Philip K. Chan

Sonophotolytic degradation of synthetic pharmaceutical wastewater: Statistical experimental design and modeling

The merits of the sonophotolysis as a combination of sonolysis (US) and photolysis (UV/H2O2) are investigated in a pilot-scale external loop airlift sonophotoreactor for the treatment of a synthetic pharmaceutical wastewater (SPWW). In the first part of this study, the multivariate experimental design is carried out using Box-Behnken design (BBD). The effluent is characterized by the total organic carbon (TOC) percent removal as a surrogate parameter. The results indicate that the response of the TOC percent removal is significantly affected by the synergistic effects of the linear term of H2O2 dosage and ultrasound power with the antagonistic effect of quadratic term of H2O2 dosage. The statistical analysis of the results indicates a satisfactory prediction of the system behavior by the developed model. In the second part of this study, a novel rigorous mathematical model for the sonophotolytic process is developed to predict the TOC percent removal as a function of time. The mathematical model is based on extensively accepted sonophotochemical reactions and the rate constants in advanced oxidation processes. A good agreement between the model predictions and experimental data indicates that the proposed model could successfully describe the sonophotolysis of the pharmaceutical wastewater.

A Computational Study into Thermally Induced Phase Separation in Polymer Solutions under a Temperature Gradient

The influence of spatial temperature on the morphological development in polymer solutions undergoing thermally induced phase separation was studied using mathematical modeling and computer simulation. The one-dimensional mathermatical model describing this phenomenon incorporates the nonlinear Cahn-Hilliard theory for spinodal decomposition (SD), the Flory-Huggins theory for polymer solution thermodynamics, and the slow-mode theory and Rouse-law for polymer diffusion. The resulting governing equation and auxiliary conditions were solved using the Galerkin finite element method. The temporal evolution of the spatial concentration profile from the computer simulation illustrates that an anisotropic morphology (see Figure) results when a temperature gradient is maintained along the polymer solution sample. The final anisotorpic morphology depends on the overali phase separation time. If phase separation is terminated at very early stages, smaller (larger droplets are formed in the lower (higher) temperature regions due to be deep (shallow) quench effect. On the other hand, if phase separation is allowed to proceed for a long period of time. then larger droplets are formed in the low-temperature regions, whereas smaller droplets are developed at higher temperatures. This is due to the fact that the low-temperature regions have entered the late stage of SD. while the high temperture regions are still in the early stage of SD.The presence of a temperature gradient during thermally induced phase separation introduced spatial variations in the change of chemical potential, which is the driving force for phase separation. These numerical results provide a better understanding or the control and optimization during the fabrication of anisotropic polymeric materials using the thermally induced phase separation technique.

Effect of concentration gradient on the thermal-induced phase separation phenomenon in polymer solutions

This paper studied the thermal-induced phase separation (TIPS) phenomenon via spinodal decomposition (SD) in a polymer solution under a linear concentration gradient. The one-dimensional model consists of the Cahn–Hilliard theory for SD and incorporates the Flory–Huggins free energy equation, the slow mode mobility theory and Rouse model for polymer diffusion. The model is able to replicate frequently reported experimental observations reported in the literature, which includes the formation of anisotropic polymer membranes using the TIPS method. We show and explain that the anisotropic morphology is due to the polymer solution undergoing SD at different rates along the sample as a result of the initial concentration gradient.

Kinetic study of photodegradation of water soluble polymers

The kinetic models of the photo-oxidative degradation of water-soluble polymers, as the main component of water-soluble composite films in aqueous solutions, by ultraviolet radiation and hydrogen peroxide (UV/H2O2) are developed. The rate expressions of the photochemical degradation of soluble polymers are developed based on the mass balance of the main chemical species in water. Continuous-distribution kinetics is applied for the kinetic modeling of the photo-oxidative degradation of polymers in aqueous solutions based on the population balance equations (PBEs). It is assumed that the random chain scission is the mechanism of the chain cleavage. The PBEs are solved by the moment operation which transforms the integro-differential equations into ordinary differential equations that could be readily solved to obtain the rate coefficients of the polymer photodegradation. The model predictions for the number average molecular weight and the number of chain scissions per molecules are in good agreement with the experimental data obtained from the open literature for the photodegradation of poly(ethylene glycol) by the UV/H2O2 process in aqueous solution. The results confirmed the random chain scission assumption. The sequential quadratic programming was used as an optimization technique to find the kinetic parameters that could be used for scaling-up purposes.

