Filtration apparatus and method

Abstract

A filtering apparatus formed by a plurality of channel systems. Each of the channel systems include an inlet port formed on an inlet side of the plate; no more than one outlet port formed on an outlet side of the plate; and a channel formed in the plate, the channel coupled to the inlet port and to the outlet port, wherein the ratio of the product of the capture area of the inlet ports of a channel system with the first transmissivity associated with the inlet ports to the product of the capture area of the outlet ports of a channel system with the second transmissivity associated with the outlet ports is greater than one. The channel system is configured to interact with objects of interest on a scale which is smaller than a value several orders of magnitude larger than the mean free path of an object of interest. Some plate embodiments are configured to interact with particles, such as air molecules, water molecules, or aerosols. Other plate embodiments are configured to interact with waves or wavelike particles, such as electrons, photons, phonons or acoustic waves.

1 . An apparatus, comprising:
 a bulk material having at least one channel system, each of said at least one channel system comprising:
 a first opening adjacent a first reservoir, the first reservoir located beyond the first opening; 
 a second opening adjacent a second reservoir, the second reservoir located beyond the second opening; 
 at least one channel, said channel coupled to said first opening and to said second opening, said channel allowing the passage of objects of interest between the first reservoir and the second reservoir via the first opening, the channel and the second opening, each object of interest being a distinct portion of a medium, 
 the channel comprising at least a first focusing segment, the first focusing segment having a first capture surface at an interface between a portion of the channel and the first focusing segment in a direction of the first opening, and the first focusing segment having a second capture surface at an interface between the portion of the channel and the first focusing segment in a direction of the second opening, 
 wherein for a static boundary condition at least a portion of a difference of an average thermodynamic property of the objects of interest between the first reservoir and the second reservoir arises from an effect of an interaction of objects of interest with the first focusing segment, wherein the thermodynamic property comprises pressure, temperature, or volumetric number density of the objects of interest, 
 wherein the interaction of objects of interest comprises focusing of trajectories of at least a portion of objects of interest passing through the first focusing segment from the first capture surface to the second capture surface, the focusing of trajectories occurring within the first focusing segment, and within a distance less than 1000 times a mean free path of the objects of interest within the first focusing segment, 
 the channel comprising a centroid extending from the first opening to the second opening, the centroid being a center of a cross-sectional area of the channel when viewed along a length of the channel. 
   
     
     
         2 . The apparatus of  claim 1 , wherein the focusing of trajectories of at least a portion of objects of interest passing through the first focusing segment from the first capture surface to the second capture surface comprises an increase in flux of objects of interest through at least a portion of the second capture surface compared to a corresponding prior flux of the objects of interest through the first capture surface, wherein the flux of objects of interest is the number density of objects of interest passing through a specified surface per unit area and per unit time. 
     
     
         3 . The apparatus of  claim 1 , wherein the focusing of trajectories of at least a portion of objects of interest passing through the first focusing segment from the first capture surface to the second capture surface comprises an increase in a component of an average momentum of the objects of interest along a first specified direction at a location of the second capture surface for at least a portion of the second capture surface compared to a corresponding prior component of an average momentum of the objects of interest along a second specified direction at a location of the first capture surface,
 wherein the first specified direction is a direction from the first reservoir to the second reservoir along the centroid of the channel at the location of the second capture surface, and   wherein the second specified direction is a direction from the first reservoir to the second reservoir along the centroid of the channel at the location of the first capture surface.   
     
     
         4 . The apparatus of  claim 1 , wherein the difference of the average thermodynamic property of objects of interest between the first reservoir and the second reservoir is an average volumetric number density of objects of interest. 
     
     
         5 . The apparatus of  claim 4 , wherein an average temperature of objects of interest in the first reservoir and the second reservoir is substantially identical. 
     
     
         6 . The apparatus of  claim 1 , wherein the difference of the average thermodynamic property of objects of interest between the first reservoir and the second reservoir is an average temperature of the objects of interest. 
     
     
         7 . The apparatus of  claim 1 , wherein the objects of interest comprise a particle, the particle comprising at least one of a photon, an atom, a molecule, a dust particle, or an aerosol. 
     
     
         8 . The apparatus of  claim 1 , wherein the objects of interest comprise a virtual particle, the virtual particle comprising a virtual photon, virtual electron, virtual positron, or a virtual quark, as described by quantum field theory. 
     
     
         9 . The apparatus of  claim 1 , wherein the objects of interest comprise a wave, the wave comprising at least one of an acoustic wave, an ocean wave, a phonon, a photon, or an electron. 
     
     
         10 . The apparatus of  claim 1 , wherein the objects of interest comprise an electron, a quasiparticle, or a hole. 
     
     
         11 . The apparatus of  claim 1 , wherein the channel system generates a net bulk flow of objects of interest from the first reservoir to the second reservoir for a dynamic boundary condition. 
     
