scholarly journals The bending of an elastic beam by a liquid drop: a variational approach

2013 ◽  
Vol 469 (2157) ◽  
pp. 20130066 ◽  
Author(s):  
Sébastien Neukirch ◽  
Arnaud Antkowiak ◽  
Jean-Jacques Marigo
Keyword(s):  
Contact Line ◽  
Variational Approach ◽  
Liquid Drop ◽  
Elastic Beam ◽  
Triple Line ◽  
Equilibrium Equations ◽  
External Forces ◽  
Contact Line Pinning ◽  
Three Phases

We study the interaction of a liquid drop with an elastic beam in the case where bending effects dominate. We use a variational approach to derive equilibrium equations for the system in the presence of gravity and in the presence or absence of contact line pinning. We show that the derived equilibrium equations for the beam subsystem reveal the external forces applied on the beam by the liquid and vapour phases. Among these, the force applied at the triple line (the curve where the three phases meet) is found to lie along the liquid–vapour interface.

A Variational Approach to Loaded Ply Structures

2003 ◽  
Vol 9 (1-2) ◽  
pp. 175-185 ◽  
Author(s):  
G. H.M. Van Der Heijden ◽  
J. M.T. Thompson ◽  
S. Neukirch
Keyword(s):  
Boundary Conditions ◽  
Energy Method ◽  
Variational Approach ◽  
Energy Analysis ◽  
Numerical Results ◽  
Equilibrium Equations

We show how an energy analysis can be used to derive the equilibrium equations and boundary conditions for an end-loaded variable ply much more efficiently than in previous works. Numerical results are then presented for a clamped balanced ply approaching lock-up. We also use the energy method to derive the equations for a more general ply made of imperfect anisotropic rods and we briefly consider their helical solutions.

Droplet spreading and absorption on rough, permeable substrates

2015 ◽  
Vol 784 ◽  
pp. 465-486 ◽  
Author(s):  
Leonardo Espín ◽  
Satish Kumar
Keyword(s):  
Surface Roughness ◽  
Contact Line ◽  
Nonlinear Evolution ◽  
Precursor Film ◽  
Radial Coordinate ◽  
Droplet Spreading ◽  
Liquid Spreading ◽  
Line Region ◽  
Influence Of Substrate ◽  
Contact Line Pinning

Wetting of permeable substrates by liquids is an important phenomenon in many natural and industrial processes. Substrate heterogeneities may significantly alter liquid spreading and interface shapes, which in turn may alter liquid imbibition. A new lubrication-theory-based model for droplet spreading on permeable substrates that incorporates surface roughness is developed in this work. The substrate is assumed to be saturated with liquid, and the contact-line region is described by including a precursor film and disjoining pressure. A novel boundary condition for liquid imbibition is applied that eliminates the need for a droplet-thickness-dependent substrate permeability that has been employed in previous models. A nonlinear evolution equation describing droplet height as a function of time and the radial coordinate is derived and then numerically solved to characterize the influence of substrate permeability and roughness on axisymmetric droplet spreading. Because it incorporates surface roughness, the new model is able to describe the contact-line pinning that has been observed in experiments but not captured by previous models.

Anomalous Contact Angle Hysteresis of a Captive Bubble: Advancing Contact Line Pinning

Langmuir ◽  
2011 ◽  
Vol 27 (11) ◽  
pp. 6890-6896 ◽  
Author(s):  
Siang-Jie Hong ◽  
Feng-Ming Chang ◽  
Tung-He Chou ◽  
Seong Heng Chan ◽  
Yu-Jane Sheng ◽  
...  
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Contact Angle Hysteresis ◽  
Contact Line Pinning

Contact Line Pinning Effects Influence Determination of the Line Tension of Droplets Adsorbed on Substrates

2018 ◽  
Vol 122 (30) ◽  
pp. 17184-17189 ◽  
Author(s):  
Hongguang Zhang ◽  
Shan Chen ◽  
Zhenjiang Guo ◽  
Yawei Liu ◽  
Fernando Bresme ◽  
...  
Keyword(s):  
Contact Line ◽  
Line Tension ◽  
Contact Line Pinning

scholarly journals Contact Line Pinning Is Not Required for Nanobubble Stability on Copolymer Brushes

