Continuum Mechanics PhD projects
This page provides a (partial) list of specific (and not so specific) PhD projects currently offered around the Continuum Mechanics topic.
Identifying an interesting, worthwhile and doable PhD project is not a trivial task since it depends crucially on the interests and abilities of the student (and the supervisor!) The list below therefore contains a mixture of very specific projects and fairly general descriptions of research interests across the School. In either case you should feel free to contact the potential supervisors to find out more if you're interested.
You should also explore the School's research groups' pages, and have a look around the homepages of individual members of staff to find out more about their research interests. You may also contact us for general enquiries.
Title 
Fluidstructure interaction effects in the sedimentation of thin elastic sheets 

Group  Continuum Mechanics 
Supervisors 

Description 
There is much current interest in socalled twodimensional materials The aim of this project is to perform a systematic study of  the effect of the sheets' aspect ratio; long narrow sheets are  the effect of wrinkling instabilities and the development of The focus of this specific project is on computational/semianalytical
COSUPERVISORS: Professor Anne Juel (School of Physics and Astronomy) START DATE: September 2018 (or as soon as possible thereafter) OTHER ASSOCIATED PROJECT AREAS: Physics FUNDING: Funding is available and would provide fees and maintenance DEADLINE: Applications are accepted at any time until the position 
Title 
Bubble dynamics in confined geometries 

Group  Continuum Mechanics 
Supervisors  
Description 
The motion of deformable bubbles, drops, capsules and cells surrounded by viscous fluid and confined in a narrow channel has applications in microfluidic devices and labonachip design. When viewed from above, the motion often appears two dimensional, suggesting that we might be able to use two dimensional, depthaveraged models to predict, design and control system behaviour. Depthaveraged models are known to be accurate in some situations, such as when the bubble is very flattened and far from any walls, and where thin films are relatively passive. However, the typical assumptions break down if two bubbles are very close to each other (e.g. coalescence or breakup), or to walls, constrictions or obstacles, when it highly likely that threedimensional effects come into play. Furthermore, the typical depthaveraged model is of lower order and dimension than the Stokes equations and hence neglects certain free boundary effects. The aim of this project is to establish the limits of 2D modelling, and to determine how we can extend our models to be valid in these extreme scenarios. This project will involve asymptotic analysis, model development, finite element computations of two or three dimensional systems in oomphlib, and likely also collaborations with experimentalists in the Manchester Centre for Nonlinear Dynamics. 
Title 
Thermoviscoacoustic metamaterials for underwater applications 

Group  Continuum Mechanics 
Supervisor  
Description 
The ability to control underwater noise has been of practical interest for decades. Such noise, radiating from e.g. offshore wind farms, turbines, and merchant vessels, frequently needs to be attenuated artificially given the close proximity of its generation to sensitive marine environments for example. Over the last century a number of materials have been designed to assist with underwater noise attenuation. However, recently there has been an explosion of interest in the topic of acoustic metamaterials and metasurfaces. Such media have special microstructures, designed to provide overall (dynamic) material properties that natural materials can never hope to attain and lead to the potential of negative refraction, wave redirection and the holy grail of cloaking. Many of the mechanisms to create these artificial materials rely on the notion of resonance, which in turn gives rise to the possibility of low frequency sound attenuation. This is extremely difficult to achieve with normal materials. The mechanisms of sound attenuation, i.e. thermal and viscous, have not yet been properly understood for the many metamaterials under study, particularly in an underwater context. The aim of this project is to study this aspect via mathematical analysis and then to optimize designs in order to design and employ metamaterials for use in underwater noise reduction applications. Although there has been some initial interest over the last few years in the “inair” context, the parameter regime underwater gives rise to new effects that need to be explored and understood thoroughly. Initially canonical geometries such as simple apertures and infinite and semiinfinite ducts shall be considered before moving on to more complex, realistic scenarios and geometries where resonance plays a key role. Mathematical modelling using the method of matched asymptotics shall be employed. This is ideally suited to the scenarios considered given the low frequency regime. Comparisons shall be drawn with direct numerical simulations using finite element methods in e.g. COMSOL. 
Title 
Fluid Mechanics of Cleaning and Decontamination 

