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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
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