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SUMMARY:From sinking spheroids to chemotactic collapse: Continuum modellin
 g of dilute active Brownian particle suspension - Dr Lloyd Fung\, DAMTP\, 
 University of Cambridge
DTSTART:20230216T123000Z
DTEND:20230216T133000Z
UID:TALK196525@talks.cam.ac.uk
CONTACT:Prof Ray Goldstein
DESCRIPTION:Active Brownian Particle (ABP) is a class of models for partic
 les whose trajectories depend on their noise orientation. It is a particul
 arly popular model for swimming microorganisms such as bacterial\, motile 
 and sinking phytoplanktons. In a dilute suspension where these particles o
 nly interact hydrodynamically through their disturbance to the fluid bulk\
 , they can be modelled as a continuum phase through the Fokker-Planck equa
 tion\, which governs the probability distribution of the particles in both
  the orientational and physical space. However\, the two-way coupling betw
 een the Fokker-Planck equation and the momentum equation governing the flo
 w\, i.e. the Navier-Stokes equation\, remains a difficult problem\, largel
 y owing to the high number of dimensions in the Fokker-Planck equation.\n\
 nIn the first half of the talk\, I am going to present a new model to redu
 ce the high-dimensional Fokker-Planck equation into a low-dimensional tran
 sport equation for the number density of the particles. This model is base
 d on a novel transformation of the Fokker-Planck equation\, which\, even w
 ithout any approximation\, can reveal physical insight into how the orient
 ational motility of ABPs affects their macro-transport. We will also compa
 re this new model with the more restrictive generalised Taylor dispersion 
 model.\n\nIn the second half of the talk\, we apply the novel transformati
 on to the modelling of two classical problems in ABP suspensions - the for
 mation of plumes in gyrotactic suspension and streamers in the sedimentati
 on of spheroids. With the help of the transformation\, we shall demonstrat
 e how the system is analogous to the Keller-Segel model that governs many 
 chemotactic phenomena. Also\, similar to chemotactic collapse\, the nonlin
 ear solution to the plume structure exhibit a finite-time blow-up when ext
 ended from 2D to 3D.
LOCATION:MR15\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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