Group  Continuum Mechanics 
Supervisor  
Description 
Cleaning and decontamination processes are important in many applications: from the daily chores of doing the dishes (with or without a dishwasher), to ensuring clean hygiene in hospitals, the food industry, or pharmaceutical companies. Although a lot of research has been done in chemistry and chemical engineering to improve detergents and cleaning devices, much less work has been done on the modelling of the underlying physical and chemical processes. In some cleaning applications, such as the neutralisation of toxic chemicals after a spill, it is crucial to avoid using strong mechanical forces in order to prevent the dispersion of the toxic material in the environment. Instead, a localised dissolution process, aided by chemical reactions neutralising the material, is used. This PhD project will investigate the advection, diffusion and reaction processes involved in this scenario. Through a combination of experiments and modelling work the student will study the influence of flow properties: such as the Reynolds number and the Péclet number; geometry: whether the material is attached to a permeable or impermeable surface; and chemical properties such as solubility, reactivity and diffusivity. This project is directly motivated by industrial applications and will suit candidates interested in using mathematical approaches to solve real challenges. Suitable candidates should have experience in the lab or a keen interest to support theoretical work in fluid dynamics by experimental evidence. Reference: Landel, Thomas, McEvoy & Dalziel (2016). Convective mass transfer from a submerged drop in a thin falling film, Journal of Fluid Mechanics, 789: 630.

Title 
Turbulent particleladen jets 

Group  Continuum Mechanics 
Supervisors  
Description 
Turbulent particleladen jets are relevant to many geophysical and industrial applications: from volcanic eruptions, to sediment resuspension, fluidisation processes and chemical reactors. Much work has been done on the dilute regime of these twophase flows, where the particles have a small impact on the fluid and can often be considered as passive tracers. In this experimental project, we focus on the poorly understood dense regime, where the coupling between the solid particles and the fluid is more complex. Many fundamental questions, of high relevance to the applications mentioned above, are still unresolved. This project will explore the impact of the particle density on turbulent entrainment processes. Entrainment processes during an explosive volcanic eruption have a considerable impact on the extent of the damages. They determine whether the eruption will collapse and form a pyroclastic flow, with local implications, or whether the eruption column will rise and form an ash cloud spreading over extended regions, such as in the case of the 2010 eruption of the Icelandic volcano Eyjafjallajökul. This project will also explore the effect on mixing processes, which are very important for instance in chemical reactors where the efficiency of the reaction depends strongly on the efficiency of the mixing. These dense particleladen jets are still poorly understood due to the considerable challenges faced analytically and numerically. Technical difficulties have also prevented progress on the experimental side for a long time. New experimental techniques, based on novel experimental design and imaging techniques, recently developed in the laboratory have allowed to probe much further into the complex dynamics of these dense particle laden jet. The main goal of this project is to pursue the development of these techniques in order to address the questions on entrainment and mixing described above. The project is suitable for an enthusiastic and creative candidate who has some experience in experimentation and good knowledge in fluid mechanics. Some knowledge in imaging analysis technique is desired but not necessary. The motivation and readiness of the candidate to learn new techniques and develop them to explore fundamental scientific questions will be key to the success of this project. 
Title 
Interactions between rocks and ice 

Group  Continuum Mechanics 
Supervisor  
Description 
Many glaciers are covered by a debris layer whose presence has multiple, competing effects on the glacier's melt rate. The debris layer shields the ice from incoming solar radiation and thus reduces its melt rate. However, since the albedo of the debris layer is much smaller than that of the ice, the debris layer is heated up very rapidly by the solar radiation, an effect that is likely to increase the melt rate. The project aims to develop theoretical/computational models to study how solid objects (rocks) which are placed on (or embedded in) an ice layer affect the ice's melt rate. The work will employ (and contribute to) the objectoriented multiphysics finiteelement library oomphlib, developed by M. Heil and A.L. Hazel and their collaborators, and available as open source software at http://www.oomphlib.org. The project would suit students with an interest in mathematical modelling, continuum mechanics and scientific computing and will be performed in close collaborations with Glaciologists at the University of Sheffield and the Bavarian Academy of Science. 
Title 
Plant tissue mechanics 

Group  Continuum Mechanics 
Supervisor  
Description 
Plant growth arises through the coordinated expansion of individual cells, allowing a plant to adapt to its environment to harness light, water and essential nutrients. Growth is driven by the high internal turgor pressure of cells and is regulated by physical and biochemical modifications of plant cell walls. Many features of this immensely complex process remain poorly understood, despite its profound societal and environmental importance. Mathematical models describing the mechanical properties of a growing plant tissue integrate features ranging from molecular interactions within an individual cell wall to the expansion, bending or twisting of a multicellular root or stem. Building on current biological understanding, this project will address the development and analysis of new multiscale models for plant tissues, exploiting a variety of computational and asymptotic techniques. Background references:

