We show how asymptotic reduction techniques are used to model the motion of sessile droplets in the presence of heat transfer, evaporation and nanoparticles. When nanoparticles are present in the drop, lubrication theory is used to model the contact line dynamics and the evolution of the nanoparticle concentration. The model accounts for the effects of surface tension, Marangoni stresses, evaporation and intermolecular forces; the effect of nanoparticles on the latter endows the film with structural disjoining pressure forces near the contact line. Our numerical simulations catalogue the different types of possible contact line dynamics, which range from spreading and retraction, to pinning and ‘terracing’; the latter phenomenon is caused by the effect of nanoparticles on the intermolecular forces.

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