Light-induced heat-conducting micro/nano spheroidal particles and their thermoosmotic velocity fields

A micro/nano spheroidal conducting particle embedded in a fluid of a uniform ambient temperature is considered for its temperature and the induced velocity fields due to thermoosmosis. The particle is assumed to be uniformly heated using for example continuous light irradiation by a conventional laser. This is a model problem of thermoplasmonics, where nano or micro particles are used for heat storage and release as in medical therapy and imaging purposes. The temperature field is governed by the Poisson heat diffusion equation and the self-induced thermoosmotic flow (STOF) field is taken as a Stokes type. Analytical closed solutions are derived for both the temperature distributions (inside and outside the particle) as well as for the STOF in the solute for both prolate and oblate configurations. They are based on using spheroidal harmonics expressed in terms of Legendre functions, where owing to orthogonality only a few terms are needed to fully prescribe the entire field. The analytical solutions thus obtained are also numerically verified for few selected cases. Results for conducting spheroidal particles with inner thermal conductivities lower or higher than the outer medium's conductivity are analysed. It is shown that the surface temperature of the particle is always highest at the tip nearest to the spheroid's centre. However, the location of the peak of the surface heat flux depends on the precise ratio between the inner and outer thermal conductivities, where it peaks at the nearest tip for a low inner thermal conductivity and at the farthest tip for a high inner thermal conductivity. Plots of temperature and heat flux distributions over the surface of both prolate and oblate spheroidal particles as well as the thermoosmotic (Soret) induced velocity, vorticity and stream-function in the liquid phase are given and analysed.