Title 
Flow and transport in the placenta 

Group  Continuum Mechanics 
Supervisor  
Description 
The placenta provides an interface beween fetal and maternal blood, supplying essential nutrients to the growing fetus. Within the placenta, fetal blood is confined to a treelike network of blood vessels that are bathed in a pool of maternal blood. The placenta's effectiveness as a transporter of oxygen, glucose, and other molecules is critically determined by its complex geometric structure; this may be compromised in disease, with adverse consequences for fetal growth and development. This project will build on recent studies of the maternal circulation [13], developing analogies with models flow through porous media and exploring new multiscale approximation techniques. The project offers opportunities for analysis, computation and interaction with experimentalists. References:

Title 
Microstructural models of the constitutive behaviour of soft tissue 

Group  Continuum Mechanics 
Supervisors  
Description 
Soft tissue such as tendon, ligament, skin, and the brain possess complex nonlinear viscoelastic constitutive behaviour which arises due to the intricate microstructures inherent in such materials. The majority of existing models for the constitutive behaviour of soft tissue are phenomenological so that the parameters involved in the model are not derivable from experiments. In this project the objective is to build models that are based on the microstructure and we will liaise with experimentalists, particularly those in imaging science, in order to ensure that the parameters involved can be directly measured. This project would suit those with a strong background in continuum mechanics and modelling and although not essential some background knowledge in nonlinear elasticity would be useful. 
Title 
Environmental fluid mechanics 

Group  Continuum Mechanics 
Supervisor  
Description 
Many problems of environmental significance require the effective prediction of particulate (contaminant) transport in a fluid system (which constitutes a `twophase' fluid/particle problem). The primary focus of this project is a suspension of solid particles (dust/ash) in a viscous incompressible fluid. Most practical cases of interest have particles that are typically fractions of a millimetre in size, but still occupy a nonsmall fraction of the total mixture mass and exist in large numbers. The simultaneous treatment of all individual particles (and the correspondingly complicated fluid domain) is computationally impractical, a state of affairs that will remain for the foreseeable future. Furthermore, the behaviour of a single particle cannot be solved in isolation of the other particles, owing to particleparticle interactions through the motion of the interstitial fluid, or by direct particle collisions at high concentration levels. In such cases, both phases of the mixture exchange momentum with the other, so that the fluid motion and the particle motion remain coupled together. Furthermore, the presence of bounding surfaces for the fluid mixture can have crucial consequences for the structural and temporal development of the flow and the distribution of suspended material. This project aims to continue the development of existing macro scale models, in which both phases are treated as coexisting (coupled) continua, through a combination of analytical and computational methods. 
Title 
Stability and separation in R>>1 flows 

Group  Continuum Mechanics 
Supervisor  
Description 
I have several projects available in the area of high Reynolds number flows, including the study of laminar separation and stability of thin films, cavity flows, breakup of separation bubbles, crossflow instability. The work can be theoretical, numerical or a mixture of both. 
Title 
Fractional differential equations and anomalous transport 

Group  Continuum Mechanics 
Supervisor  
Description 
This project is concerned with anomalous transport, which cannot be described by standard calculus. Instead it requires the use of fractional differential equations involving fractional derivatives of non integer order. This is a new, exciting area of research because anomalous transport is a widespread natural phenomenon. Examples include flight of albatross, stock prices, human migration, social networks, transport on fractal geometries, proteins on cell membranes, bacterial motion, and signalling molecules in the brain. 
Title 
Mathematical theory of diffraction 

Group  Continuum Mechanics 
Supervisor  
Description 
There is a long history of mathematicians working on canonical diffraction (or scattering) problems. The mathematical theory of diffraction probably started with the work of Sommerfeld at the end of the 19th century and his famous solution to the diffraction of acoustic waves by a solid halfplane. Since, some very ingenious mathematical methods have been developed to tackle such problems. One of the most famous being the WienerHopf technique. 
Title 
Combustion instabilities 

