◽  
Xiaoyu Li ◽  
Yongsheng Zhao
Keyword(s):  
Heat Transfer ◽  
Surface Tension ◽  
Organic Compounds ◽  
Marangoni Convection ◽  
Steam Injection ◽  
Average Concentration ◽  
Low Permeability ◽  
Heterogeneous Aquifers ◽  
Heterogeneous Aquifer ◽  
Mass And Heat Transfer

Steam injection is an effective technique for the remediation of aquifers polluted with volatile organic compounds. However, the application of steam injection technology requires a judicious selection of stratum media because the remediation effect of hot steam in heterogeneous layers with low permeability is not suitable. In this study, the removal effect of nitrobenzene in an aquifer was investigated through a series of two-dimensional sandbox experiments with different stratigraphic structures. Four types of alcohols were used during steam injection remediation to enhance the removal effect of nitrobenzene (NB)-contaminated heterogeneous aquifers. The principle of the removal mechanism of alcohol-enhanced organic compounds is that alcohols can reduce the surface tension of the contaminated water, resulting in Marangoni convection, thereby enhancing mass and heat transfer. The addition of alcohol may also reduce the azeotropic temperature of the system and enhance the volatility of organic compounds. The study revealed that all four alcohol types could reduce the surface tension from 72 mN/m to <30 mN/m. However, among these, only ethanol reduced the azeotropic temperature of NB by 15 °C, thereby reducing energy consumption and remediation costs. Therefore, ethanol was selected as an enhancing agent to reduce both surface tension and azeotropic temperature during steam injection. In the 2-D simulation tank, the interface between the low-and high-permeability strata in the layered heterogeneous aquifer had a blocking effect on steam transportation, which in turn caused a poor remediation effect in the upper low-permeability stratum. In the lens heterogeneous aquifer, steam flows around the lens, thereby weakening the remediation effect. After adding ethanol to the low-permeability zone, Marangoni convection was enhanced, which further enhanced the mass and heat transfer. In the layered and lens heterogeneous aquifers, the area affected by steam increased by 13% and 14%, respectively. Moreover, the average concentration of NB was reduced by 51% in layered heterogeneous aquifers and by 58% in low-permeability lenses by ethanol addition. These findings enhance the remediation effect of steam injection in heterogeneous porous media and contribute to improve the remediation efficiency of heterogeneous aquifers by steam injection.

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