Stress jump boundary condition capturing for the lattice Boltzmann simulation methods

Lead Research Organisation: Sheffield Hallam University


Multi-phase flows occur when two or more different phases or types of fluid are brought together. They are seen to occur in a vast range of both physical and industrial type systems. Such systems are, to name but only a few, in processing, production and transportation of foods, oil, gas, waste and slurries; in energy production from evaporators, condensers, pumps and turbines; in natural systems such as geophysical and geochemical flows, reservoir extraction / filtration, biological and biochemical flows. In such systems the point at which different phases meet is termed an interface and this interfacial area gives rise to a host of complex rheological phenomena due to stresses that occur. Phenomena such as suspension dynamics, wetting, jamming, coalescence, break-up, collision and capillarity are all heavily interface dominated flows and are not readily mathematically easy to predict in typical engineering scenarios.

In these cases numerical computer simulations have proved an invaluable tool in successfully understanding, diagnosing, predicting and optimising systems. A growing current state of the art class of numerical computer simulation methods used for engineering multi-phase flow is called the lattice Boltzmann method. However, in this promising method, a drawback is the large amounts of resources that are spent smoothing and broadening interfaces in order to resolve and calculate the necessary flow details. This severely restricts the physical representative size of a simulation and the range of industrially useful applications that can benefit from this type of predictive modelling which is often needed to avoid long development delays.

This programme of research will develop brand new techniques for the numerical lattice Boltzmann methods in order to apply the mathematically correct stress jump boundary conditions in a sharp exacting manner. This will free up expensive computational resources which means (i) that existing simulations can be modified to take a fraction (estimated at up to 4 times less) of the time and memory, (ii) that a new range of larger more physically representative, accurate and industrially relevant multi-phase flows can be modelled. To ensure the correctness of the newly developed techniques they will be tested against known data and compared against the present day techniques in order to demonstrate the significant enhancements expected to be achieved through this research.

The types of research that will use the techniques developed in this research work will predominantly be multi-phase related but it is noted that the techniques developed will apply to any transport phenomena that involves stress boundaries within the lattice Boltzmann methods. For example the junction of an open fluid flowing into a porous media model contains a stress jump. More specifically this research will go on to be applied to the explicit modelling of emulsions and suspension. These are flows that contain a large number of particles with multiply interacting interfaces dominating the emergent complex rheological behaviour. Such flows are prevalent in the foods, drinks, creams, pastes, bio-fluids (blood) and other processing industries and the modelling tools developed here will lead to improved constitutional theories of non-Newtonian fluids, knowledge transfer and process optimisation for many years to come.

Planned Impact

The research proposed addresses important methodological advancements in multi-phase fluids modelling for soft matter materials that will enable improved scientific understanding to guide design, characterisation and optimisation for a myriad of sectors. There is broad and palpable relevance to not only academic (as detailed separately) but also a range of industry sectors such as food, pharmaceuticals, personal care, health care, functional materials, biotechnology, display technology, geological/environmental remediation or extraction/storage, nuclear and energy storage. Many of these industries feature in the Research Councils themes and priorities such as those in Manufacturing the Future, Energy, Healthcare Technologies and Mathematical Sciences.

There is substantial potential for impact on the successful completion of this research programme which will lead to new predictive modelling mechanisms. Taking an example from the pharmaceuticals, foods or personal care product sectors: it can take six plus years to develop new product lines yet due to dynamic environmental and health regulations and evolving market demands, it can require product reformulation at short notice. Despite these sectors being technologically advanced it is still often the case that even small ingredient changes/substitutions can cause existing formulations and processes to fail having expensive consequences. Such scenarios might be avoided if product formulation of such soft matter were more firmly grounded with scientific understanding provided uniquely through advanced modelling of the type this proposed research aims to establish.

The ability to rationally design soft matter materials and the processing of soft matter materials can lead to shorter lead times, lower associative costs and may also lead to new methods/products that may otherwise never come to market. Avenues to these industry sectors will be pursued through our current establish teaching and research links to companies that have both strong UK and international operations and directly involve the manufacture and processing of soft matter materials (Nestle Uk, PepsiCo UK, Warburtons, Mars, Unilever, Premier Foods).

Many areas of the economy could benefit from the systematic development through our modelling paradigm rather than design by trial and error. Some specific examples include new display technology using liquid crystals or dielectrophoretically controlled inks; enhanced cell scaffolds used in tissue engineering for health; novel food gel phases and colloidosomes that deliver specific health benefits; new energy storage materials - batteries and fuel cells; optimised extraction/storage/clean-up of material in geological reservoirs; safe processing and treatment of nuclear products; and patient specific diagnosis with design of clinical interventions. So many of these conceptual ideas will benefit from the resolved scientific understanding that this research seeks to complete.
Description Sharp interface boundary conditions for multiphase lattice Boltzmann (LB) methods have been investigated, literature reviewed and ideas developed. It was identified that improvements can be made to existing periodic pressure boundary conditions in the LB literature of engineering flows. At present periodic pressure boundary conditions in the LB can only work in single phase flows and in simple geometry. In contrast many industrial flows are multiphase. This work has identified and developed a new periodic jump pressure boundary condition capable of both single phase and multiphase flow up to many hundreds of particles by modifying the equilibrium distribution functions of the LB method. Comparisons are made against published literature. The work was presented at the annual department research symposium in May 2015 and has currently been written up for submitting to the journal Physical Review E for publication 2017. It allows accurate methods of simulating pressure driven flows of multiphase in contrast to present methods that only allow single phase.
Further technical issues are currently being worked on to modify the non-equilibrium parts of the LB distribution functions at fluid interfaces in a jump manner in order to meet the mathematically correct continuum boundary conditions. While viscosity jumps have been implemented and validated density jumps are as yet unstable and represent an unsolved problem for LB methods. A poster was given at the annual ICMMES conference Hamburg, Germany July 2016. A presentation was given on multiphase flows viscosity at the IOP Topical Research Meeting on Physics in Food Manufacturing, January 2017. A presentation was also made at the annual DSFD 2017 Conference in Erlangen, Germany.
Exploitation Route The main publications to come from the research work is of interest to the academic LB community and software developers of LB methods.
Sectors Agriculture, Food and Drink,Energy,Environment,Pharmaceuticals and Medical Biotechnology,Other

