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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 feature becomes.

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 operational tools.

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 the same.

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 tools.

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 [4] 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 [7] 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 under way.


  1. Shikhmurzaev, Y. D. 1993 The moving contact line on a smooth solid surface. Intl J. Multiphase Flow 19, 589-610.
  2. Shikhmurzaev, Y. D. 1994 Mathematical modeling of wetting hydrodynamics. Fluid Dyn. Res. 13, 45-64.
  3. Shikhmurzaev, Y. D. 1996 Dynamic contact angles and flow in vicinity of moving contact lines. AIChE J. 42, 601-612.
  4. Shikhmurzaev, Y. D. 1997 Spreading of drops on solid surfaces in a quasi-static regime. Phys. Fluids 9, 266-275.
  5. Shikhmurzaev, Y. D. 1997 Moving contact lines in liquid/liquid/solid systems. J. Fluid Mech. 334, 211-249.
  6. Shikhmurzaev, Y. D. 1998 On cusped interfaces. J. Fluid Mech. 359, 313-328.
  7. Billingham, J. 1997 The unsteady motion of three phase contact lines. In IUTAM Symposium on Non-Linear Singularities in Deformation and Flow (D. Durban and J. R. A. Pearson, eds) Kluwer Acad. Publ., 99-110.
  8. Blake, T. D., Clarke, A. and Ruschak, K. J. 1994 Hydrodynamics assist of dynamic wetting. AIChE J. 40, 229-242.
  9. 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.