Simultaneous use of temperature and concentration gradients to control polymer solution morphology development during thermal-induced phase separation

Temperature and initial concentration gradients have been used independently during thermal-induced phase separation to create anisotropic functional porous polymeric materials.In this paper, we developed and implemented a mathematical model that combines both linear temperature and initial linear concentration gradients during the thermal-induced phase separation process. The numerical results show that the ensuing anisotropic morphology depends largely on the directions of both the temperature and concentration gradients. This allows for a better understanding and control of the fabrication process of porous functional polymeric materials. The numerical results are explained using existing spinodal decomposition theory.

Computer simulation of elongated bipolar nematic droplets 1. External field aligned parallel to the droplet axis of symmetry

The magnetically-induced transient nematic director reorientation dynamics, confined in elongated bipolar droplets, is studied in this paper. Numerical results are obtained by solving the Leslie-Ericksen continuum theory in ellipses. The aspect ratio is varied to determine the effect of droplet shape on director reorientation dynamics. The magnetic field is restricted to the droplet axis of symmetry direction, which has not yet been studied but is fundamentally important in polymer dispersed liquid crystal (PDLC) film operation. The numerical results replicate frequently-reported experimental observations on the performance of PDLC films. These observations include the familiar exponential increases followed by saturation in light transmittance as the external applied field increases and the exponential increase (decrease) followed by saturation as time increases in the on- (off-) state. In addition, the experimental observation that switching field strength increases while decay time decreases as the dro...

The effects of elongated nematic bipolar droplet orientation on the performance of polymer-dispersed liquid crystal films

Abstract The effects that the elongated nematic bipolar droplet orientation has on the performance of polymer-dispersed liquid crystal (PDLC) films are elucidated in this paper using modeling and simulation. Important performance criteria are low switching field strength in the on-state, good light contrast between the on- and off-states, and fast relaxation time in the off-state. In particular, the model incorporates the Leslie–Ericksen and Frank liquid crystal theories and an external magnetic field. The model is solved in two-dimensions within an ellipse of aspect ratio 1.5. The numerical results indicate that the PDLC film should be designed with the bipolar droplet axis of symmetry normal to the film plane in order to minimize both the required switching field strength and relaxation time. On the other hand, the PDLC film should be designed with the bipolar droplet axis of symmetry oriented within the film plane in order to maximize the light contrast between the on- and off-states.

Computational study of the texture formation in mesophase pitch‐based carbon fibres

This paper studies the thermal relaxation phenomena after melt‐extrusion of a rigid discotic uniaxial nematic mesophase pitch using mathematical modelling and computer simulation. The Ericksen and Landau–de Gennes continuum theories are used to investigate the structure development and texture formation across mesophase pitch‐based carbon fibres. The two‐dimensional model captures five types of transverse patterns, which match the commonly observed textures for mesophase pitch‐based carbon fibres. They are: random, zig‐zagged radial, radial, quasi‐onion and onion. These textures represent the various combinations possible from the interplay between structure (i.e. texture) development and cooling during the fibre spinning process. During the thermal relaxation after the cessation of extensional flow the discotic nematic molecules store elastic free energy decays. The distorted nematic molecular profiles reorient to release the stored elastic free energy. The difference in time scales for molecular reorientation and thermal relaxation result in different transverse textures. The rate at which the fibres are cooled is the main factor in controlling the structure development. A slow cooling rate would permit the nematic discotic molecules to reorient to a well‐developed (radial or onion) texture. The random texture is a result of rapid quenching. The numerical results are consistent with published experimental observations.

A computational study of multiple surface-directed phase separation in polymer blends under a temperature gradient

The surface-directed phase separation (SDPS) phenomena of a model binary polymer blend quenched into the unstable region of its binary symmetric upper critical solution temperature phase diagram is numerically investigated using a mathematical model composed of the nonlinear Cahn–Hilliard (CH) theory for phase separation along with the Flory–Huggins–de Gennes (FHdG) free energy functional. The SDPS occurs in a square domain with a linear temperature gradient along the horizontal direction and with all sides having short range surface potential h 1. The effects of different quench depth, diffusion coefficient, surface potential, and temperature gradient were studied numerically. The numerical results indicate that there is a simultaneous competition between the four surfaces in attracting the preferred polymer. The side with a higher surface potential would win the competition against the side with a lower surface attraction in the case of a uniform quench. The numerical results also indicated a later transition time for higher values of h 1. As surface potential increased, the transition time from complete wetting to partial wetting occurred at a later time on the surface. The impact of different temperature gradient ΔT*/Δx* values on the surface enrichment rate with fixed temperature at one surface and higher temperature at the opposite surface was studied for the first time within a multiple surface potential set up. The results showed that higher values of ΔT*/Δx* increased the growth rate of the preferred polymer on the surface adding to the thickness of the wetting layer. The transition time from complete wetting to partial wetting occurred slightly later at the lower temperature side.