Rotational Taylor dispersion in linear flows
arxiv(2024)
摘要
The coupling between advection and diffusion in position space can often lead
to enhanced mass transport compared to diffusion without flow. An important
framework used to characterize the long-time diffusive transport in position
space is the generalized Taylor dispersion theory. In contrast, the dynamics
and transport in orientation space remains less developed. In this work, we
develop a rotational Taylor dispersion theory that characterizes the long-time
orientational transport of a spheroidal particle in linear flows that is
constrained to rotate in the velocity-gradient plane. Similar to Taylor
dispersion in position space, the orientational distribution of axisymmetric
particles in linear flows at long times satisfies an effective
advection-diffusion equation in orientation space. Using this framework, we
then calculate the long-time average angular velocity and dispersion
coefficient for both simple shear and extensional flows. Analytic expressions
for the transport coefficients are derived in several asymptotic limits
including nearly-spherical particles, weak flow, and strong flow. Our analysis
shows that at long times the effective rotational dispersion is enhanced in
simple shear and suppressed in extensional flow. The asymptotic solutions agree
with full numerical solutions of the derived macrotransport equations and
results from Brownian dynamics simulations. Our results show that the interplay
between flow-induced rotations and Brownian diffusion can fundamentally change
the long-time transport dynamics.
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