  We investigate the interplay of thermophoretic force and interfacial tension
on the capillary filling dynamics of a Newtonian nanofluid in a microchannel.
In our model, we also consider an intricate thermofluidic coupling by taking
the temperature dependence of viscosity aptly into account. This, in turn,
determines the evolution of the viscous resistive force as the capillary front
progresses, and presents an involved inter-connection between the driving
thermophoretic force and the viscous resistive force. The two distinct regimes
of particle transport in a fluid medium, delineated by particle size, are
expounded to peruse the impact of imposed thermal gradients and particle size
on particle retaining propensity of the nanofluid. Additionally, we witness a
significant reduction in particle bearing proclivity of the nanofluid with
enhancement in a thermal gradient. The results demonstrate the efficacy of the
thermophoretic actuation towards the filling of narrow capillaries under the
influence of a thermal gradient.
