# Self-funded PhD opportunities

## Mathematical Modelling of Brewing Coffee

• Application end date: Saturday 1 July 2017
• Funding Availability: Self-funded PhD students only
• Department: Mathematics
• PhD Supervisor: William Lee, Jamie Foster & Andrew Osbaldestin

This project will develop and analyse mathematical models of brewing coffee using homogenisation, asymptotic analysis and finite element methods.

Coffee is one of the most popular beverages world wide and the global market in coffee brewing equipment is worth billions of pounds per year. Despite this the science of brewing coffee is poorly understood leading making it difficult to design coffee machines that robustly produce high quality coffee. Currently there is a high degree of trial and error in the design of coffee machines.

Coffee brewing is complex on three fronts. Firstly there is chemical complexity – coffee is in fact a solution of over a thousand different chemicals. Secondly there is geometric complexity, especially in filter coffee brewing the coffee bed has a complex shape. Finally, there are multiple scales involved individual coffee cells are micron sized, grains are millimetre sized and the coffee bed in centimetre sized. This PhD will focus on addressing the multiscale nature of the system and complex geometries – as yet there is little experimental data available that can be used to address the question of chemical complexity.

In this project the multiscale nature of the system will be addressed using homogenisation, a technique for multiscale modelling based on two-scale perturbation theory. This will be used to derive a system of partial differential equations describing coffee extraction in terms of variables such as size distribution of coffee grains, flow rate of water through the coffee and porosity and permeability of the coffee bed.

These equations will be used to investigate three brewing systems. Fixed bed coffee extraction with flow rates and particle size distributions appropriate for filter coffee brewing and espresso brewing and coffee extraction from a bed geometry seen in conical filters. Nondimensionlisation and asymptotic analysis will also be used to analyse and reduce the system of equations. In reduced form the equations should give a clear interpretation of the dominant physics of extraction for these systems and also allow technology transfer to practitioners. Solutions of the reduced equations will be checked by also solving the equations numerically using the finite element method.

The PhD student undertaking this research will be part of the newly formed Industrial Mathematics group at the University of Portsmouth and will benefit from opportunities to meet with industrialists collaborating with the group and to contribute to the group's research activities including collaborative research with Industry. Participation in European Study Groups with Industry (ESGIs) and ECMI Modelling Weeks will be actively encouraged and form a key part of the researcher's training.

### How to apply

To apply or make an enquiry, please visit postgraduate research: Mathematics and Physics

Applications should use our standard application forms and follow the instructions given under the ‘Research Degrees’ heading on the following webpage: http://www.port.ac.uk/application-fees-and-funding/applying-postgraduate/#rd

When applying please note the project code: MPHY3310217

Funding Notes: Home/EU applicants only. Please use the online application form and state the project code and studentship title in the personal statement section.

An appropriate first or upper second class honours degree of any United Kingdom university or a recognised equivalent non-UK degree of the same standard honours degree or equivalent in a relevant subject or a master’s degree in an appropriate subject. Exceptionally, equivalent professional experience and/or qualifications will be considered.