scholarly journals Surfactant spreading in a two-dimensional cavity and emergent contact-line singularities

2021 ◽  
Vol 930 ◽  
Author(s):  
Richard Mcnair ◽  
Oliver E. Jensen ◽  
Julien R. Landel
Keyword(s):  
Contact Line ◽  
Dynamic Compression ◽  
Decay Rates ◽  
Two Dimensional ◽  
Insoluble Surfactant ◽  
Surfactant Transport ◽  
Confined Domains ◽  
Weak Surface ◽  
Singular Flow ◽  
Line Singularities

We model the advective Marangoni spreading of insoluble surfactant at the free surface of a viscous fluid that is confined within a two-dimensional rectangular cavity. Interfacial deflections are assumed small, with contact lines pinned to the walls of the cavity, and inertia is neglected. Linearising the surfactant transport equation about the equilibrium state allows a modal decomposition of the dynamics, with eigenvalues corresponding to decay rates of perturbations. Computation of the family of mutually orthogonal two-dimensional eigenfunctions reveals singular flow structures near each contact line, resulting in spatially oscillatory patterns of shear stress and a pressure field that diverges logarithmically. These singularities at a stationary contact line are associated with dynamic compression of the surfactant monolayer. We show how they can be regularised by weak surface diffusion. Their existence highlights the need for careful treatment in computations of unsteady advection-dominated surfactant transport in confined domains.

scholarly journals Spreading of Micrometer-Sized Droplets under the Influence of Insoluble and Soluble Surfactants: A Numerical Study

2019 ◽  
Vol 3 (3) ◽  
pp. 56
Author(s):  
Thomas Antritter ◽  
Peter Hachmann ◽  
Tatiana Gambaryan-Roisman ◽  
Bernhard Buck ◽  
Peter Stephan
Keyword(s):  
Numerical Study ◽  
Sorption Kinetics ◽  
Small Scale ◽  
Surfactant Adsorption ◽  
Insoluble Surfactant ◽  
Surfactant Transport ◽  
Soluble Surfactants ◽  
The One ◽  
Printing Processes ◽  
Soluble Surfactant

Wetting and spreading of surfactant solutions play an important role in many technical applications. In printing processes, the size of individual droplets is typically on the order of a few tens of microns. The purpose of this study is to develop a better understanding of the interaction between spreading and surfactant transport on these small length and related time scales. Therefore, numerical simulations based on the volume-of-fluid method including Marangoni stresses and transport of an insoluble or soluble surfactant are performed. The results for an insoluble surfactant show competing effects of Marangoni flow on the one hand, and a decreasing surfactant concentration as the droplet spreads on the other hand. Even in the case of a soluble surfactant, adsorption and desorption could only partly mitigate these effects, demonstrating the importance of the sorption kinetics for fast, small scale wetting processes.

Thermocapillary migration of a two-dimensional liquid droplet on a solid surface

1995 ◽  
Vol 294 ◽  
pp. 209-230 ◽  
Author(s):  
Marc K. Smith
Keyword(s):  
Temperature Gradient ◽  
Solid Surface ◽  
Contact Line ◽  
Liquid Droplet ◽  
Perturbation Technique ◽  
Contact Angles ◽  
Two Dimensional ◽  
Line Speed ◽  
Dynamic Relationship ◽  
Steady State Responses

A two-dimensional liquid droplet placed on a non-uniformly heated solid surface will move towards the region of colder temperatures if the temperature gradient in the solid surface is large enough. Such behaviour is analysed for a thin viscous droplet using lubrication theory to develop an evolution equation for the shape of the droplet. For the small mobility capillary numbers examined in this work, the contact-line motion is controlled by a dynamic relationship posed between the contact-line speed and the apparent contact angle. Results are obtained numerically and also approximately using a perturbation technique for small heating. The initial spreading or shrinking of the droplet when placed on the heated solid is biased toward the direction of decreasing temperature on the solid. Possible steady-state responses are either a motionless droplet or one moving at a constant velocity down the temperature gradient without change in shape. These behaviours are the result of a thermocapillary recirculation cell inside the droplet that distorts the free surface and alters the apparent contact angles. This change in the apparent contact angles then modifies the contact-line speed.

