gwyn@brl-vld@sri-unix.UUCP (09/01/83)
From: Doug Gwyn (VLD/VMB) <gwyn@brl-vld> Biologists know this phenomenon better as semi-permeable membranes. They can be used for "sorting" molecules based on size. However, the second law of thermodynamics has nothing to do with this.
wendt@arizona.UUCP (09/05/83)
(This copy has no tabs in the diagram) Several years ago John Galloway, Dave Pearson, and I ran some simulations of particles approaching and bouncing off simple funnel shapes (trapezoids, actually). Assuming perfect reflection, the surprising result was that it can be up to 3 times easier to throw a ball through the narrow end of a funnel than through the wide end!! For these simulations the funnels were actually trapezoidal channels cut through walls. I can see one of two possibilities here: first, molecules don't reflect perfectly. Undoubtedly. Second, if we set up a wall full of little holes in a good enough vacuum (and with small enough holes), so that the inter-molecular collisions can be neglected, shortly the pressure on the wide side of the funnels would be three times that on the narrow side!! It seems strange to me that the second law of thermodynamics should depend so critically on the characteristics of molecular impact with surfaces. If we use big enough molecules we ought to start approaching perfect reflection. Can somebody explain this please? Can somebody make a such a wall which is thin enough and with lots of sufficiently small holes (45% angles are fine)? Perhaps by dropping very fine sand on a very thin sheet of glass in a vacuum? By way of more explanation: _____________________________________________________________________________ | |####| | | |####| | | |####| | | |####| | | |####| | | |###/ | | |##/ | | |#/ | | |/ | | | | | | |\ | | |#\ | | |##\ | | |###\ | | |####| | | |####| | | |####| | | |####| | | |####| | ----------------------------------------------------------------------------- Think of this as a pool table with a couple of wedges set up in the middle. Forty-five degree angles are fine. We ran simulations starting from some fixed distance from both sides of the wedge, aiming in random directions, and counted the ones that bounced back in and the ones that got through the funnel. We got the ratio as high as three-to-one by tweaking the geometry. We didn't consider reflections off the back or sides of the pool table, and we considered the particle to have zero size. We did consider reflections off the sides of the funnel, and assumed angle i = angle r. What happens is this: coming from the narrow side, any particle that hits the aperture at any angle from 0 to 180 gets through. So the "effective width" of the narrow side is the narrow aperture diameter times 180 degrees. The "effective width" going the other way is the angle made by the funnel times the narrow aperture -- it has to get through both. The funnel sides raise the effective width of the wide side somewhat by sometimes bouncing particles toward the aperture, but not nearly enough to compensate -- most of the time that a particle hits a side of the funnel, instead of going through it gets bounced out. If you try to imagine a particle getting bounced through the aperture, you'll see how glancing a shot it would have to be in order to get bounced through. Alan Wendt