TY - ELEC
AU - Voller, Vaughan
PY - 2018
TI - Anomalous Infiltration into Heterogeneous Porous Media: Simulations and Fractional Calculus Models
LA - eng
M3 - Moving Image
AB - There has been some recent interest in exploring applications of fractal calculus in transport models. One of the
motivations for this is that such models are able to generate anomalous transport signals. For example, when
fractional calculus is employed to define diffusion transport fluxes (heat, mass etc.) the exponent n in the
space-time scaling differs from the classical value of n = Ã Ë . In this talk we have two objectives. The first
objective is to identify physically realizable systems that exhibit anomalous transport behaviors. The second is to
arrive at suitable fractional governing equations that can model these systems. To these ends we will build direct
simulations of the infiltration of moisture into a porous media containing a distribution of flow obstacles. When
the obstacles form a repeating pattern, this problem can be viewed as a limit case of the classical one-phase Stefan
melting problem and the measure of the advance of the infiltration length changes with the square root of time.
When the obstacles are distributed in a fractal pattern, however, the infiltration shows a sub-diffusive behavior,
where the time exponent is less that the square root. Through considering the time scaling of Brownian motion in a
fractal obstacle filed we are bale to directly associate this sub-diffusive time exponent to the fractal dimension
of the obstacle filed. This in turn, allows us to develop fractional calculus based governing equations, with a
closed particular solution, for moisture infiltration into a fractal obstacle field. The talk will close with
considerations as to how these findings can be associated with more general Stefan problem that incorporated
fractional calculus treatments.
N2 - There has been some recent interest in exploring applications of fractal calculus in transport models. One of the
motivations for this is that such models are able to generate anomalous transport signals. For example, when
fractional calculus is employed to define diffusion transport fluxes (heat, mass etc.) the exponent n in the
space-time scaling differs from the classical value of n = Ã Ë . In this talk we have two objectives. The first
objective is to identify physically realizable systems that exhibit anomalous transport behaviors. The second is to
arrive at suitable fractional governing equations that can model these systems. To these ends we will build direct
simulations of the infiltration of moisture into a porous media containing a distribution of flow obstacles. When
the obstacles form a repeating pattern, this problem can be viewed as a limit case of the classical one-phase Stefan
melting problem and the measure of the advance of the infiltration length changes with the square root of time.
When the obstacles are distributed in a fractal pattern, however, the infiltration shows a sub-diffusive behavior,
where the time exponent is less that the square root. Through considering the time scaling of Brownian motion in a
fractal obstacle filed we are bale to directly associate this sub-diffusive time exponent to the fractal dimension
of the obstacle filed. This in turn, allows us to develop fractional calculus based governing equations, with a
closed particular solution, for moisture infiltration into a fractal obstacle field. The talk will close with
considerations as to how these findings can be associated with more general Stefan problem that incorporated
fractional calculus treatments.
UR - https://open.library.ubc.ca/collections/48630/items/1.0376914
ER - End of Reference