An extended standard blocking filtration law for exploring membrane pore internal fouling due to rate-determining adsorption

Membrane internal fouling due to foulant adsorption onto the pore walls is a critical aspect of fouling. The classical "standard blocking law" for internal fouling simplistically assumes instantaneous adsorption such that the adsorbed amount grows linearly with the filtered liquid volume, which is inadequate to describe realistic internal fouling with varied adsorption rates. In this study, an extended standard blocking law for scenarios involving time dependent adsorption is proposed and yields an expression of the form dR/dV similar to R-N (where R is filtration resistance and V is filtrate volume). Two ultimate scenarios of the law, i.e. the 1st kind for sufficiently fast adsorption with the characteristic exponent N approximate to 1.5 (similar to the classical standard blocking) and the 2nd-kind for sufficiently slow adsorption with N approximate to 2.5 are experimentally verified via microfiltration of model polysaccharide (alginate) solutions using hydrophobic and hydrophilic membranes. Transition between the 1st-kind and 2nd kind laws is related to the rates of adsorption versus filtrational mass transfer. The extended law provides an improved tool to evaluate internal fouling, particularly that associated with adsorption of hydrophilic matter (such as polysaccharides) into hydrophilic membranes.