Statistical description of the shear–induced diffusion of a suspension of non–Brownian particles
I. Santamaría–Holekª, G. Barriosª and J.M. Rubib
ª Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito exterior de Ciudad Universitaria, 04510, D.F., México.
b Facultat de Física, Universitat de Barcelona. Av. Diagonal 647, 08028, Barcelona, Spain.
Recibido el 21 de enero de 2009 ]]> Aceptado el 13 de marzo de 2009
Abstract
Using mesoscopic nonequilibrium thermodynamics, we calculate the entropy production of a dilute suspension of non–Brownian particles subject to an oscillatory shear flow. We find that an Onsager coupling leads to a breakdown of the fluctuation–dissipation theorem and to the shear induced diffusion effect observed in experiments. By contracting the description, we derive a Smoluchowski equation from which the scaling of the mean square displacement on the shear rate and particle diameter reported in experiments is obtained. We also perform lattice Boltzmann simulations to show the shear induced diffusion effects, and how the transition to irreversibility can be characterized through the power spectra of particle trajectories.
Keywords: Mesoscopic entropy; irreversibility; shear induced diffusion; lattice Boltzmann.
Resumen
Usando la termodinámica de no equilibrio mesoscópica, calculamos la producción de entropía de una suspensión diluida de partículas no Brownianas sujetas a un flujo cortante oscilatorio. Encontramos que un acoplamiento de Onsager produce una violación del teorema de fluctuación disipación asociada a la difusión inducida por corte que ha sido observada previamente en experimentos. Al contraer la descripción, obtenemos la ecuación de Smoluchowski a partir de la cual se obtiene el desplazamiento cuadrático medio de las partículas. También realizamos simulaciónes numéricas con el método de la ecuación de Boltzmann en redes mostrando que el flujo cortante oscilatorio induce efectos difusivos. La transición a la irreversibilidad puede ser caracterizada a través del espectro de potencia de la trayectoria de las partículas.
Descriptores: Entropía mesoscópica; irreversibilidad; difusión inducida por corte; ecuación de Boltzmann en redes.
]]> PACS: 05.70.–a; 05.70.Ln
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Acknowledgments
ISH and GBV wish to acknowledge financial support by DGAPA–UNAM under grant IN–102609.
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