1 January - 30 June 1996

**Organisers **: Tom McLeish (Leeds), Anthony Pearson (Cambridge) and Ken Walters (Aberystwyth)

Many fluids of industrial, biological and environmental importance (e.g. molten plastics, salad dressings, whole blood, sinovial fluid, clay and cement slurries, volcanic lavas) respond in a complicated fashion when deformed. The reasons for this complexity can be traced back to their molecular structure, which may itself be very elaborate, to microscopic supramolecular structures into which they assemble themselves and to the fluid mechanical forces that act between molecules and structures.

Many theories and explanations for their behaviour have been developed, using the techniques of statistical mechanics, thermodynamics and continuum mechanics. However many of these theories only cover part of this complex behaviour and are not readily applicable to industrial, medical or geomechanical problems, where quantitative predictions are required.

The key concept for constitutive behaviour is a mathematical model embodying physical insight into the behaviour of a particular material. Covering the full range of behaviour of most systems involves modelling on a wide range of length and time scales. Much of the difficulty experienced in seeking complete explanations of behaviour is connected with passage from smaller to larger length scales; in embedding the rheological equation of state into the conservation equations governing mass, momentum and energy. Most of the mathematical problems that arise involve non-linear differential, integro-differential and integral equations: a full range of analytical and numerical techniques has to be employed to obtain solutions.

The aim of the Programme was to bring together experts in all these approaches; to confront the assumptions of one group with the predictions of another; to discover what underlying problems were preventing progress and whether an extension of conventional approaches could overcome this; to widen the horizons of all.

DCF programme ran in 1996 and was popular enough to have have a reunion DCF programme 10 years later. This has been called **DCF 10**.

A report of the programme can be found **here**

Other Reports are available under the left menu 'Publications'.