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UID:0-210@aerospace.technion.ac.il

DTSTART;TZID=Asia/Jerusalem:20220214T133000

DTEND;TZID=Asia/Jerusalem:20220214T143000

DTSTAMP:20230403T122011Z

URL:https://aerospace.technion.ac.il/events/the-dynamics-and-diffusion-of-
 brownian-particles-in-unsteady-flows/

SUMMARY:The dynamics and diffusion of Brownian particles in unsteady flows
DESCRIPTION:Lecturer:Nan Wang\n Faculty:Applied Mathematics\n Institute:Tec
 hnion – Israel Institute of Technology\n Location:https://technion.zoom.
 us/j/98061754875?pwd=WVV1NTlrYlRTamlqelB3VENBdDhsQT09\n Zoom: \n Abstract:
  \n Details: \n Brownian motion\, the random motion of particles suspended
  in a medium\, was first studied mathematically by Einstein and Smoluchows
 ki. They obtained the particle's mean square displacement (MSD) in a quies
 cent medium. Compared to the classical Brownian diffusion described by the
  Einstein-Smoluchowski equation\, where the MSD is proportional to time\, 
 the anomalous Brownian diffusion\, where the MSD has a non-linear function
  of time\, is studied based on the Langevin equations. Contrary to previou
 s studies in this field\, we investigate Brownian diffusion using stochast
 ic calculus instead of classical calculus.\nFirst\, we investigate the sto
 chastic dynamics of free Brownian particles in a sinusoidal wave flow. It 
 indicates that flows in which the velocity depends only on time will not a
 ffect the particle’s diffusion. Then\, the stochastic dynamics of free B
 rownian particles in two-dimensional laminar flows in which the velocity p
 rofiles are polynomial functions of the transverse coordinate are studied.
  Our new method is validated for two different flow cases without boundary
  effects: Couette flow and Plane Poiseuille flow. We show that for time sc
 ales much smaller than the particle relaxation time scales\, the particle 
 almost travels at its initial velocity and that the Brownian diffusion is 
 virtually the same as in quiescent or uniform fluids. On the other hand\, 
 to leading order and for long time scales\, the time dependency of the var
 iance is . This is due to Brownian diffusion affected by the flow's veloci
 ty gradients\, where the particle may be carried by the flow to a wide ran
 ge in the streamwise direction. It reveals that Brownian motion in transve
 rse directions and the velocity profile of the flow make a significant dif
 ference to the particle's diffusion in the streamwise direction.\nFinally\
 , we explore the response of Brownian particles to a flow propagating by a
  horizontally oscillating plate. We found an analytical solution for the p
 article dynamics. A new exact solution is provided for the cases in which 
 Brownian motion is negligible. We show that the diffusion in the horizonta
 l direction is greatly affected by Brownian motion in the vertical directi
 on and the function of the flow's velocity\, which also verifies our study
  on Brownian diffusion of the polynomial case.\nZoom Meeting
CATEGORIES:Seminars
LOCATION:https://technion.zoom.us/j/98061754875?pwd=WVV1NTlrYlRTamlqelB3VEN
 BdDhsQT09

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