Group  Continuum Mechanics 
Supervisor  
Description 
Combustion is essential to energy generation and transport needs, and will remain so for the foreseeable future. Mitigating its impact on the climate and human health, by reducing its associated emissions, is thus a priority. One suggested strategy to reduce NOx is to operate combustors at lean conditions. Unfortunately, combustion instability is more likely to occur in the lean regime, and may have catastrophic consequences on the components of combustion chambers, such as vibrations and structural fatigue. Ramjet engines, rocket engines and in general any type of gas turbine engines may be subject to this detrimental instability. The ability to predict and control the instability is crucial for implementing the lean burn strategy. Combustion instability involves an intricate interplay of several key physical processes, which take place in regions of different length scales. Due to this multiscale, multiphysics nature of the problem, direct numerical simulations of realistic combustors are extremely challenging. For this reason, simplified mathematical models capturing qualitatively and quantitatively the main characteristics of combustion instability are essential. In particular, by exploiting the scale disparity, systematic asymptotic analyses may be carried out to derive relevant models on first principles, and to provide guidance for developing reliable and efficient numerical algorithms. 
Title 
Complex deformations of biological soft tissues 

Group  Continuum Mechanics 
Supervisors  
Description 
The answers to many open questions in medicine depend on understanding the mechanical behaviour of biological soft tissues. For example, which tendon is most appropriate to replace the anterior cruciate ligament in reconstruction surgery? what causes the onset of aneurysms in the aorta? and how does the mechanics of the bladder wall affect afferent nerve firing? Current work at The University of Manchester seeks to understand how the microstructure of a biological soft tissue affects its macroscale mechanical properties. Most of the work to date has focused on simple deformations (e.g. longitudinal extension under tension) for which analytical solutions can be found. However, the geometry and deformation of many soft tissues in vivo is sufficiently complex to prohibit analytical solutions. 
Title 
Mathematical Combustion and Flame Instabilities 

Group  Continuum Mechanics 
Supervisor  
Description 
Several projects are available related to the mathematical theory of flame propagation, a fascinating multidisciplinary area of applied mathematics involving ordinary and partial differential equations; combustion basics will be introduced to candidate. The approach will typically adopt a combination of analytical techniques (asymptotic methods) and/or numerical techniques (solution of ODEs or PDEs). The multidisciplinary experience in combustion involved will be useful for tackling research problems in other fields of application, and will constitute a valuable asset for jobs in industry (such as the automobile or the aeronautics industry). Depending on the preference of the candidate, each of the projects can be tailored in its scope and the methodology of study. Suggested sample projects:

Title 
Taylor dispersion and hydrodynamic lubrication theory in premixed combustion 

Group  Continuum Mechanics 
Supervisor  
Description 
In 1953, the British physicist G.I. Taylor published an influential paper describing the enhancement of diffusion processes by a (shear) flow, a phenomenon later termed Taylor dispersion. This has generated to date thousands of publications in various areas involving transport phenomena, none of which, surprisingly, in the field of combustion. In 1940, the German chemist G. Damköhler postulated two hypotheses which have largely shaped current views on the propagation of premixed flames in turbulent flow fields. The project consists of pioneering investigations linking Taylor dispersion and Damköhler’s hypotheses, and is expected to provide significant insight into turbulent combustion. The work will be carried out in the framework of lubrication theory, generalized to combustion situations, and will include interesting stability problem such as the SaffmanTaylor instability in a reactive mixture. Methodology: The approach will typically adopt a combination of analytical techniques (asymptotic methods) and/or numerical techniques (solution of ODEs or PDEs), depending on the preference of the candidate. 
Title 
Laminar aspects of turbulent combustion/ Flame propagation in a multiscale flow 

Group  Continuum Mechanics 
Supervisor  
Description 
The idea is to ask if the fundamental questions of turbulent combustion can be answered for simple laminar flows. Since the answer is often no, we shall formulate and study problems to answer these questions in simpler laminarflow situations. An exciting topic! Methodology: The approach will typically adopt a combination of analytical techniques (asymptotic methods) and/or numerical techniques (solution of ODEs or PDEs), depending on the preference of the candidate. 
Title 
Generalized Flame Balls and their Stability 

Group  Continuum Mechanics 
Supervisor  
Description 
Flame balls are balls of burnt gas in a reactive mixture, which constitute stationary solutions to nonlinear Poisson's equations. These were first described by the famous Russian physicist Zeldovich (the father of Combustion Theory) about 70 years ago. The fact that these solutions are typically unstable provides a powerful fundamental criterion for successful ignition, i.e. determines the minimum energy (of the spark) required to generate propagating flames. Several projects are available to extend the study of these fascinating flames (mainly their existence and stability) to take into account realistic effects such as the presence of flowfield, nonuniformity of the reactive mixture, proximity of walls, etc. Methodology: The approach will typically adopt a combination of analytical techniques (asymptotic methods) and/or numerical techniques (solution of ODEs or PDEs), depending on the preference of the candidate. 