NFFDy Summer Programme 2024: Bayesian Data assimilation and Model Selection
Workshops, Fluid Institute, University of Leeds, Leeds, UK
This workshop is part of the National Fellowships in Fluid Dynamics Summer Programme 2024, funded by the UK EPSRC.
Talks and presentations
From sinking spheroids to chemotactic collapse: Continuum modelling of dilute active Brownian particle suspension
Seminar, Mathematical Biology Seminar, Department of Mathematics, University College London, London, UK
Active Brownian Particle (ABP) is a class of models for particles whose trajectories depend on their noise orientation. It is a particularly popular model for swimming microorganisms such as bacterial, motile and sinking phytoplanktons. In a dilute suspension where these particles only interact hydrodynamically through their disturbance to the fluid bulk, they can be modelled as a continuum phase through the Fokker-Planck equation, which governs the probability distribution of the particles in both the orientational and physical space. However, the two-way coupling between the Fokker-Planck equation and the momentum equation governing the flow, i.e. the Navier-Stokes equation, remains a difficult problem, largely owing to the high number of dimensions in the Fokker-Planck equation.
From sinking spheroids to chemotactic collapse: Continuum modelling of dilute active Brownian particle suspension
Seminar, Mathematical Biology Seminar, Department of Mathematics, University of York, York, UK
Active Brownian Particle (ABP) is a class of models for particles whose trajectories depend on their noise orientation. It is a particularly popular model for swimming microorganisms such as bacterial, motile and sinking phytoplanktons. In a dilute suspension where these particles only interact hydrodynamically through their disturbance to the fluid bulk, they can be modelled as a continuum phase through the Fokker-Planck equation, which governs the probability distribution of the particles in both the orientational and physical space. However, the two-way coupling between the Fokker-Planck equation and the momentum equation governing the flow, i.e. the Navier-Stokes equation, remains a difficult problem, largely owing to the high number of dimensions in the Fokker-Planck equation.
From sinking spheroids to chemotactic collapse: Continuum modelling of dilute active Brownian particle suspension
Seminar, Biolunch, DAMTP, Cambridge, Cambridge, UK
Active Brownian Particle (ABP) is a class of models for particles whose trajectories depend on their noise orientation. It is a particularly popular model for swimming microorganisms such as bacterial, motile and sinking phytoplanktons. In a dilute suspension where these particles only interact hydrodynamically through their disturbance to the fluid bulk, they can be modelled as a continuum phase through the Fokker-Planck equation, which governs the probability distribution of the particles in both the orientational and physical space. However, the two-way coupling between the Fokker-Planck equation and the momentum equation governing the flow, i.e. the Navier-Stokes equation, remains a difficult problem, largely owing to the high number of dimensions in the Fokker-Planck equation.
From sinking spheroids to chemotactic collapse: Continuum modelling of dilute active Brownian particle suspension
Seminar, Fluid Dynamics Seminar, Department of Mathematics, Imperial College London, London, UK
Active Brownian Particle (ABP) is a class of models for particles whose trajectories depend on their noise orientation. It is a particularly popular model for swimming microorganisms such as bacterial, motile and sinking phytoplanktons. In a dilute suspension where these particles only interact hydrodynamically through their disturbance to the fluid bulk, they can be modelled as a continuum phase through the Fokker-Planck equation, which governs the probability distribution of the particles in both the orientational and physical space. However, the two-way coupling between the Fokker-Planck equation and the momentum equation governing the flow, i.e. the Navier-Stokes equation, remains a difficult problem, largely owing to the high number of dimensions in the Fokker-Planck equation.
Continuum model for the transport of active Brownian particles in arbitrary flow field
Conferences, From Stokesian suspension dynamics to particulate flows in turbulence, Toulouse, France
Understanding the transport of Stokesian swimmers such as motile microorganisms and artificial swimmers in complex flow is vital to many ecological and industrial applications. In particular, it is important to capture the two-way interactions between the flow and the swimmers. While individual-based modelling is of great merit in capturing these interactions and remains a vital avenue to test theories, continuum modelling is also as important in enabling a deep theoretical un- derstanding of the suspension dynamics. There were numerous examples, from the instability of pusher suspension [1] to the modelling of bioconvection [2] and gyrotactic focusing [3], where a continuum model has made deep insight into suspension dynamics possible. This is partly attributed to the wide range of classical fluid mechanical tools made available by the continuum modelling of these suspensions.
Transport of orientable motile or sedimenting plankton in turbulence
Conferences, Biofilm and Bioactive Fluids Conference, Liverpool, UK
Understanding the transport of Stokesian swimmers such as motile microorganisms and artificial swimmers in complex flow is vital to many ecological and industrial applications. In particular, it is important to capture the two-way interactions between the flow and the swimmers. However, a key challenge in the continuum modelling for active suspension is that the transport of swimmers is coupled with the orientation, while the orientation is determined by the local flow field. Therefore, accurately modelling the swimmer phase as a continuum requires solving a variable in both positional and orientational space. When coupled with the flow equation, the direct numerical simulation of the equations would be too expensive unless some simplification is made.