Description The overall long term end goal of this research work was always to be able to better inform industries that deal with processing, producing and transport of foods, oils, wastes, biological and biochemical flowing materials. This research has made a significant first stride towards this goal. The research work has been applied, successfully, to model the naturally emergent non-Newtonian properties of flowing emulsions, a type of multi-phase fluid, from the very low concentration all the way to the very high concentration ranges. The individual droplet surface tensions, viscosity ratios, droplet distribution sizes are all tuneable input parameters to the model and macroscopic non-Newtonian laws emerge naturally, over bounded ranges, with embedded shear thinning and shear thickening behaviour. While this represents the first significant step the next step to gaining impact and more widespread use will be to take the newly predicted viscosity and sheared self-diffusion data and pass it up the length scales to macroscopic models such as Phillips R. J., Armstrong R. C., Brown R. A, "A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration," Physics of Fluids, Vol. 4, no. 30, 1992. This is work that is underway from partners at Sheffield Hallam University Engineering and Mathematics Department. The key benefit in doing this is to enable access to industrially relevant length scales of manufacturing processes used in industry that the first stage explicit model cannot yet reach due to limits of computational power and time. This work has now begun and its aim is to prove the validity of such in-silico methods to sectors that produce, process, transport and store emulsion like fluids that feature heavily in the UK and worldwide manufacturing sectors.
First Year Of Impact 2020
Sector Agriculture, Food and Drink,Education,Manufacturing, including Industrial Biotechology
Impact Types Societal,Economic

Description PhD Scholarship
Amount £75,000 (GBP)
Organisation Sheffield Hallam University 
Sector Academic/University
Country United Kingdom
Start 11/2014 
End 11/2017
Description Blood flow in arteries 
Organisation University of Sheffield
Country United Kingdom 
Sector Academic/University 
PI Contribution Development validation and execution of mathematical models and codes to import scanned arteries and stents. Calculation of flow characteristics on vessel boundaries such as wall shear stress maps for comparison to localised areas of artery damage. I performed computer predictions of flow and compare with invitro experiment and invivo experiment.
Collaborator Contribution Biological in-vitro and in-vivo experiments testing biological interventions in arteries and stents for promoting endothelial repair.
Impact Published articles: DOI: 10.1093/cvr/cvu087.6 DOI: 10.1136/heartjnl-2014-306118.219 DOI: 10.1093/cvr/cvw210 DOI: 10.1160/TH16-03-0214 All this work is multi-disciplinary combining cardiovascular scientists invivo and invitro work with engineers performing theoretical and numerical analysis.
Start Year 2015
Description Multiphase vesicle boundaries 
Organisation National Research Council
Department Insititute of Applied Mathematics (IAC)
Country Italy 
Sector Public 
PI Contribution Development of mathematical models. Write and validate numerical lattice Boltzmann based code against published literature to implement models. Course graining the data to fit macroscopic parameters
Collaborator Contribution Development of mathematical models. Execution of numerical developed codes to collect data.
Impact Published article. 10.1103/PhysRevE.94.023306 Article Submitted: I. Halliday, S. V. Lishchuk, T. J. Spencer, G. Pontrelli, and P. C. Evans Velocity-Dependant Forces in Lattice Boltzmann Equation Vesicle Journal of computational Physics November 2016 Book chapter 2017 Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes Editors: Cerrolaza, M., Shefelbine, S.J. Garzón-Alvarado, Diego A. MULTI-COMPONENT LATTICE-BOLTZMANN FLOWS FOR BIOLOGICAL APPLICATIONS Andrea Montessori, S. Succi, I. Halliday, S. V. Lishchuk, T. J. Spencer, Giuseppe Pontrelli
Start Year 2010
Description Numerical integration and fitting for semiconductor luminescence. 
Organisation Sheffield Hallam University
Country United Kingdom 
Sector Academic/University 
PI Contribution Written numerical methods to solve advanced integral equations and fitting routines.
Collaborator Contribution Literature review. Development of theoretical analysis and comparison to experiment. Execution of numerical codes.
Impact Accepted for publication: Chijioke I. Oriakua, Timothy J. Spencer, X. Yang, J. P. Zubelli, Mauro F. Pereira. Analytical Expressions for the Luminescence of Dilute Quaternary InAs(N,Sb) Semiconductors Journal of Nanophotonics Article: JNP 17008
Start Year 2016
Description Conference Organisation 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact The annual British Liquid Crystal Society conference 2015 was held Sheffield Hallam University. Prof Doug Cleaver and Dr Tim Spencer were the organisers of the conference and scientific programme. One hundred participants from around the UK and some international participants attended the successful three day conference allowing presentation and discussion of latest research. Useful contact/discussions where had with members from University of Edinburgh Parallel Computing Centre.
Year(s) Of Engagement Activity 2015