Membrane separation is known as an economic and environmental friendly mode of separation and is used in various types of separation processes. The major challenges regarding membrane separation are the internal and external fouling of the membrane which reduces the permeate flux of the membranes by inducing extra resistance to flow. Synthetic membranes are designed and implemented to separate solutes or particles in a feed stream by rejecting them and permitting the liquid to pass through the membrane pores; however, most of the feed streams, such as wastewaters, contain more than one type of solute. This yields a distribution of particle sizes in the feed. Many wastewaters contain supracolloidal particles (1-100µm). Most membrane separations aim to remove these particles from the feed solution. Wastewaters also contain colloidal particles (0.001-1µm). These particles are less concentrated than supracolloidal particles in the feed but they are more problematic since they are able to penetrate into the membrane pores and cause internal fouling which is the main source of irreversible flux decline. Fouling mechanisms are traditionally classified into four types. Among these mechanisms, standard pore blocking (pore constriction) refers to internal fouling while the other types model external fouling. On the effect of pore geometry, as a morphological factor, studies to date have been limited to external membrane fouling. However, it is believed that up to 80% of the permeate flux can be affected by pore constriction which is caused by particle penetration and deposition into membrane pores (internal fouling). The effect of pore geometry, as a factor, in flux decline due pore constriction of membranes was investigated in this work. Pore constriction by particles was approximated by maximum particle deposition onto the interior wall of the pores and simulated using MATLAB image processing toolbox (MIPT). Sixteen different basic geometries were considered for the simulation of pore constriction by particles. These include circular pores, 3 groups of rectangular, triangular and oval geometries at four different aspect ratios (3, 7, 15 and 30) and three combined geometries of star, cross and a rectangle with rounded ends. The simulation of maximum particle deposition onto pore walls was carried out for a range of particle diameters to pore hydraulic diameters (λ) of 0.1 to the complete rejection of the particle by the pore. As the result of the simulation, the ratio of the available pore cross-sectional area after pore constriction to initial pore cross-sectional area (α) and the ratio of pore channel hydraulic diameter after pore constriction to initial pore hydraulic diameter (β) were measured and recorded. It was observed that for λ<0.2 (small particles compared to pore size) some geometries showed the same values of α and β. However, for λ>0.2, other geometries showed different values of α and β. It was also observed that several geometries reject the particle at different λ ratios. Using the values of α and β, the fluxes of membranes having different pore geometries, after pore constriction by particles, were calculated and compared. These results show that for a very small particle size, compared to pore size, there is no preference for a specific geometry over another; however, for intermediate particle sizes, membranes having triangular and star pore shapes provide higher fluxes compared to other membranes. The effect of pore aspect ratio (PAR) on the flux of membranes after pore constriction was also examined. In order to compare the combined effect of pore geometry on particle rejection and pore constriction, fluxes of membranes having different pore shapes were compared in light of several pore size distributions (PSDs). For this part of the study, the pore geometries of circular, rectangular, triangular and oval were considered at four PARs. Different values for the hydraulic diameter of the largest rejecting pore (D_(H,LRP)) were observed for different geometries. Rectangular pores showed the largest values of D_(H,LRP), at a constant PAR, which affirms their superior rejection behavior. The overall flux of the membranes after pore constriction was determined by a combination of three effects: the position of D_(H,LRP) in the PSD, the pore constriction behavior of the pore geometry and the shape of the PSD. Generally, for the PSDs for which most of the pores in the membrane physically reject the particles, membranes having rectangular pores showed higher fluxes, due to the greater rejection of particles. However, for PSDs for which a major number of pores are constricted by the particles, membranes with triangular pores offered higher flux after membrane pore constriction. The results of this work indicate a new direction for the design of membranes having defined pore geometries.

Membrane separation is known as an economic and environmental friendly mode of separation and is used in various types of separation processes. The major challenges regarding membrane separation are the internal and external fouling of the membrane which reduces the permeate flux of the membranes by inducing extra resistance to flow. Synthetic membranes are designed and implemented to separate solutes or particles in a feed stream by rejecting them and permitting the liquid to pass through the membrane pores; however, most of the feed streams, such as wastewaters, contain more than one type of solute. This yields a distribution of particle sizes in the feed. Many wastewaters contain supracolloidal particles (1-100µm). Most membrane separations aim to remove these particles from the feed solution. Wastewaters also contain colloidal particles (0.001-1µm). These particles are less concentrated than supracolloidal particles in the feed but they are more problematic since they are able to penetrate into the membrane pores and cause internal fouling which is the main source of irreversible flux decline. Fouling mechanisms are traditionally classified into four types. Among these mechanisms, standard pore blocking (pore constriction) refers to internal fouling while the other types model external fouling. On the effect of pore geometry, as a morphological factor, studies to date have been limited to external membrane fouling. However, it is believed that up to 80% of the permeate flux can be affected by pore constriction which is caused by particle penetration and deposition into membrane pores (internal fouling). The effect of pore geometry, as a factor, in flux decline due pore constriction of membranes was investigated in this work. Pore constriction by particles was approximated by maximum particle deposition onto the interior wall of the pores and simulated using MATLAB image processing toolbox (MIPT). Sixteen different basic geometries were considered for the simulation of pore constriction by particles. These include circular pores, 3 groups of rectangular, triangular and oval geometries at four different aspect ratios (3, 7, 15 and 30) and three combined geometries of star, cross and a rectangle with rounded ends. The simulation of maximum particle deposition onto pore walls was carried out for a range of particle diameters to pore hydraulic diameters (λ) of 0.1 to the complete rejection of the particle by the pore. As the result of the simulation, the ratio of the available pore cross-sectional area after pore constriction to initial pore cross-sectional area (α) and the ratio of pore channel hydraulic diameter after pore constriction to initial pore hydraulic diameter (β) were measured and recorded. It was observed that for λ<0.2 (small particles compared to pore size) some geometries showed the same values of α and β. However, for λ>0.2, other geometries showed different values of α and β. It was also observed that several geometries reject the particle at different λ ratios. Using the values of α and β, the fluxes of membranes having different pore geometries, after pore constriction by particles, were calculated and compared. These results show that for a very small particle size, compared to pore size, there is no preference for a specific geometry over another; however, for intermediate particle sizes, membranes having triangular and star pore shapes provide higher fluxes compared to other membranes. The effect of pore aspect ratio (PAR) on the flux of membranes after pore constriction was also examined. In order to compare the combined effect of pore geometry on particle rejection and pore constriction, fluxes of membranes having different pore shapes were compared in light of several pore size distributions (PSDs). For this part of the study, the pore geometries of circular, rectangular, triangular and oval were considered at four PARs. Different values for the hydraulic diameter of the largest rejecting pore (D_(H,LRP)) were observed for different geometries. Rectangular pores showed the largest values of D_(H,LRP), at a constant PAR, which affirms their superior rejection behavior. The overall flux of the membranes after pore constriction was determined by a combination of three effects: the position of D_(H,LRP) in the PSD, the pore constriction behavior of the pore geometry and the shape of the PSD. Generally, for the PSDs for which most of the pores in the membrane physically reject the particles, membranes having rectangular pores showed higher fluxes, due to the greater rejection of particles. However, for PSDs for which a major number of pores are constricted by the particles, membranes with triangular pores offered higher flux after membrane pore constriction. The results of this work indicate a new direction for the design of membranes having defined pore geometries.