Continuum models for active suspension
Workshops, Biofilm and Bioactive Fluids ECR Day, Liverpool, UK (Online)
Active suspensions, which consist of suspended self-propelling particles such as swimming microorganisms, often exhibit non-trivial transport properties. Continuum models are frequently employed to elucidate phenomena in active suspensions, such as shear trapping of bacteria, bacterial turbulence, and bioconvection patterns in suspensions of algae. Yet, these models are often empirically derived and may not always agree with the individual-based description of active particles. Here we establish a more rigorous foundation for macroscopic continuum modelling based on the respective microscopic dynamics and fully develop a continuum model through coarse-graining. All the assumptions needed to reach popular continuum models from a multi-particle Fokker-Planck equation, which governs the probability of the full configuration space, are explicitly presented. In the dilute limit, this approach leads to the mean-field model (a.k.a. Doi-Saintillan-Shelley model). We then introduce various methods to further reduce the high-dimensional Fokker-Planck equation into a particle density equation, which allows tractable numerical modelling of the various phenomena.
Transport of orientable motile or sedimenting plankton in turbulence
Conferences, Microscale Ocean Biophysics 6.0, Mallorca, Spain
The transport of plankton is often imposed by the flow through the passive advection and the orientable motility, but the buoyancy of the plankton may also affect the local flow field. Therefore, at the meso-scale, one shall model the suspended plankton and the turbulent flow as a coupled system. At this scale, individual-based modelling is impractical, but continuum modelling using the Fokker-Planck (Smoluchowski) equation is also expensive as it requires simultaneously solving the orientation and spatio-temporal distribution of the planktons. While reducing the equation is possible, past macro-transport models are either not accurate (Pedley & Kessler 1990, J. Fluid Mech. 212) or not generalised enough (Hill & Bees 2002, Phys. Fluids 14 (8)) to be applicable in a turbulent flow. We will present a new local approximation model that gives the effective transport as a function of the local flow field and the motility of the plankton. It can be applied to study phenomenon at the meso-scale, such as the patchiness of motile phytoplankton driven by turbulence (Durham et al. 2014, Nat. Commun. 4). It can also be extended to estimate the orientation-dependent sedimentation and dispersion of long non-motile planktons.
Revisiting Continuum Modelling for a Dilute Suspension of Micro-swimmers
Conferences, TJP80 Conference: Biological Fluids & Flows, Cambridge, UK
Singular plume in a dilute gyrotactic swimmer suspension
Seminar, Fluid Seminar, DAMTP, Cambridge, Cambridge, UK
Bifurcation and stability of a suspension of gyrotactic swimmer in a vertical pipe
Conferences, ICTAM 2020+1, Milano, Italy (Online)
Modelling the collective behaviour of gyrotactic micro-swimmers in a dilute suspension
Seminars, BioActive Fluids ECR Seminars, Online
Bottom-heavy motile micro-organisms (swimmers) orient themselves under the influence of gravitational and viscous torque. In a downflowing pipe, the balance between the two torques will cause the micro-organism to swim towards the centre, forming a focused beam-like structure. This sideway drift of bottom-heavy swimmers is known as gyrotaxis. Gyrotaxis is responsible for many naturally occurring phenomena, such as bioconvection and the formation of thin phytoplankton layers in some part of the ocean where shearing is strong.
Continuum Model for the Collective Behaviour of Gyrotactic Micro-Swimmers
Seminars, Applied Maths Seminar Series, U of Birmingham, Birmingham, UK
Bottom-heavy motile micro-organisms orient themselves under the influence of gravitational and viscous torque. In a downflowing pipe, the balance between the two torques will cause the micro-organism to swim towards the centre, forming a focused beam-like structure. The structure, known as a gyrotactic plume, may further break down into blips.
Continuum Model for Collective Behaviour of Micro-Swimmers
Seminars, Biolunch, DAMTP, Cambridge, Cambridge, UK
The key to quantify phenomena such as gyrotactic plume formation and bioconvection requires a macroscopic view of their collective behaviour. Instead of modelling micro-swimmers individually, one can model the collective as a continuum using an advection-diffusion-typed equation. Using the gyrotactic swimmer, Dunaliella salina, in a downflowing pipe (Kessler, 1986 JFM ) as an example setup, I am going to discuss the success and challenges in developing the continuum model. The advantage of the continuum equation is that one can couple swimmers with non-linear flow pattern like bioconvection with the full Navier-Stokes equation for the flow. However, the challenge lies in the lack of an accurate model for the effective diffusivity of these swimmers. The earlier model by Prof. Pedley (Pedley & Kessler, 1990 JFM ) is not as accurate at high shear, while the recent model using Generalised Taylor Dispersion (GTD), although accurate in some cases (Croze et al., 2017 JFM ), fails at strain-dominant region (Bearon et al., 2011 JFM ). Lastly, I am going to present a roadmap towards a Direct Numerical Simulation of the suspension of swimmers.