Statistical moment characterization of Rayleigh-Benard convection using optical tweezer-trapped microsphere probes

This study introduces an innovative application of optical tweezers technology to investigate Rayleigh-Benard convection. We characterize the convective phase transition process through the statistical moments, mean square displacement (MSD) and skewness, and kurtosis of single-particle displacements. The optical tweezer stiffness, ?, was calibrated using the power spectrum method. Correction formulas for the MSD and higher-order moments under optical-tweezer-free conditions were derived to eliminate the influence of the optical potential well on true particle motion. By dynamically adjusting optical tweezer power to accommodate varying temperature difference intensities, DTc, and utilize both experimental and simulation methods for particle tracking, the critical temperature difference DTc ? 23 K (corresponding to Rayleigh number Rc ? 1780) was identified. Analysis reveals that at small ?T, the MSD remains low while skewness and kurtosis exhibit significant oscillations due to the non-random Brownian motion. With the increase of DT, due to the appearance of transient convective rolls, some data points on the MSD image start to be much higher than the main data points, and at the same time, the oscillation amplitude of the data points on the skew and kurtosis images decreases. Near and beyond DTc, steady-state convection emerges: the MSD in-creases dramatically by several orders of magnitude, while skewness and kurtosis converge toward stable values. The convergence value precisely corresponds to the analyzable value that is uniformly distributed mathematically. This work demonstrates that higher-order statistical moments exhibit high sensitivity to sub-critical transient convective rolls and supercritical steady-state convective evolution. It establishes a novel high-precision detection tool for microscopic fluid phase-change dynamics, offering significant value for the research into convection/turbulence mechanisms and industrial heat transfer optimization.