Continuum mathematics at the nanoscale

Abstract

In this paper we discuss three examples where continuum theory may be applied to describe nanoscale phenomena: \begin{enumerate} \item[1.] Enhanced flow in carbon nanotubes (CNTs) -- This model shows that the experimentally observed enhancement can be explained using standard flow equations but with a depletion layer between the liquid and solid interfaces. \item[2.] Nanoparticle melting -- Nanoparticles often exhibit a sharp increase in melting rate as the size decreases. A mathematical model will be presented which predicts this phenomena. \item[3.] Nanofluids -- Experimental results concerning the remarkable heat transfer characteristics of nanofluids are at times contradictory. We develop a model for the thermal conductivity of a nanofluid, which provides much higher predictions than the standard Maxwell model and a better match to data. \end{enumerate}