We report on the Lagrangian statistics of acceleration of small (sub-Kolmogorov) bubbles and tracer particles with Stokes number St ≪1 in turbulent flow. At decreasing Reynolds number, the bubble accelerations show deviations from that of tracer particles, i.e. they deviate from the Heisenberg-Yaglom prediction and show a quicker decorrelation despite their small size and minute St. Using direct numerical simulations, we show that these effects arise due the drift of these particles through the turbulent flow. We theoretically predict this gravity-driven effect for developed isotropic turbulence, with the ratio of Stokes to Froude number or equivalently the particle driftvelocity governing the enhancement of acceleration variance and the reductions in correlation time and intermittency. Our predictions are in good agreement with experimental and numerical results. The present findings are relevant to a range of scenarios encompassing tiny bubbles and droplets that drift through the turbulent oceans and the atmosphere. They also question the common usage of micro-bubbles and micro-droplets as tracers in turbulence research.Heavy and light particles caught up in turbulent flows often behave differently from fluid tracers. The reason for this is usually the particle's inertia, which can drive them along trajectories that differ from those of the surrounding fluid elements [1][2][3][4]. Due to their inertia, measured by the Stokes number St 1 , such particles depart from fluid streamlines and distribute nonhomogeneously even when the carrier flow is statistically homogeneous [3,[5][6][7][8][9][10][11]). Numerical studies have captured several interesting effects of particle inertia through point-particle simulations in homogeneous isotropic turbulence [7,[12][13][14]. For instance, with increasing inertia, light particles showed an initial increase in acceleration variance (up to a value a 2 ∼ 9 times the tracer value) followed by a decrease, while heavy particles showed a monotonic trend of decreasing acceleration variance [15]. Such modifications of acceleration statistics arose primarily from the slow temporal response of these inertial particles, i.e when St was finite [9,[16][17][18][19]. In comparison, a lower limit of inertia can be imagined (St ≪ 1), when the particles respond to even the quickest flow fluctuations and, hence, are often deemed good trackers of the turbulent flow regardless of their density ratio [3,15,16,20]. The widespread use of small bubbles and droplets in flow visualization and particle tracking setups (e.g. Hydrogen bubble visualization and droplet-smoke-generators) is founded on this one assumption − that St ≪ 1 renders a particle responsive to the fastest fluctuations of the flow [21][22][23][24][25].In many practical situations, particles are subjected 1 Stokes number, St ≡ τp/τη , where τp is the particle response time, and τη is the Kolmogorov time scale of the flow.to body forces, typically gravitational or centrifugal [26]. This can be the case for rain droplets and aerosols set...

Particles suspended in turbulent flows are affected by the turbulence and at the same time act back on the flow. The resulting coupling can give rise to rich variability in their dynamics. Here we report experimental results from an investigation of finite-sized buoyant spheres in turbulence. We find that even a marginal reduction in the particle's density from that of the fluid can result in strong modification of its dynamics. In contrast to classical spatial filtering arguments and predictions of particle models, we find that the particle acceleration variance increases with size. We trace this reversed trend back to the growing contribution from wake-induced forces, unaccounted for in current particle models in turbulence. Our findings highlight the need for improved multi-physics based models that account for particle wake effects for a faithful representation of buoyant-sphere dynamics in turbulence.

A numerical computer simulation has been developed for the electrostatic spray paint process. The theoretical model describes the path of a cloud of charged drops. It takes into account the drop size, temperature, density, viscosity of paint and air, charge of the drops, potential of the sprayer head, the use of air assistance, air-paint ratio, paint flow, wind and turbulence and the distance towards the object. Especially the influence of the wind and wind turbulence on the spraying process was investigated. With increasing crosswind a higher charge, larger drops or air-assisted spraying will keep the efficiency high. Too much charge on the drops will cause the cloud to expand too much. Painting in the open air with a mild wind is possible using the electrostatic spray paint process.