Review on the Dynamics of Isothermal Liquid Bridges

2019 ◽  
Vol 72 (1) ◽  
Author(s):  
José M. Montanero ◽  
Alberto Ponce-Torres
Keyword(s):  
Nonlinear Behavior ◽  
Forced Oscillations ◽  
Liquid Bridges ◽  
Contact Lines ◽  
Surfactant Monolayers ◽  
Weakly Nonlinear ◽  
Nonlinear Motion ◽  
Bridge Problem ◽  
Equilibrium Shapes ◽  
Streaming Flows

Abstract In this review, we describe both theoretical and experimental results on the dynamics of liquid bridges under isothermal conditions with fixed triple contact lines. These two major restrictions allow us to focus on a well-defined body of literature, which has not as yet been reviewed in a comprehensive way. Attention is mainly paid to liquid bridges suspended in air, although studies about the liquid–liquid configuration are also taken into account. We travel the path from equilibrium to nonlinear dynamics of both Newtonian liquid bridges and those made of complex fluids. Specifically, we consider equilibrium shapes and their stability, linear dynamics in free and forced oscillations under varied conditions, weakly nonlinear behavior leading to streaming flows, fully nonlinear motion arising during stretching and breakup of liquid bridges, and problems related to rheological effects and the presence of surfactant monolayers. Although attention is mainly paid to fundamental aspects of these problems, some applications derived from the results are also mentioned. In this way, we intend to connect the two approaches to the liquid bridge problem, something that both theoreticians and experimentalists may find interesting.

Stretching liquid bridges with moving contact lines: The role of inertia

2011 ◽  
Vol 23 (9) ◽  
pp. 092101 ◽  
Author(s):  
Shawn Dodds ◽  
Marcio Carvalho ◽  
Satish Kumar
Keyword(s):  
Liquid Bridges ◽  
Contact Lines ◽  
Moving Contact ◽  
Moving Contact Lines

The dynamics of three-dimensional liquid bridges with pinned and moving contact lines

2012 ◽  
Vol 707 ◽  
pp. 521-540 ◽  
Author(s):  
Shawn Dodds ◽  
Marcio S. Carvalho ◽  
Satish Kumar
Keyword(s):  
Contact Line ◽  
Liquid Bridge ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Liquid Bridges ◽  
Contact Lines ◽  
Flat Surfaces ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
Contact Line Friction

AbstractLiquid bridges with moving contact lines are relevant in a variety of natural and industrial settings, ranging from printing processes to the feeding of birds. While it is often assumed that the liquid bridge is two-dimensional in nature, there are many applications where either the stretching motion or the presence of a feature on a bounding surface lead to three-dimensional effects. To investigate this we solve Stokes equations using the finite-element method for the stretching of a three-dimensional liquid bridge between two flat surfaces, one stationary and one moving. We first consider an initially cylindrical liquid bridge that is stretched using either a combination of extension and shear or extension and rotation, while keeping the contact lines pinned in place. We find that whereas a shearing motion does not alter the distribution of liquid between the two plates, rotation leads to an increase in the amount of liquid resting on the stationary plate as breakup is approached. This suggests that a relative rotation of one surface can be used to improve liquid transfer to the other surface. We then consider the extension of non-cylindrical bridges with moving contact lines. We find that dynamic wetting, characterized through a contact line friction parameter, plays a key role in preventing the contact line from deviating significantly from its original shape as breakup is approached. By adjusting the friction on both plates it is possible to drastically improve the amount of liquid transferred to one surface while maintaining the fidelity of the liquid pattern.

scholarly journals Weakly nonlinear oscillations of nearly inviscid axisymmetric liquid bridges

1996 ◽  
Vol 328 ◽  
pp. 95-128 ◽  
Author(s):  
José A. NicoláS ◽  
José M. Vega
Keyword(s):  
Boundary Layer ◽  
Thermocapillary Convection ◽  
Nonlinear Oscillations ◽  
Amplitude Equation ◽  
Liquid Bridges ◽  
Small Oscillations ◽  
Weakly Nonlinear ◽  
Steady Streaming ◽  
Weakly Nonlinear Analysis ◽  
Axial Vibrations

A weakly nonlinear analysis is presented of the small oscillations of nearly inviscid liquid bridges subjected to almost resonant axial vibrations of the disks. An amplitude equation is derived for the evolution of the complex amplitude of the oscillations that exhibits hysteresis and period doublings. We also analyse the steady streaming in the bulk forced by the oscillatory boundary layers near the disks; the boundary layer near the free surface produces no forcing terms. In particular some experimentally observed patterns are explained, and some new, non-observed ones are predicted. We conclude that the structure of this steady flow is not the appropriate one to counterbalance steady thermocapillary convection, but our results indicate how to get the desired counterbalancing effect.

scholarly journals Thick drops climbing uphill on an oscillating substrate

2018 ◽  
Vol 840 ◽  
pp. 131-153 ◽  
Author(s):  
J. T. Bradshaw ◽  
J. Billingham
Keyword(s):  
Contact Angle ◽  
Contact Line ◽  
Contact Angle Hysteresis ◽  
Contact Angles ◽  
Boundary Integral ◽  
Static Contact Angle ◽  
Rise Velocity ◽  
Contact Lines ◽  
Weakly Nonlinear ◽  
Static Contact

Experiments have shown that a liquid droplet on an inclined plane can be made to move uphill by sufficiently strong, vertical oscillations (Brunet et al., Phys. Rev. Lett., vol. 99, 2007, 144501). In this paper, we study a two-dimensional, inviscid, irrotational model of this flow, with the velocity of the contact lines a function of contact angle. We use asymptotic analysis to show that, for forcing of sufficiently small amplitude, the motion of the droplet can be separated into an odd and an even mode, and that the weakly nonlinear interaction between these modes determines whether the droplet climbs up or slides down the plane, consistent with earlier work in the limit of small contact angles (Benilov and Billingham, J. Fluid Mech. vol. 674, 2011, pp. 93–119). In this weakly nonlinear limit, we find that, as the static contact angle approaches $\unicode[STIX]{x03C0}$ (the non-wetting limit), the rise velocity of the droplet (specifically the velocity of the droplet averaged over one period of the motion) becomes a highly oscillatory function of static contact angle due to a high frequency mode that is excited by the forcing. We also solve the full nonlinear moving boundary problem numerically using a boundary integral method. We use this to study the effect of contact angle hysteresis, which we find can increase the rise velocity of the droplet, provided that it is not so large as to completely fix the contact lines. We also study a time-dependent modification of the contact line law in an attempt to reproduce the unsteady contact line dynamics observed in experiments, where the apparent contact angle is not a single-valued function of contact line velocity. After adding lag into the contact line model, we find that the rise velocity of the droplet is significantly affected, and that larger rise velocities are possible.

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