Scalar transport in closed potential flows is investigated for the specific case of a periodically reoriented dipole
flow. For scalar advection, Lagrangian chaos can be achieved with breakdown of the regular Hamiltonian structure,
which is governed by symmetry conditions imposed by the dipole flow. Instability envelopes associated
with period-doubling bifurcations of fixed points govern which regions of the flow control parameter space admits
global chaos. These are further refined via calculation of Lyapunov exponents. These results suggest
significant scalar transport enhancement is possible within potential flows, given appropriate programming of
stirring protocols.
Complex interactions between advection and diffusion give rise to enhanced scalar transport in cases where the
advective field generates Lagrangian chaos. As the dispersion rate is a complex function of scalar diffusivity and
parameters controlling the flow field, resolution of scalar dispersion over this parameter space is useful for better
understanding interactions between advection and diffusion. In this paper we resolve the fine-scale structure
asymptotic transport over the flow parameter space for Peclet numbers from 100 to 105 for a physically realizable
flow, yielding a 50-fold acceleration of scalar dispersion at Pe = 105. These results generate considerable insight
into the global structure of transport and facilitate identification of mechanisms governing scalar dispersion;
features include fractal distributions of dispersion rate, solution mode-locking, an order-disorder transition and
localisation of transport optima.
In nature dissipative fluxes of fluid, heat, and/or reacting species couple to each other and may also couple
to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy
flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying
fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flow and chemical
concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially
open flow, in which parts of the flow remain in the cell forever and parts pass through with residence time and
exit time distributions that have self-similar features in the control parameter space of the stirring.
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