NOVELTY - Apparatus for processing fluids in a reactor contains an elastic permeable barrier (2), an upstream storage area (3), and a downstream storage area (4). A driving force is placed across the elastic permeable barrier. It cyclically varies with time and is calculated as the difference between the fluid pressure in the upstream storage area and the fluid pressure in the downstream storage area less any pressure losses resulting from flow through the elastic permeable barrier. The fluid flow rate through the elastic permeable barrier cyclically varies with time.    USE - The apparatus is used for processing fluids in a reactor used to undertake fluid separation, fluid filtration, heat generation, power generation, energy capture, and/or fluid absorption/adsorption/desorption. It is used to undertake catalytic reactions, non-catalytic reactions, and/or biological reactions (all claimed). The reactor is an oscillating flow reactor used for catalytic processes, non-catalytic processes, filtration processes, fluid adsorption processes, fluid separation processes, concentrating kinetic energy, and/or concentrating potential energy. The apparatus is used for the processing (treatment, filtration, adsorption) of storm water runoff, process water, wastewater, foul water, riparian water, water from reservoir, or water from any other source to produce water for riparian discharge, industrial purposes, chemical purposes, process purposes, manufacturing purposes, agricultural purposes, infiltration purposes, and/or drinking purposes; processing of flue gases, exhaust gases, waste gases, and other gases to remove carbon dioxide and manufacture of oil and/or organic chemicals from gases containing e.g. carbon monoxide and carbon dioxide and hydrogen containing gases; production of organic chemicals from synthesis gas; manufacture of synthesis gas; production of products using fermentation processes including biogas, alcohol, acetic acid, and acetate; processing of blood (e.g. dialysis); manufacture of biodiesel and biofuels from vegetable oils and/or biomass; recovery of metals from waste materials and mineral ores; production of metals and metal nanocatalysts; production of metal carbonyls production of carbon nanotubes and carbon nanocatalysts; pyrolysis, carbonization, gasification, and coking processes; removal of sulfur compounds from natural gas, synthesis gas, and process gas; filtration, absorption, and desorption processes; fluid separation processes; and increasing the effective storage capacity of carbon dioxide sequestration reservoir.    ADVANTAGE - The apparatus can allow the product yield to increase with increasing space velocity. The potential energy and kinetic energy are concentrated during different stages of the driving force wave. This allows dispersed energy to be concentrated for use in separation processes as potential energy, and kinetic energy to be concentrated for recovery as motive or electrical power. The apparatus is highly flexible and can accommodate a feed, which is delivered at a constant rate, variable rate, irregular rate, intermittently, or episodically; can accommodate a demand for product from the reactor, which is continuous, intermittent, or variable; and can be structured to operate at a lower internal pressure for a specific feed flow rate than a fixed bed reactor or fluidized bed reactor, for a specific length of catalyst bed and feed flow rate.    DETAILED DESCRIPTION - Apparatus for processing fluids in a reactor contains an elastic permeable barrier (2), an upstream storage area (3), and a downstream storage area (4). A driving force is placed across the elastic permeable barrier. It cyclically varies with time and is calculated as the difference between the fluid pressure in the upstream storage area and the fluid pressure in the downstream storage area less any pressure losses resulting from flow through the elastic permeable barrier. The fluid flow rate through the elastic permeable barrier cyclically varies with time and is independent of the flow rate into the upstream storage area through the upstream conduit (5), or is partially dependent on the flow rate into the upstream storage area through the upstream conduit. The fluid flow rate through the elastic permeable barrier cyclically varies with time and is independent of the flow rate from the downstream storage area into the downstream conduit (7), or is partially dependent on the flow rate from the downstream storage area into the downstream conduit. Part or all of the kinetic energy contained in the fluid entering the upstream storage area through the upstream conduit is transferred into potential energy or another form of energy on entering the upstream storage area. Part or all of the potential energy contained in the fluid within the upstream storage area is transferred into kinetic energy or another form of energy on entering the elastic permeable barrier. Part or all of the kinetic energy contained in the fluid entering the downstream storage area from the elastic permeable barrier is transferred into potential energy or another form of energy on entering the downstream storage area. Fluid flow rate cycles have a constant duration, a variable duration, or an irregular duration. Fluid flow through the elastic permeable barrier is continuous, irregular, intermittent, or episodic. Fluid flow through the elastic permeable barrier oscillates between higher and lower flow rates. The low flow rates can be 0 m3/s. The high flow rates are greater than the average flow rate received by the upstream storage area from upstream conduit(s).    DESCRIPTION OF DRAWING(S) - The drawing is a schematic view of apparatus for processing fluids in a reactor.    Elastic permeable barrier (2)    Upstream storage area (3)    Downstream storage area (4)    Upstream conduit (5)    Downstream conduit (7)