Pattern Formation in Slowly Drained Granular-Fluid Systems
We present a new pattern formation process where labyrinthine structures emerge during slow drainage of a confined granular-fluid mixture. Capillary and frictional forces govern the process, and the resulting pattern has a characteristic wavelength that i
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Department of Physics, University of Oslo, P.O.Box 1048 Blindern, 0316 Oslo, Norway [email protected] School of Chemical and Biomolecular Engineering, University of Sydney, NSW 2006, Australia
Summary. We present a new pattern formation process where labyrinthine structures emerge during slow drainage of a confined granular-fluid mixture. Capillary and frictional forces govern the process, and the resulting pattern has a characteristic wavelength that is a function of both the initial volume fraction of granular material in the mixture, and also the system thickness.
1 Introduction There are many examples of pattern formation in granular systems driven out of equilibrium: ripples in wind-blown sand, segregation of grains in granular flows [1], the Rayleigh-Taylor instability in falling grains [2], and various patterns in vertically and horizontally vibrated granular layers [3]. Here we present a new pattern formation process where the central ingredients are a granular medium submerged in a Newtonian fluid [4–6]. The granular-fluid system is confined between the parallel glass plates of a HeleShaw cell, and as the cell is gradually drained, the receding fluid-air interface gathers and pushes the grains ahead of it as fingers of air invade the system. When the cell is fully drained, all the granular material that was originally uniformly distributed in the cell has been reorganized into a branching labyrinth structure of compacted grains. From a combination of experiments, simulations and theory we characterize the governing forces in the system, and show that a well defined wavelength develops as a compromise between capillary forces and friction. Emphasis is here placed on the experimental system and results, while the simulations are given a similar treatment in a parallel report [7].
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Bjørnar Sandnes et al.
Fig. 1. a) Picture of the experimental setup. b) Illustration of a cross-section of the Hele-Shaw cell including outlet and height adjustment mechanism.
2 Experimental Setup Figure 1a) shows a picture of the experimental setup including the Hele-Shaw cell, a syringe pump (to the left in the picture), and a Nikon D100 camera placed underneath the cell acquiring images in time lapse mode. A schematic drawing of the cell is shown in Fig. 1b). The dimensions of each of the two glass plates are 50×50×1 cm, and they are kept separated by metal spacers of well defined thickness. The cell is mounted in a frame with three adjustment screws resting on a table such that the cell can be leveled accurately. A square “window” is cut in the table allowing imaging from underneath where no tubes or other equipment blocks the view. A small hole, approximately 5 mm diameter, is drilled through the top glass plate, and a brass tube connector is glued on. This serves as both inlet during loading of the granular-fluid mixture into the cell, and as outlet when the fluid is subsequently withdrawn. A plastic tube connects the cell to the syringe pump. In the experiments reported here we use a granular medium consisting of poly-disperse gl
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