scholarly journals Reflections on the article “Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models and some new challenges” by Yulii D. Shikhmurzaev

2020 ◽  
Vol 229 (10) ◽  
pp. 1979-1987 ◽  
Author(s):  
Dieter Bothe
Keyword(s):  
Mathematical Models ◽  
Contact Line ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Sharp Interface ◽  
Contact Lines ◽  
Moving Contact ◽  
Moving Contact Lines ◽  
New Challenges ◽  
Litmus Test

Abstract We carefully consider the ‘litmus test’ proposed by Yulii D. Shikhmurzaev [Y.D. Shikhmurzaev, Eur. Phys. J. Special Topics 229, 1945 (2020)] in the context of the sharp-interface/sharp-contact line model.

scholarly journals Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models, accomplishments and new challenges

2020 ◽  
Vol 229 (10) ◽  
pp. 1945-1977 ◽  
Author(s):  
Yulii D. Shikhmurzaev
Keyword(s):  
Contact Angle ◽  
Mathematical Models ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Dynamic Wetting ◽  
Line Speed ◽  
Moving Contact ◽  
New Challenges ◽  
Litmus Test

Abstract After a brief overview of the ‘moving contact-line problem’ as it emerged and evolved as a research topic, a ‘litmus test’ allowing one to assess adequacy of the mathematical models proposed as solutions to the problem is described. Its essence is in comparing the contact angle, an element inherent in every model, with what follows from a qualitative analysis of some simple flows. It is shown that, contrary to a widely held view, the dynamic contact angle is not a function of the contact-line speed as for different spontaneous spreading flows one has different paths in the contact angle-versus-speed plane. In particular, the dynamic contact angle can decrease as the contact-line speed increases. This completely undermines the search for the ‘right’ velocity-dependence of the dynamic contact angle, actual or apparent, as a direction of research. With a reference to an earlier publication, it is shown that, to date, the only mathematical model passing the ‘litmus test’ is the model of dynamic wetting as an interface formation process. The model, which was originated back in 1993, inscribes dynamic wetting into the general physical context as a particular case in a wide class of flows, which also includes coalescence, capillary breakup, free-surface cusping and some other flows, all sharing the same underlying physics. New challenges in the field of dynamic wetting are discussed.

Sharp-interface limit of the Cahn–Hilliard model for moving contact lines

2010 ◽  
Vol 645 ◽  
pp. 279-294 ◽  
Author(s):  
PENGTAO YUE ◽  
CHUNFENG ZHOU ◽  
JAMES J. FENG
Keyword(s):  
Contact Line ◽  
Diffusion Length ◽  
Slip Length ◽  
Sharp Interface ◽  
Diffuse Interface ◽  
Contact Lines ◽  
Sharp Interface Limit ◽  
Interface Models ◽  
Moving Contact ◽  
Moving Contact Lines

Diffuse-interface models may be used to compute moving contact lines because the Cahn–Hilliard diffusion regularizes the singularity at the contact line. This paper investigates the basic questions underlying this approach. Through scaling arguments and numerical computations, we demonstrate that the Cahn–Hilliard model approaches a sharp-interface limit when the interfacial thickness is reduced below a threshold while other parameters are fixed. In this limit, the contact line has a diffusion length that is related to the slip length in sharp-interface models. Based on the numerical results, we propose a criterion for attaining the sharp-interface limit in computing moving contact lines.

Experimental study of rivulet formation on an inclined plate by fluorescent imaging

1999 ◽  
Vol 394 ◽  
pp. 339-354 ◽  
Author(s):  
M. F. G. JOHNSON ◽  
R. A. SCHLUTER ◽  
M. J. MIKSIS ◽  
S. G. BANKOFF
Keyword(s):  
Contact Line ◽  
Thin Liquid Film ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Fluorescent Imaging ◽  
Circulation System ◽  
Imaging Method ◽  
Inclined Plate ◽  
Moving Contact Line ◽  
Moving Contact

The instability of a two-dimensional moving contact line is studied for a thin liquid film flowing down an inclined plane, leading to the formation of rivulets. A fluorescent imaging method was developed to facilitate accurate measurement of the spacing between rivulets, tip velocity, three-dimensional shape and dynamic contact line. A fluid circulation system produced steady films at constant volumetric flux, in contrast to time-varying films at constant total volume, as in previous measurements. Comparisons are made with the existing data for constant-volume films, and with theoretical predictions for the wavelength of the rivulets formed at constant inlet flow rate. Data were also obtained for rivulet shapes, tip speeds and contact angles as functions of the angle of inclination of the plate and liquid Reynolds number.

Dynamic contact angles and hydrodynamics near a moving contact line

1993 ◽  
Vol 70 (18) ◽  
pp. 2778-2781 ◽  
Author(s):  
John A. Marsh ◽  
S. Garoff ◽  
E. B. Dussan V.
Keyword(s):  
Contact Line ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Moving Contact Line ◽  
Moving Contact

Moving contact lines on a two-dimensional rough surface

1985 ◽  
Vol 154 ◽  
pp. 1-28 ◽  
Author(s):  
Kalvis M. Jansons
Keyword(s):  
Contact Angle ◽  
Rough Surface ◽  
Rough Surfaces ◽  
Contact Angle Hysteresis ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Contact Lines ◽  
Stick Slip ◽  
Moving Contact ◽  
Moving Contact Lines

The dynamic contact angle for a contact line moving over a solid surface with random sparse spots of roughness is determined theoretically in the limit of zero capillary number. The model exhibits many of the observed characteristics of moving contact lines on real rough surfaces, including contact-angle hysteresis and stick-slip. Several types of rough surface are considered, and a comparison is made between periodic and random rough surfaces.

The spreading of surfactant-laden liquids with surfactant transfer through the contact line

2001 ◽  
Vol 440 ◽  
pp. 205-234 ◽  
Author(s):  
ENRIQUE RAMÉ
Keyword(s):  
Contact Line ◽  
Liquid Surface ◽  
Fluid Motion ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Moving Contact Line ◽  
Surface Diffusivity ◽  
Moving Contact ◽  
Pure Fluid ◽  
Surfactant Transfer

We examine the spreading of a liquid on a solid surface when the liquid surface has a spread monolayer of insoluble surfactant, and the surfactant transfers through the contact line between the liquid surface and the solid. We show that, as in surfactant-free systems, a singularity appears at the moving contact line. However, unlike surfactant-free systems, the singularity cannot be removed by the same assumptions as long as surfactant transfer takes place. In an attempt to avoid modelling difficulties posed by the question of how the singularity might be removed, we identify parameters which describe the dynamics of the macroscopic spreading process. These parameters, which depend on the details of the fluid motion next to the contact line as in the pure-fluid case, also depend on the state of the spread surfactant in the macroscopic region, in sharp contrast to the pure-fluid case where actions at the macroscopic scale did not affect material spreading parameters. A model of the viscous-controlled region near the contact line which accounts for surfactant transfer shows that, at steady state, some ranges of dynamic contact angles and of capillary number are forbidden. For a given surfactant–liquid pair, these disallowed ranges depend upon the actual contact angle and on the transfer flux of surfactant.We also examine a possible inner model which accounts for the transfer via surface diffusivity and regularizes the stress via a slip model. We show that the asymptotic behaviour of this model at distances from the contact line large compared to the inner length scale matches to the viscous-controlled region. An example of how the information propagates is given.

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.

Sign in / Sign up

Export Citation Format

Share Document