2018 ◽  
Vol 9 (15) ◽  
pp. 4239-4244 ◽  
Author(s):  
David S. Bull ◽  
Nathaniel Nelson ◽  
Danielle Konetski ◽  
Christopher N. Bowman ◽  
Daniel K. Schwartz ◽  
...  
Keyword(s):  
Contact Line ◽  
Copolymer Brushes ◽  
Contact Line Pinning

Shear flow over a liquid drop adhering to a solid surface

1996 ◽  
Vol 307 ◽  
pp. 167-190 ◽  
Author(s):  
Xiaofan Li ◽  
C. Pozrikidis
Keyword(s):  
Contact Angle ◽  
Shear Flow ◽  
Contact Line ◽  
Simple Shear ◽  
Liquid Drop ◽  
Contact Angle Hysteresis ◽  
Boundary Integral ◽  
Simple Shear Flow ◽  
Contact Lines ◽  
Transient Deformation

The hydrostatic shape, transient deformation, and asymptotic shape of a small liquid drop with uniform surface tension adhering to a planar wall subject to an overpassing simple shear flow are studied under conditions of Stokes flow. The effects of gravity are considered to be negligible, and the contact line is assumed to have a stationary circular or elliptical shape. In the absence of shear flow, the drop assumes a hydrostatic shape with constant mean curvature. Families of hydrostatic shapes, parameterized by the drop volume and aspect ratio of the contact line, are computed using an iterative finite-difference method. The results illustrate the effect of the shape of the contact line on the distribution of the contact angle around the base, and are discussed with reference to contact-angle hysteresis and stability of stationary shapes. The transient deformation of a drop whose viscosity is equal to that of the ambient fluid, subject to a suddenly applied simple shear flow, is computed for a range of capillary numbers using a boundary-integral method that incorporates global parameterization of the interface and interfacial regriding at large deformations. Critical capillary numbers above which the drop exhibits continued deformation, or the contact angle increases beyond or decreases below the limits tolerated by contact angle hysteresis are established. It is shown that the geometry of the contact line plays an important role in the transient and asymptotic behaviour at long times, quantified in terms of the critical capillary numbers for continued elongation. Drops with elliptical contact lines are likely to dislodge or break off before drops with circular contact lines. The numerical results validate the assumptions of lubrication theory for flat drops, even in cases where the height of the drop is equal to one fifth the radius of the contact line.

Contact Line Pinning and Depinning Prior to Rupture of an Evaporating Droplet in a Simulated Soil Pore

2020 ◽  
Author(s):  
Partha P. Chakraborty ◽  
Melanie M. Derby
Keyword(s):  
Contact Line ◽  
Pressure Difference ◽  
Liquid Droplet ◽  
Liquid Droplets ◽  
Water Contact ◽  
Marginal Rate ◽  
Vapor Interface ◽  
Hydrophobic Pore ◽  
Contact Line Pinning ◽  
Liquid Vapor

Abstract Altering soil wettability by inclusion of hydrophobicity could be an effective way to restrict evaporation from soil, thereby conserving water resources. In this study, 4-μL sessile water droplets were evaporated from an artificial soil millipore comprised of three glass (i.e. hydrophilic) and Teflon (i.e. hydrophobic) 2.38-mm-diameter beads. The distance between the beads were kept constant (i.e. center-to-center spacing of 3.1 mm). Experiments were conducted in an environmental chamber at an air temperature of 20°C and 30% and 75% relative humidity (RH). Evaporation rates were faster (i.e. ∼19 minutes and ∼49 minutes at 30% and 75% RH) from hydrophilic pores than the Teflon one (i.e. ∼24 minutes and ∼52 minutes at 30% and 75% RH) due in part to greater air-water contact area. Rupture of liquid droplets during evaporation was analyzed and predictions were made on rupture based on contact line pinning and depinning, projected surface area just before rupture, and pressure difference across liquid-vapor interface. It was observed that, in hydrophilic pore, the liquid droplet was pinned on one bead and the contact line on the other beads continuously decreased by deforming the liquid-vapor interface, though all three gas-liquid-solid contact lines decreased at a marginal rate in hydrophobic pore. For hydrophilic and hydrophobic pores, approximately 1.7 mm2 and 1.8–2 mm2 projected area of the droplet was predicted at 30% and 75% RH just before rupture occurs. Associated pressure difference responsible for rupture was estimated based on the deformation of curvature of liquid-vapor interface.

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