Self-thermophoresis of laser-heated spherical Janus particles

E J Avital,T Miloh

doi:10.1140/epje/s10189-021-00128-4

E J Avital, T Miloh

Open Access

https://doi.org/10.1140/epje/s10189-021-00128-4

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Abstract

An analytic framework is presented for calculating the self-induced thermophoretic velocity of a laser-heated Janus metamaterial micro-particle, consisting of two conducting hemispheres of different thermal and electric conductivities. The spherical Janus is embedded in a quiescent fluid of infinite expanse and is exposed to a continuous light irradiation by a defocused laser beam. The analysis is carried under the electrostatic (Rayleigh) approximation (radius small compared to wavelength). The linear scheme for evaluating the temperature field in the three phases is based on employing a Fourier–Legendre approach, which renders rather simple semi-analytic expressions in terms of the relevant physical parameters of the titled symmetry-breaking problem. In addition to an explicit solution for the self-thermophoretic mobility of the heated Janus, we also provide analytic expressions for the slip-induced Joule heating streamlines and vorticity field in the surrounding fluid, for a non-uniform (surface dependent) Soret coefficient. For a ‘symmetric’ (homogeneous) spherical particle, the surface temperature gradient vanishes and thus there is no self-induced thermophoretic velocity field. The ‘inner’ temperature field in this case reduces to the well-known solution for a laser-heated spherical conducting colloid. In the case of a constant Soret phoretic mobility, the analysis is compared against numerical simulations, based on a tailored collocation method for some selected values of the physical parameters. Also presented are some typical temperature field contours and heat flux vectors prevailing in the two-phase Janus as well as light-induced velocity and vorticity fields in the ambient solute and a new practical estimate for the self-propelling velocity.Graphic abstract

Highlights

Thermophoresis is generally a process where a particle is propelled by an imposed temperature gradient in the solute [15,16,17,18,19,20,21] or by a Soret-type force due to temperature variations over its surface
An analytic model was developed for obtaining the self-thermophoretic mobility of a light-activated Jouleheated Janus particle (JP) composing of two distinct material hemispheres and surface-dependent mobility, embedded in a quiescent conductive liquid
The temperature, velocity and vorticity fields are governed by the linear Poisson equation and the creeping flow (Stokes) model

Summary

Introduction

Thermophoresis is generally a process where a particle is propelled by an imposed temperature gradient in the solute [15,16,17,18,19,20,21] or by a Soret-type force due to temperature variations (non-uniformity) over its surface. The case of a photoactive spheroidal JP, assuming a large contrast (i.e. ideally dielectric and perfectly conducting halves) has been analytically discussed in [14] Both inner and outer temperature fields were explicitly obtained under these restrictive conditions and the JP’s mobility, depending on its eccentricity was obtained. One expects that a sharp contrast between the thermal conductivities of the JP hemispheres should have a considerable effect on both the ‘inner’ and ‘outer’ temperature distributions and as a result on the induced self-thermophoretic velocity field Some discussions of the analytic results and numerical simulations found are presented in Sects. 4 and 5, followed by a conclusion section

The linearized ‘symmetry-breaking’ physical model

Solution methodology

Results and discussion for the developed JP model of two hemispheres

Conclusions