     
         12 . The apparatus of  claim 11 , wherein a net thrust acts on the channel system, at least a portion of the net thrust being a result of generation of a bulk flow of objects of interest. 
     
     
         13 . The apparatus of  claim 11 , further comprising a valve capable of regulating a mass flow rate of objects of interest through the channel system. 
     
     
         14 . The apparatus of  claim 13 , wherein the valve includes a translating spike valve. 
     
     
         15 . The apparatus of  claim 11 , wherein the objects of interest include photons, and wherein a net bulk flow of photons is associated with a transfer of thermal energy, wherein the transfer of thermal energy is from one object to a hotter object or to a colder object. 
     
     
         16 . The apparatus of  claim 1 , wherein a cross-sectional area of the channel viewed along the length of the channel is circular, rectangular, polygonal, or elliptical. 
     
     
         17 . The apparatus of  claim 1 , wherein an equivalent radius of a cross-sectional area of the channel within at least a portion of the first focusing segment increases linearly along the centroid along at least a portion of the length of the channel in a direction from the first opening to the second opening, the equivalent radius being a square root of a cross-sectional area of the channel divided by pi, and the cross-sectional area being measured perpendicularly to the centroid. 
     
     
         18 . The apparatus of  claim 1 , wherein an equivalent radius of a cross-sectional area of the channel within at least a portion of the first focusing segment increases at a decreasing rate along the centroid along at least a portion of the length of the channel in a direction from the first opening to the second opening, the equivalent radius being a square root of a cross-sectional area of the channel divided by pi, and the cross-sectional area being measured perpendicularly to the centroid. 
     
     
         19 . The apparatus of  claim 1 , wherein an equivalent radius of a cross-sectional area of the channel within at least a portion of the first focusing segment increases at an increasing rate along the centroid along at least a portion of the length of the channel in a direction from the first opening to the second opening, the equivalent radius being a square root of a cross-sectional area of the channel divided by pi, and the cross-sectional area being measured perpendicularly to the centroid. 
     
     
         20 . The apparatus of  claim 1 , wherein the channel system comprises at least one second focusing segment arranged in parallel with the first focusing segment between the first reservoir and the second reservoir. 
     
     
         21 . The apparatus of  claim 1 , wherein the channel system comprises at least one second focusing segment arranged in series with the first focusing segment between the first reservoir and the second reservoir. 
     
     
         22 . The apparatus of  claim 21 , wherein the apparatus comprises at least one third focusing segment arranged in parallel with at least one of the first focusing segment or the second focusing segment between the first reservoir and the second reservoir. 
     
     
         23 . The apparatus of  claim 1 , wherein the apparatus comprises an array of at least 1000 channel systems between the first reservoir and the second reservoir. 
     
     
         24 . The apparatus of  claim 1 , wherein the focusing comprises a specular reflection of objects of interest off a surface geometry. 
     
     
         25 . The apparatus of  claim 24 , wherein the surface geometry comprises a concave surface. 
     
     
         26 . The apparatus of  claim 24 , wherein the surface geometry comprises a convex surface. 
     
     
         27 . The apparatus of  claim 1 , wherein the first focusing segment comprises a channel of decreasing cross-sectional area along the length of the channel in a direction from the first opening to the second opening. 
     
     
         28 . The apparatus of  claim 1 , wherein the first focusing segment comprises a channel of increasing cross-sectional area along the length of the channel in a direction from the first opening to the second opening. 
     
     
         29 . The apparatus of  claim 1 , wherein the focusing comprises a refraction of objects of interest through a lens material. 
     
     
         30 . The apparatus of  claim 1 , wherein the focusing comprises an increase in a volumetric number density of objects of interest passing through the first focusing segment from the first capture surface to the second capture surface. 
     
     
         31 . The apparatus of  claim 30 , wherein the increase in the volumetric number density of objects of interest is an isothermal reduction in entropy for objects of interest. 
     
     
         32 . The apparatus of  claim 1 , wherein the focusing comprises an increase in an average magnitude of a component of momentum of the objects of interest in a specified direction, wherein the specified direction is a direction from the first reservoir to the second reservoir along the centroid of the channel, wherein the objects of interest are passing through the first focusing segment from the first capture surface to the second capture surface. 
     
     
         33 . The apparatus of  claim 1 , wherein a trajectory of an object of interest entering the first focusing segment via the first capture surface forms an acute first influx angle with respect to a direction of the centroid of the channel at the first capture surface, and wherein the trajectory of the object of interest subsequently exiting the first focusing segment via the second capture surface forms an acute first outflux angle with respect to a direction of the centroid of the channel at the second capture surface,
 wherein the focusing comprises a reduction in the average first outflux angle relative to the average first influx angle for at least a portion of the objects of interest.   
     
