Statistical properties of thermally expandable particles in soft Rayleigh-Benard convection

TL;DR

This study investigates how thermally expandable particles behave in Rayleigh-Bénard convection, revealing how their residence time in boundary layers depends on thermal response and expansion properties, supported by DNS and a simplified model.

Contribution

The paper introduces a detailed analysis of thermally expandable particles in convection, including a new DNS study and a 1D model explaining boundary layer residence times.

Findings

Residence time is constant for small thermal response times.

Residence time increases with thermal response time for larger values.

Thermal boundary layer residence time increases as particle expansion coefficient decreases.

Abstract

The dynamics of inertial particles in Rayleigh-B\'{e}nard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS). We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes' force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, $\tau_T$, and the thermal expansion coefficient of particles relative to that of the fluid, $K = \alpha_p / \alpha_f$. In particular, the residence time is constant for small thermal response times, $\tau_T \lesssim 1$, and increasing with $\tau_T$ for larger thermal response times, $\tau_T \gtrsim 1$. Also, the thermal BL residence time is increasing with decreasing $K$. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with $\tau_T$ for larger response times, thus explaining the trends in the DNS data well.