Determining Brownian and shear-induced diffusivity of nano- and micro-particles for sustainable membrane filtration

Abstract

Membrane filtration for sustainable wastewater reuse has been encountering particle deposition (i.e., particle cake fouling) with mostly micron-sized particles including bacteria, and nano-sized colloids/particles as well. Particle size may influence membrane fouling and flux decline through cake formation as particles with different sizes exhibit different back diffusivity and packing density of the cake. A theoretical diffusivity equation was proposed by Einstein (1906) [1]; thermodynamic and drag (i.e., resistance or mobility relation) forces were compared in equilibrium. The diffusivity relationship, ratio of thermodynamic and drag forces, was combined with steady-state convection and diffusion equation and finally came up with a relationship between retention times from flow field-flow-fractionation (f1-FFF) and diffusivity of a particle. An asymmetric f1-FFF system (Postnova, Germany) equipped with a regenerated cellulose membrane with molecular weight cutoff of 1,000 molecular mass and a micro-channel employing both laminar channel and cross flows, was used to obtain chromatography using an UV detector. A wide range of colloids and particles were used; both traceable polymer and latex microsphere colloids/particles with nominal diameters of 0.09 (i.e., 90 rim), 0.152, 0.2, 0.5, 0.701, 0.82, 0.993, 1.0 mu m (Duke Scientific, US), and micro silica particles with nominal diameters of 3.0, 6.0, 10.0 mu m (Nanotech, Korea). Each colloid or particle was characterized in terms of either its size or diffusivity with analyses of chromatography obtained from f1-FFF. It was found in this work that ca. 0.5 mu m is a critical size below and above which diffusivity of a particle increases (i.e., particle of 0.5 mu m has a minimum diffusivity). An empirical equation for the shear-induced diffusivity will be suggested in the presentation based on the results obtained from the fl-FFF. There may be many important implications on this observation; for example, bacteria with a 0.5 mu m size may provide significant cake deposition and subsequently flux decline and possibly bio-fouling. These nano-/micro-size and diffusivity information is being investigated in conjunction with membrane filtration with the corresponding particles and various membranes