     
         34 . The apparatus of  claim 1 , wherein a trajectory of an object of interest entering the first focusing segment via the first capture surface forms an acute first influx angle with respect to a direction of the centroid of the channel at the first capture surface, and wherein the trajectory of the object of interest subsequently exiting the first focusing segment via the second capture surface forms an acute first outflux angle with respect to a direction of the centroid of the channel at the second capture surface,
 wherein the focusing comprises a modification of a statistical distribution of first influx angles over a range of all possible first influx angles compared to a statistical distribution of first outflux angles over a range of all possible first outflux angles.   
     
     
         35 . The apparatus of  claim 34 , wherein the modification of the statistical distribution comprises a reduction in a standard deviation of the statistical distribution of first outflux angles over the range of all possible first outflux angles compared to a standard deviation of the statistical distribution of first influx angles over the range of all possible first influx angles. 
     
     
         36 . The apparatus of  claim 34 , wherein the modification of the statistical distribution comprises a reduction in the range of all possible first outflux angles compared to the range of all possible first influx angles. 
     
     
         37 . The apparatus of  claim 1 , wherein the first focusing segment is configured to focus substantially radial trajectories of objects of interest at the first capture surface into substantially parallel trajectories of the objects of interest at the second capture surface for objects of interest passing through the first focusing segment in a direction from the first reservoir to the second reservoir. 
     
     
         38 . The apparatus of  claim 1 , wherein the focusing of at least a portion of the trajectories of objects of interest passing through the first focusing segment from the first capture surface to the second capture surface comprises an increase in flux of objects of interest through at least a portion of the second capture surface compared to a corresponding prior flux of the objects of interest through the first capture surface, wherein the flux of objects of interest is the number density of objects of interest passing through a specified surface per unit area and per unit time,
 wherein the first focusing segment is configured to focus substantially parallel trajectories of objects of interest at the first capture surface into substantially radial trajectories of the objects of interest at the second capture surface for objects of interest passing through the first focusing segment in a direction from the first reservoir to the second reservoir.   
     
     
         39 . The apparatus of  claim 1 , wherein a characteristic length of the first focusing segment is less than 1000 times a mean free path of the objects of interest within the first focusing segment, and wherein a characteristic width of the first focusing segment is less than 1000 times a mean free path of the objects of interest within the first focusing segment. 
     
     
         40 . The apparatus of  claim 1 , wherein the first focusing segment has a first transmissivity, the first transmissivity being a probability of an object of interest subsequently exiting the first focusing segment through the second capture surface given that the object of interest has entered the first focusing segment through the first capture surface,
 wherein the first focusing segment has a second transmissivity, the second transmissivity being a probability of an object of interest subsequently exiting the first focusing segment through the first capture surface given that the object of interest has entered the first focusing segment through the second capture surface,   the first capture surface having a first capture surface area and the second capture surface having a second capture surface area,   the ratio of a first product to a second product being greater than unity for a static boundary condition, the first product being a product of the first capture surface area and the first transmissivity, the second product being a product of the second capture surface area and the second transmissivity,   wherein at least a portion of a difference in transmissivity of objects of interest is facilitated by the first focusing segment.   
     
     
         41 . The apparatus of  claim 1 , wherein the passage of objects of interest from the first reservoir through the first opening, through the channel system and through at least one focusing segment, and through the second opening to the second reservoir comprises diffusion of objects of interest, and/or the Brownian motion of objects of interest. 
     
     
         42 . The apparatus of  claim 1 , wherein the first reservoir or the second reservoir comprises the atmosphere of earth. 
     
     
         43 . The apparatus of  claim 1 , wherein the first reservoir or the second reservoir comprises a vacuum, or wherein the first reservoir or the second reservoir comprises an electrical conductor. 
     
     
         44 . The apparatus of  claim 1 , wherein the first reservoir and the second reservoir are identical. 
     
     
         45 . The apparatus of  claim 1 , wherein the first reservoir and the second reservoir are thermally insulated from each other. 
     
     
         46 . The apparatus of  claim 1 , wherein the bulk material comprises a metal, a glass, a crystalline material, a ceramic, an electrical insulator, an electrical semi-conductor, an electrical conductor, or an electrical superconductor. 
     
     
         47 . The apparatus of  claim 1 , wherein the medium comprises a gas, liquid, solid, or a vacuum, or
 wherein the medium comprises a metal, a glass, a crystalline material, a ceramic, an electrical semi-conductor, or an electrical conductor.   
     
     
         48 . The apparatus of  claim 1 , wherein at least a portion of the channel system is bounded by a surface of the bulk material. 
     
     
         49 . The apparatus of  claim 1 , wherein the channel system is a set of all possible trajectories of objects of interest passing from the first reservoir via the first opening and the second opening to the second reservoir, or from the second reservoir via the second opening and the first opening to the first reservoir. 
     
     
         50 . The apparatus of  claim 1 , wherein a further interaction comprises defocusing of at least a portion of the trajectories of objects of interest passing through the first focusing segment from the second capture surface to the first capture surface, the defocusing occurring within the first focusing segment and within a distance less than 1000 times the mean free path of the objects of interest within the first focusing segment.