Geometry-induced asymmetric diffusion
- *ProtoLife, Via della Libertá 12, 30175 Venezia, Italy;
- ‡European Center for Living Technology, S. Marco 2847, 30124 Venezia, Italy;
- §Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501; and
- ¶Center for Nonlinear Dynamics and Department of Physics, University of Texas, Austin, TX 78712
-
Contributed by Harry L. Swinney, April 18, 2007 (received for review February 26, 2007)
-
Fig. 1.Snapshots of a binary mixture of hard sphere disks, initially all on the right side, that diffuse through an asymmetric membrane whose pores are smaller on the right end in A and on the left end in B. Flow through the membrane is highly reduced with the membrane geometry of B. The larger particles in the gas mixture are slightly too large to pass through the pores, and the smaller particles are just small enough to pass. The left chamber is initially empty, and the elapsed time is the same for A and B.
-
Fig. 2.Number of particles in the (initially empty) left-hand chamber (cf. Fig. 1) in simulation and experiment. In each graph, the upper curve corresponds to pores with their small end on the right, and the lower curve corresponds to the reverse orientation of the pores. The upper curves show a large diffusion rate (slope of the curves), whereas the lower curves illustrate that the pores rapidly clog and the diffusion rate approaches zero. (Inset) Clogging for three different experimental trials. The right-hand chamber initially had 1,350 disks in the simulation and 2,000 beads in the experiment, which used a membrane of thickness 9.53 mm; the data shown are an average of three experiments. In both cases, 20% of the particles were large and the remainder were small.
-
Fig. 3.The experimental system and pictures of the granular gas. (A) Diagram of the experimental setup. (B) Cross-section of a circular pore that has a reduced diameter on the right end, too small for the larger particles in the binary mixture to pass. (C) Side view image of 50 beads in a chamber. (D) Side view image of 250 beads in a chamber.
-
Fig. 4.Number of small beads measured to cross the membrane after 3 min, as a function of membrane thickness, for the two flow directions (cf. Fig. 3). The loaded side of the membrane initially had a mixture of 1,600 small beads and 400 large beads.
-
Fig. 5.Number of beads measured to pass through a membrane (9.53 mm thick), as a function of time, when only small beads were present. Flow in the direction from the large to the small end of the pores is enhanced relative to that for the reverse orientation of the pores. There was a total of 200 beads; those residing in the pores were not observed.
-
Fig. 6.Time-dependent variation of concentration of small disks (solid lines) in the chamber on the right (the “inside”) in Fig. 1 B, in response to variation of number of small disks in the left-hand (“outside”) chamber (dashed lines). The number of large disks in the inside chamber is 200, and the number of large disks in the outside chamber is zero. (A) When the number of disks outside is linearly increased to 1,200 and then decreased linearly at the same rate, the number of disks on the inside adiabatically follows. (B) When the number of small disks outside is linearly increased as in A and then suddenly decreased to zero, the membrane pores clog as a consequence of the sudden strong cross-membrane gradient, and the number of small particles on the inside remains nearly constant for a long time.
Footnotes
- †To whom correspondence may be addressed. E-mail: rob{at}protolife.net or swinney{at}chaos.utexas.edu
- © 2007 by The National Academy of Sciences of the USA
