Capillary Effects and Industrial Problems
In this section, you can find information which could help you to see whether
theoretical results obtained already and those in the pipeline are relevant
to your problems and, if this is the case, to decide what would be
the best form of collaboration. If you need more information, you are welcome
to contact me at any time.
Are capillary effects really relevant to industrial processes?
In practically every industrial process which at some stage deals with
a liquid one comes across a situation where the free surface of the liquid
meets a solid boundary, thus forming the so-called three-phase-contact
line. Once formed, the contact line can, and in most cases should, move
along the solid surface leading to its `wetting' or `de-wetting'. The well-known
examples of industrially-related flows involving moving contact lines are
the spreading of films over solid substrates (the so-called `coating' flows
of different kind), interactions of drops and bubbles with solid walls,
fibres and particles (for example, in ink-jet printing and painting, filtering,
flotation, boiling, etc), flow of foams and emulsions, and many others.
Sketches of some processes are given below.
Figure 1. Sketches of industrial processes illustrating relevance of
capillary effects: curtain coating (a), ink-jet printing (b), boiling (c).
The basic feature of the flows with moving (or static) contact lines
known from experiments is that, once the contact lines appear, the whole
flow domain in the range of influence of capillary effects becomes dependent
on how the contact lines respond to the flow conditions and what (dynamic)
contact angle is formed between the free surface and the solid. Hence,
the smaller the size of the system in question, the more important this
In many cases, one has to deal with additional factors involved in the
coating process, such as the porosity of the solid substrate (paper industry),
surfactants (most of chemical industries), multicomponent nature of the
coating fluid (paints, composites), external electric field, thermal effects
etc, and combinations of these factors. Since in industrial applications
the materials used are usually determined by the desired properties of
the final product, flow conditions and external fields become the main
Can the problem be addressed in a conventional way?
Although the necessity to model processes associated with moving contact
lines is obvious, an attempt to do so on the basis of the existing knowledge
accumulated in the area of fluid mechanics encounters a paradox: the corresponding
mathematical problems have in principle no solutions. This problem - known
in the literature as the famous `moving contact-line problem' - has been
the subject of intensive research over the last forty years. This effort
has led to a disapponting conclusion: although there are many `conventional'
ways to remove the above paradox, the resulting models
are in a qualitative conflict with what is observed in experiments.
Thus, to put it pictorially, the gap between theory and experiment remains
Can semi-empirical models help?
An important aspect of the problem is that empirical approaches, which
are very often successful for industrial purposes at least in a limited
range of the parameter space, are of little value in the situations involving
the process of dynamic wetting. The reason is, firstly, that the details
of wetting, which determine the quality of the final product, do not manifest
themselves through macroscopic parameters which could be put into an empirical
model. Secondly, experiments on the influence of flow geometry on dynamic
wetting show that this approach cannot work in principle. And in any case
an empirical model would not allow one to incorporate external influences
(thermal and electric fields), which are gradually becoming the key operational
The situation today
The progress made in recent years in the modelling of dynamic wetting
is associated with a new theory [1-6] which addresses the moving contact-line
problem as a particular case of a more general physical phenomenon, namely
the interface disappearance-formation process. This approach allows one
not only to solve the moving contact-line problem (as a by-product), but
also to remove its `eccentricity' by putting it into the general context
of modern physics and to verify its predictions independently in different
ways. By now, the theory has passed the `academic' stage, where the goal
was to validate (or otherwise) the theory by comparing its predictions
with the corresponding experiments for model flows.
It has been found that in all situations studied so far, the theory
is in excellent agreement with experimental observations
[1, 4, 5]. In particular, the theory allows one to describe steady coating
processes (such as roll or dip tank coating) without using any empirical
correlations. The study of a quasi-steady regime of the drop spreading
and the subsequent comparison of the results with experiments  confirmed
the applicability of the theory to this type of processes. The work on
essentially unsteady regimes of flow, which could lead to a comprehensive
description, for example, of defect formation in the process of coating
is currently under way. The first results obtained in this direction 
suggest that for unsteady processes the dependence of the dynamic contact
angle on the contact-line speed cannot be prescribed in principle even
for simple flow domains. The theory also predicts that the dynamic contact
angle will depend on the flow field/geometry so that ad hoc and
empirical assumptions addressing its behaviour will not allow one to make
any conclusions about the role of hydrodynamic factors. This
feature has been recently discovered in experiments [8, 9] and is of
crucial importance to industrial operations with fluids.
The results already obtained in the framework of the new theory made
it possible to enter a new stage, namely the application of the theory
to industrially-oriented research. Two projects of such a kind are currently
Shikhmurzaev, Y. D. 1993 The moving contact line on a smooth solid surface.
J. Multiphase Flow 19, 589-610.
Shikhmurzaev, Y. D. 1994 Mathematical modeling of wetting hydrodynamics.
Dyn. Res. 13, 45-64.
Shikhmurzaev, Y. D. 1996 Dynamic contact angles and flow in vicinity of
moving contact lines. AIChE J. 42, 601-612.
Shikhmurzaev, Y. D. 1997 Spreading of drops on solid surfaces in a quasi-static
regime. Phys. Fluids 9, 266-275.
Shikhmurzaev, Y. D. 1997 Moving contact lines in liquid/liquid/solid systems.
Fluid Mech. 334, 211-249.
Shikhmurzaev, Y. D. 1998 On cusped interfaces.
J. Fluid Mech. 359,
Billingham, J. 1997 The unsteady motion of three phase contact lines. In
Symposium on Non-Linear Singularities in Deformation and Flow (D. Durban
and J. R. A. Pearson, eds) Kluwer Acad. Publ., 99-110.
Blake, T. D., Clarke, A. and Ruschak, K. J. 1994 Hydrodynamics assist of
dynamic wetting. AIChE J. 40, 229-242.
Blake, T. D., Bracke, M. and Shikhmurzaev, Y. D. 1999 Experimental evidence
of nonlocal hydrodynamic influence on the dynamic contact angle. Phys.
Fluids 11, 1995-2007.