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

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 (fl-FFF) and diffusivity of a particle. An asymmetric fl-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 nm), 0.152, 0.2, 0.5, 0.701, 0.82, 0.993, 1.0 µm (Duke Scientific, US), and micro silica particles with nominal diameters of 3.0, 6.0, 10.0 µm (Nanotech, Korea). Each colloid or particle was characterized in terms of either its size or diffusivity with analyses of chromatography obtained from fl-FFF. It was found in this work that ca. 0.5 µm is a critical size below and above which diffusivity of a particle increases (i.e., particle of 0.5 µm 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 µm 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.