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

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.

scholarly journals On contact-line dynamics with mass transfer

2015 ◽  
Vol 26 (5) ◽  
pp. 671-719 ◽  
Author(s):  
J. M. OLIVER ◽  
J. P. WHITELEY ◽  
M. A. SAXTON ◽  
D. VELLA ◽  
V. S. ZUBKOV ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Surface Tension ◽  
Asymptotic Analysis ◽  
Contact Line ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Leading Order ◽  
Vapour Transport ◽  
Gravity Surface ◽  
Matched Asymptotic Analysis

We investigate the effect of mass transfer on the evolution of a thin, two-dimensional, partially wetting drop. While the effects of viscous dissipation, capillarity, slip and uniform mass transfer are taken into account, other effects, such as gravity, surface tension gradients, vapour transport and heat transport, are neglected in favour of mathematical tractability. Our focus is on a matched-asymptotic analysis in the small-slip limit, which reveals that the leading-order outer formulation and contact-line law depend delicately on both the sign and the size of the mass transfer flux. This leads, in particular, to novel generalisations of Tanner's law. We analyse the resulting evolution of the drop on the timescale of mass transfer and validate the leading-order predictions by comparison with preliminary numerical simulations. Finally, we outline the generalisation of the leading-order formulations to prescribed non-uniform rates of mass transfer and to three dimensions.

Growth of Giant Two-Dimensional Crystal of Protein Molecules from a Three-Phase Contact Line

Langmuir ◽  
2008 ◽  
Vol 24 (22) ◽  
pp. 12836-12841 ◽  
Author(s):  
Yasuhiro Ikezoe ◽  
Yoshikazu Kumashiro ◽  
Kaoru Tamada ◽  
Takuro Matsui ◽  
Ichiro Yamashita ◽  
...  
Keyword(s):  
Contact Line ◽  
Two Dimensional ◽  
Phase Contact ◽  
Three Phase ◽  
Protein Molecules ◽  
Dimensional Crystal

Three-dimensional theory of water impact. Part 1. Inverse Wagner problem

2001 ◽  
Vol 440 ◽  
pp. 293-326 ◽  
Author(s):  
Y.-M. SCOLAN ◽  
A. A. KOROBKIN
Keyword(s):  
Free Surface ◽  
Contact Line ◽  
Three Dimensional ◽  
The Body ◽  
Two Dimensional ◽  
Elliptic Paraboloid ◽  
Dimensional Effects ◽  
The Impact ◽  
Elliptic Contact ◽  
Wagner Theory

The three-dimensional problem of blunt-body impact onto the free surface of an ideal incompressible liquid is considered within the Wagner theory. The theory is formally valid during an initial stage of the impact. The problem has been extensively studied in both two-dimensional and axisymmetric cases. However, there are no exact truly three-dimensional solutions of the problem even within the Wagner theory. At present, three-dimensional effects in impact problems are mainly handled approximately by using a sequence of two-dimensional solutions and/or aspect-ratio correction factor. In this paper we present exact analytical rather than approximate solutions to the three-dimensional Wagner problem. The solutions are obtained by the inverse method. In this method the body velocity and the projection on the horizontal plane of the contact line between the liquid free surface and the surface of the entering body are assumed to be given at any time instant. The shape of the impacting body is determined from the Wagner condition. It is proved that an elliptic paraboloid entering calm water at a constant velocity has an elliptic contact line with the free surface. Most of the results are presented for elliptic contact lines, for which analytical solutions of the inverse Wagner problem are available. The results obtained can be helpful in testing other numerical approaches and studying the influence of three-dimensional effects on the liquid flow and the hydrodynamic loads.

Ring formation on an inclined surface

2015 ◽  
Vol 775 ◽  
Author(s):  
Xiyu Du ◽  
R. D. Deegan
Keyword(s):  
Asymptotic Analysis ◽  
Contact Line ◽  
Narrow Band ◽  
Two Dimensional ◽  
A Posteriori ◽  
Drop Volume ◽  
Line Region ◽  
Initial Drop ◽  
Inclined Surface ◽  
Lower Contact

A drop dried on a solid surface will typically leave a narrow band of solute deposited along the contact line. Here we examine variations of this deposit due to the inclination of the substrate using numerical simulations of a two-dimensional drop, equivalent to a strip-like drop. An asymptotic analysis of the contact line region predicts that the upslope deposit will grow faster at early times, but the growth of this deposit ends sooner because the upper contact line depins first. From our simulations we find that the deposit can be larger at either the upper or lower contact line depending on the initial drop volume and substrate inclination. For larger drops and steeper inclinations, the early lead in deposited mass at the upper contact line is wiped out by the earlier depinning of the upper contact line and subsequent continued growth at the lower contact line. Conversely, for smaller drops and shallower inclinations, the early lead of the upper contact line is insurmountable despite its earlier termination in growth. Our results show that it is difficult to reconstruct a posteriori the inclination of the substrate based solely on the shape of the deposit.

Simulation of Blob Dynamics Inside a Channel Under Acoustic Excitation

2013 ◽  
Author(s):  
Pitambar Randive ◽  
Amaresh Dalal ◽  
Partha P. Mukherjee
Keyword(s):  
Frequency Response ◽  
Lattice Boltzmann Method ◽  
Contact Line ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Acoustic Excitation ◽  
Two Dimensional ◽  
The Mean ◽  
Boltzmann Method

The displacement of a three-dimensional immiscible blob subject to oscillatory acoustic excitation in a channel is studied with the Lattice Boltzmann method. The effects of amplitude of the force, viscosity and frequency on blob dynamics are investigated. The trend for variation of mean displacement of blob and frequency response is in agreement to that of the previous two-dimensional studies reported in literature. The response of the blob with pinned contact line shows underdamped behavior. It is also found that increasing the amplitude of the force increases the mean displacement and frequency response.

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.

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