The effects of rejecting nanoparticles at the solid-liquid interface of a colloid on the development of the solid-liquid interface, temperature and concentration profiles are investigated. The Rubinstein problem will be used in the current study which admits a closed-form analytical solution. A model NePCM based on cyclohexane as a solvent mixed with copper nanoparticles (diameters of 7, 5 and 2 nm) with various initial volume fractions of the nanoparticles will be considered. The rejection rate of the particles will be controlled through the segregation coefficient (I being the case of no rejection of particles, 0.1, 0.01, and 0.001). It was found that for the case of no particle rejection, the expected 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, for most cases with particle rejection considered the solid-liquid interface is decelerated with respect to pure cyclohexane as the volume of the nanoparticles is increased, and this deceleration is more pronounced as the particle size decreases. This deceleration is attributed to solidification with the rejection of the particles switched from diffusion- to solute-controlled solidification, and also due to the development of constitutionally-supercooled liquid in front of the solid-liquid interface. The maximum value of the concentration at the solid-liquid interface decreases as the concentration of the particles is increased; however, the value of the interface temperature is decreased as the concentration of the particles is increased. It was found that the transition segregation coefficient is the non-dimensional parameter that controls the transition from diffusion- to solute-controlled solidification, which is increased with the increase of the particle's volume fraction and with the decrease of the particle size. (C) 2013 Elsevier Ltd. All rights reserved.