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Details of Grant 

EPSRC Reference: EP/T021365/1
Title: Feedback Control of Deformable Bubbles
Principal Investigator: Thompson, Dr AB
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: Mathematics
Organisation: University of Manchester, The
Scheme: New Investigator Award
Starts: 01 October 2020 Ends: 30 September 2023 Value (£): 234,174
EPSRC Research Topic Classifications:
Continuum Mechanics Control Engineering
Fluid Dynamics
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
25 Feb 2020 EPSRC Mathematical Sciences Prioritisation Panel February 2020 Announced
Summary on Grant Application Form
Many physical objects can, in principle, balance perfectly in a number of different orientations, but only some of these orientations are stable. For example, if we try to balance a bicycle upright, it will always fall to one side or another - we say that this is an unstable steady state. We can prevent the bicycle from falling over by continually observing the system and making frequent adjustments based on the latest observations. These adjustments and observations are called feedback control, and if chosen carefully will enable the system to remain in unstable steady states.

In this research project, we will use feedback control in the form of "control-based continuation" to investigate the unstable steady states of a deformable air bubble moving through a very viscous fluid. This is a classical problem in applied mathematics, and has applications in microfluidic devices, oil extraction and airway reopening. Previous experiments and mathematical modelling for this system have shown that the bubble can propagate in a wide range of different shapes, but without feedback control these experiments were unable to definitively identify the unstable possibilities and hence to fully test the validity of the model predictions.

The idea of control-based continuation is to apply feedback control towards a wide range of different target states, and to seek in particular target states where no input is required for the bubble to remain exactly at equilibrium. These states would be steady states even without any control, and are stabilised by the real-time feedback. Importantly, the control-based continuation process can be carried out equally well in an experimental setup or in a numerical simulation. In this project, we will use numerical testing and theoretical analysis to develop control-based continuation routines that can work when subject to realistic constraints, and will carry out simple experiments to show this succeeding in practice.

The propagation of a deformable air bubble is a rich scientific problem and has been studied using different forms of applied mathematics for many years. However, the feedback control techniques we develop here should ultimately be applicable across a much broader range of systems. These techniques would be particularly important for systems where theoretical models are not yet developed or are very complicated (such as blood cells and capsules), but where we would still like to understand and characterise the body motion or interface deformation in fluid flow.

Key Findings
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Organisation Website: http://www.man.ac.uk