On the effect of lubrication forces on the collision statistics of cloud droplets in homogeneous isotropic turbulence

Abstract

Abstract

Particle radial velocity and concentration kernels estimation in isotropic grid turbulence experiments of inertialess particles at small separation distances

“…and could be due to lubrication effects, whose consequences perhaps persist at those large distances. A similar behaviour was also recently reported in Ababaei et al (2021) where lubrication effects and long-range many-body interactions were found to decrease the RDF and modify the relative velocity scaling for r/D < 3.5 at low but finite Stokes numbers. This scaling is compared to the numerical integration of (3.7) in figure 5(a) and provides a good agreement for all flow conditions.…”

“…The time scale associated with physical collisions of real particles (i.e. D ≈ 0.116 mm in the present study) is much smaller than the temporal resolution of the experimental set-up (Yang & Hunt 2006;Monchaux et al 2010;Marshall 2011;Ababaei et al 2021). Instead, we consider analogous particles (Hill, Nowell & Jumars 1992), which are fluid volumes centred on real particles with effective diameters larger than D. The conditional concentration detection was thus based on the effective particle diameters d (which are adjustable) to obtain a relationship between conditional concentration kernels and thereby analogous collision kernels versus effective particle diameter.…”

“…For inertialess particles, the picture is somewhat different, since hydrodynamic effects can prevent particles coming near contact and can span large inter-particle distances because of the viscous nature of the flow. The recent DNS of inertial particles in homogeneous turbulence by Ababaei et al (2021) shows that the RDF can drop well below unity when r/D < 3.5, St k < 0.1, and when long-range many-body interactions and lubrication forces are taken into account. Thus, it is essential to take g(r) into account when measuring conditional concentration kernels when the separation distance is small, even for inertialess particles.…”

“…To date, though, collision kernels for finite-size inertialess particles have not been measured in an experiment, and only the direct numerical simulations (DNS) from Wang et al (1998) and Ten Cate et al (2004) have shown that hydrodynamic interactions can lead to important effects. In particular, the lubrication forces are known to be the dominant repulsion force for this particular regime, which prevents particles from approaching one another when near contact (Ababaei et al 2021). To the best of our knowledge, inertialess particles with a finite size (but smaller than the Kolmogorov length scale) is a regime where experiments have not been yet performed.…”

“…In this study, we use 3-D PTV and OpenPTV (http://www.openptv.net) software (Maas, Gruen & Papantoniou 1993) to measure both kinematic and dynamic concentration kernels of near-zero-inertia solid particles in isotropic turbulence for separation distances that are small but larger than the sphere's diameter. We compare the measured concentration kernels with the Saffman & Turner (1956) prediction, which does not take into account hydrodynamic interactions induced, for instance, by the motion of the fluid around the particle, which is known to alter particle-particle interactions (Ababaei et al 2021). The aim is to obtain a dynamic kernel and thereby estimate real particle conditional concentration potentially leading to collisions in turbulence.…”