Numerical Investigation of the Solidification of Nanoparticle-Based Colloidal Suspensions

Abstract

In this dissertation, analytical and numerical approaches were used for analysis of the solidification process of nanoparticle-based colloidal suspensions, with a special emphasis to those used as nanostructured-enhanced phase change materials (NePCM). A one-dimensional freezing model based on an extended version of the Rubinstein Problem will be used to analyze the solidification process of cyclohexane-copper suspensions. The chosen diameters for the nanoparticles are 7, 5 and 2 nm. The value of the initial volume fraction of the nanoparticles was varied. The rejection rate of the particles was controlled through the value of the segregation coefficient value (1 corresponding to no rejection of particles, 0.1, 0.01, and 0.001). With no particle rejection, the expedited movement of the solid-liquid interface with respect to the pure cyclohexane as the volume fraction of the particles increases is not always guaranteed for the same cold side surface temperature. However, with particle rejection, for most cases tested the solid-liquid interface is decelerated with respect to pure cyclohexane as the volume fraction of the nanoparticles is increased, and this deceleration is more pronounced as the particle size decreases. This deceleration is attributed to solidification when the rejection of the particles is switched from thermal- to solutal-controlled solidification and due to the development of a constitutionally supercooled liquid on the liquid side of the interface. The maximum attained value of the concentration at the solid-liquid interface is decreasing as the initial concentration of the particles is increased; however, the value of the interface temperature is decreased as the concentration of the particles is increased. The transition segregation coefficient that is the non-dimensional parameter that controls the transition from thermal- to solutal-controlled solidification is increased with the increase of the particle's volume fraction and with the decrease of the particle size. A two-dimensional model, which includes the effect of the fluid flow, will be implemented to simulate the freezing of water-copper suspension frozen from the bottom side of a square cavity. The diameter of the particles is 5 and 2 nm, and the particles' mass fraction is 10%. The model is based on the combination of a one-fluid-mixture approach with the single-domain enthalpy porosity model for phase change and assuming a linear dependence of the liquidus and solidus temperatures of the mushy zone on the local concentration of the nanoparticles subject to a constant value of the segregation coefficient. Thermal-solutal convection and the Brownian and thermophoretic effects are taken into account. The solid-liquid interface for the colloidal suspension with 5 nm particle size was almost planar throughout the solidification process. However, for the suspension with particle size of 2 nm, the solid-liquid interface evolved from a stable planar shape to an unstable dendritic structure. This transition was attributed to the constitutional supercooling effect, whereby the rejected particles that are pushed away from the interface into the liquid zone form regions of high concentration thus leading to a lower solidus temperature. Using the same two-dimensional model, the suspension of water-copper will be solidified unidirectionally from the left vertical side investigating the effect of different parameters on the thermal-solutal convection formed during the freezing process. Initially, the flow in the melt consisted of two vortices rotating in opposite directions. However, at later times only one counter clockwise rotating cell survived. Changing the material of the particle to alumina results in a crystallized phase with a higher concentration of particles if it is compared to that of the solid phase resulting from freezing the copper-water colloidal suspension. Decreasing the segregation coefficient destabilize the solid-liquid interface and increases the intensity of the convection cell with respect to that of no particle rejection. At slow freezing rates, the resulting crystal phase consisted of lower particle content if it is compared to that resulted from higher freezing rate.