Abstract: A method of increasing the time-averaged cross-flow filtration flux of a liquid through a porous filter medium over the period of a filtration run, comprising the steps of: (a) flowing the liquid transversely through the filter medium by establishing a pressure differential across the filter medium; and (b) maintaining the filtration flux rate through the filter medium at a preselected substantially constant value during the entire filtration run by applying a variable throttling pressure on the filtrate side of the filter medium and reducing the throttling pressure during the run to control the instantaneous value of the pressure differential as required to maintain the preselected flux rate, such flux rate being greater than the equilibrium flux rate.

Abstract: A method for softening a fluid containing hardness constituents, comprising the steps of: (a) mixing the fluid with sufficient amounts of a softening agent, and previously precipitated hardness constituents in a reactor to establish a softening reaction in the reactor for precipitating a substantial portion of the hardness constituents contained in the fluid; (b) removing a portion of the fluid and precipitated hardness constituents from the reactor as a slurry and filtering the slurry through a cross-flow microfiltration module containing at least one elongated filtration tube, whereby substantially all of the precipitated hardness constituents are removed from the portion of the fluid exiting from the module as filtrate; and (c) returning at least a portion of the filtered out precipitated hardness constiuents exiting from the module to the reactor as the previously precipitated hardness constituents.