Nonlinear dynamics of a microparticle in a hydro-thermophoretic trap

Controlling the translational and rotational motion of microparticles is a topic of current interest in soft matter and statistical mechanics. Roll rotation of a microparticle in a hydro-thermophoretic trap – which is a device that uses the flow of fluids and thermophoresis to trap and manipulate microparticles – was recently reported (Nalupurackal et al., 2023). Here, we study the coupled translational and rotational motion of a microparticle in a hydro-thermophoretic trap. We demonstrate, using experiments and theory, that the dynamical system describing the motion of the microparticle undergoes bifurcations when the power of lasers used in a hydro-thermophoretic trap is changed. We show that the advective fluid flow from laser heating and thermophoresis depend on the power of the laser through two distinct exponents. We obtain these exponents from experimental data. Using these exponents and a linear stability analysis of the equations of motion, we show that locations at which a microparticle can be trapped (stable fixed points of the dynamical system) can be tuned by changing the power of the lasers at the two hotspots. At higher power values, we find that there are no stable fixed points; hence, the microparticle can no longer be trapped. Our experimental findings support these theoretical results.