# BTG Travel Grants Second Call - Funds Awarded

The Bridging the Gap board granted three travel awards in the second round of calls. We were impressed with the variety and quality of the proposals. See below for an overview of the projects funded.

### Modeling Biological Systems - Serafim Bakalis, School Of Chemical Engineering

Eating and digestion is a problem that genuinely involves a range of scales and forces. Food is eaten (scale of cm) broken to smaller pieces mixed with bile fluids and finally nutrients are absorbed through the intestinal membrane (scale of nm).

Engineering sciences have generated a range of fluid dynamics models able to predict mixing and flow behaviour in processing equipment. While the physical phenomena occurring in- vivo are to some extend similar (e.g. mixing of digesta with bile salts) the time scales and overall complexity of the problem make an engineering approach non trivial, as this is a multiscale flow problem involving mixing, reactions, physical interactions with mucus layer, active transport etc. Furthermore, even a fluid dynamic approach is non trivial as this is a genuine multiphase flow of time dependent properties and geometries involving a range of scales. The complexity of the system will require use of the computational facilities within the University of Birmingham.

Typically there is fragmentation of skills and resources among traditional sciences. As such formulation of a problem and identification of critical steps would be the first step required towards an integrated multiscale, validated model. Significant simplifications will have to be made to develop a working model. For example the gastrointestinal tract has a length of about 6 m and this would not be possible to be implemented in a numerical simulation. There will be a number of parameters in the model (e.g. frequency of peristalsis and segmentation movements, permeability of active substances through the mucus layer and the epithelial wall) the values of which will be have to be optimised during comparison with experimental data (e.g. Taylor, Wolever et al. 1980). This will require non trivial optimisation techniques to have be used.

### Simulation of flocculation in water treatment using a coupled CFD / PBM approach - John Bridgeman, Civil Engineering

The size and strength of particles play a major role in the removal of contaminants from water in physico-chemical treatment processes. These particles (or flocs) are generally formed from the reaction of inorganic coagulants with suspended solids or organic matter found in most surface water sources. The main solid separation processes are based on the removal of flocs using either flotation or sedimentation processes. Therefore changes in floc characteristics can significantly affect floc removal. Despite the importance of optimized coagulation and flocculation for both water quality and operational efficiency purposes, flocculator design has traditionally been based on empiricism due to a lack of accurate flocculation models. Previous work has provided a quantitative analysis of floc formation. Bridgeman has furthered this work by using computational fluid dynamics (CFD) on an HPC facility to further our understanding of the hydrodynamic environments to which flocs are exposed, and postulated floc breakage thresholds for certain types of floc. Further work is now required to consider the flocculation process itself and to assess the impact of turbulence on the floc formation and breakage processes. These evolutionary and destructive processes which govern floc growth and breakage can be simulated via the use of population balance models (PBM) in conjunction with CFD. Nopens is an acknowledged global expert in PBM (organiser of the last two international PBM conferences; guest editor of two special issues of Chem Eng Sci on the topic of PBM).

Bridgeman and Nopens wish to develop an interdisciplinary, cross-institutional research proposal, the objective of which would be to combine data arising from experimental and numerical techniques to investigate the mechanisms involved in the flocculation process and, in particular, the inter-relationships between fluid dynamics and water chemistry, in order to develop accurate numerical models of the flocculation process itself (including floc growth, breakage and trajectory). Whilst previous work in the field has examined optimisation of flocculation chemistry, this novel and innovative work will consider both the chemistry and the hydrodynamic environment within which the processes occur. The deep, fundamental insight into the relationships between water chemistry and hydrodynamics gained from this work will then facilitate the development of novel design criteria for optimized low energy input flocculators which will enable water utilities to derive greater efficiencies by reducing operational expenditure and also reducing resource usage.

### Inverse Problems in Cell Biology - B. Tomas Johansson, School of Mathematics

In the exocytotic fusion pore opening of certain cells (such as mast cells in the beige mouse) the concentration of biogenic amines can be assumed governed by the heat equation. To model the opening of the cell over time a certain mixed boundary value problem for the heat equation has to be considered where the boundary conditions change in time. This is a challenging problem from a mathematical point of view. We shall undertake mathematical investigations about the asymptotic expansions of the solution to such problems and investigate numerical schemes for calculating an approximate solution. Moreover, it is intended to investigate certain inverse problems such as identifying missing parameters in the model. This type of inverse parameter identification problems are usually ill-posed i.e. unstable with respect to noisy measurements and therefore certain methods for the stable calculations of the relevant biological parameters will be proposed and investigated.