Two-Dimensional Capillary Origami with Pinned Contact Line

2015 ◽  
Vol 75 (3) ◽  
pp. 1275-1300 ◽  
Author(s):  
N. D. Brubaker ◽  
J. Lega
Keyword(s):  
Contact Line ◽  
Two Dimensional

Two-Dimensional Correlation Analysis of Polyimide Films Using Attenuated Total Reflection-Based Dynamic Compression Modulation Step-Scan Fourier Transform Infrared Spectroscopy

2007 ◽  
Vol 61 (8) ◽  
pp. 873-881 ◽  
Author(s):  
Yuji Nishikawa ◽  
Tatsuhiko Nakano ◽  
Isao Noda
Keyword(s):  
Dynamic Response ◽  
Intermolecular Interactions ◽  
Density Functional ◽  
Sequential Analysis ◽  
Dynamic Compression ◽  
Correlation Study ◽  
Total Reflection ◽  
Attenuated Total Reflection ◽  
Two Dimensional ◽  
Spectral Simulation

Attenuated total reflection (ATR)-based dynamic compression modulation two-dimensional (2D) correlation study of poly(p-phenylene biphenyltetracarboximide) film is carried out in combination with spectral simulation analysis by density functional theory (DFT). The dynamic 2D infrared (IR) correlation spectra in the region of imide I (C=O stretching mode) show three distinct correlation peaks located around 1777, 1725, and 1708 cm−1. The band at 1708 cm−1 is the lower wavenumber shift component of 1777 or 1735 cm−1 peaks and is attributed to the results from intermolecular interactions, according to the DFT analysis. The 1708 cm−1 band also shows the largest dynamic response, suggesting that these intermolecular interactions may enhance the dynamic response. The dynamic 2D IR correlation spectra in the region of imide II (C–N–C axial stretching mode) vibrations also show three correlation peaks located around 1335, 1355, and 1370 cm−1, although the imide II band is shown to consist substantially of one component by the DFT analysis. These multiple peaks may be attributed to the compression-induced wavenumber shift of the band in the backbone structures. The sequential analysis of 2D correlation data show that, upon applying the dynamic compression, the response of the backbone regions (imide II) occurs first, followed by that of the side-chain regions (imide I, C=O).

Numerical studies of cusp formation at fluid interfaces in Stokes flow

1998 ◽  
Vol 357 ◽  
pp. 29-57 ◽  
Author(s):  
C. POZRIKIDIS
Keyword(s):  
Surface Tension ◽  
Stokes Flow ◽  
Boundary Integral ◽  
Numerical Results ◽  
Boundary Integral Method ◽  
Fluid Interfaces ◽  
Two Dimensional ◽  
Numerical Studies ◽  
Insoluble Surfactant ◽  
Cusp Formation

Numerical studies are performed addressing the development of regions of high curvature and the spontaneous occurrence of cusped interfacial shapes in two-dimensional and axisymmetric Stokes flow. In the numerical simulations, the velocity field is computed using a boundary-integral method, and the evolution of the concentration of an insoluble surfactant over an evolving interface is computed using an implicit finite-volume method. Three configurations are considered in detail, and the results are used to elucidate three different aspects of cusp formation. In the first series, the deformation of a two-dimensional bubble immersed in a family of straining flows devised by Antanovskii, and of an axisymmetric bubble immersed in an analogous family of flows devised by Sherwood, are examined. The numerical results indicate that highly elongated and cusped two-dimensional shapes, and pointed or cusped axisymmetric shapes, are unstable and should not be expected to occur in practice. In the second series of studies, the role of an insoluble surfactant on the transient deformation of bubbles subject to the Antanovskii or Sherwood flow is investigated. Under certain conditions, the reduced surface tension at the tips raises the local curvature to high values and causes the ejection of a sheet or column of gas by means of tip streaming. In the third series of studies, the coalescence of a polygonal formation of five viscous columns of a fluid placed in an arrangement that differs only slightly from one proposed recently by Richardson is examined. The numerical results confirm Richardson's predictions that transient cusps may occur at a finite time in the presence of surface tension. The underlying physical mechanism is discussed on the basis of reversibility of surface-driven Stokes flow and with reference to the regularity of the motion driven by negative surface tension. Replacing the inviscid ambient gas with a slightly viscous fluid whose viscosity is as low as one hundredth the viscosity of the cylinders suppresses the cusp formation.

scholarly journals The effect of a submerged barrier on the natural freqencies and radiation damping of a shallow basin connected to open water

1980 ◽  
Vol 22 (1) ◽  
pp. 104-128 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Shallow Water ◽  
Radiative Decay ◽  
Open Water ◽  
Decay Rates ◽  
Two Dimensional ◽  
Aperture Size ◽  
Constant Depth ◽  
Closed Basin ◽  
Matching Procedure ◽  
Shallow Basin

AbstractA theory is provided for the natural seiching frequencies and radiative decay rates for a shallow-water basin whose connection to open water is restricted by a submerged wall or reef. The transition from an essentially-open basin to a closed basin, as the aperture reduces to zero, is discussed using a matching procedure. Graphs of frequencies and damping factors as functions of aperture size are obtained for idealized two-dimensional shelf configurations, involving a constant-depth shallow basin connected to constant-depth, but not necessarily shallow, open water.

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