Axisymmetric thermoviscous and thermal expansion flows for microfluidics

Recent microfluidic experiments have explored the precise positioning of micron-sized particles in liquid environments via laser-induced thermoviscous flow. From micro-robotics to biology at the subcellular scale, this versatile technique has found a broad range of applications. Through the interplay between thermal expansion and thermal viscosity changes, the repeated scanning of the laser along a scan path results in fluid flow and hence net transport of particles, without physical channels. Building on previous work focusing on two-dimensional microfluidic settings, we present an analytical, theoretical model for the thermoviscous and thermal expansion flows and net transport induced by a translating heat spot in three-dimensional, unconfined fluid. We first numerically solve for the temperature field due to a translating heat source in the experimentally relevant limit. Then, in our flow model, the small, localised temperature increase causes local changes in the mass density, shear viscosity and bulk viscosity of the fluid. We derive analytically the instantaneous flow generated during one scan and compute the net transport of passive tracers due to a full scan, up to quadratic order in the thermal expansion and thermal shear viscosity coefficients. We further show that the flow and transport are independent of bulk viscosity. In the far field, while the leading-order instantaneous flow is typically a three-dimensional source or sink, the leading-order average velocity of tracers is instead a source dipole, whose strength depends on the relative magnitudes of the thermal expansion and thermal shear viscosity coefficients. Our quantitative results reveal the potential for future three-dimensional net transport and manipulation of particles at the microscale.