# Bottlenecks for the growth of particles suspended in turbulent fluids

Project: Research

## Research areas and keywords

### UKÄ subject classification

**Astronomy, Astrophysics and Cosmology**

### Description

Small particles suspended in turbulent fluids (turbulent aerosols) are fundamental to our understanding of chemical and kinetic processes in many different areas in science and technology. Often the suspended particles are observed to grow in size, for instance by collisional aggregation, but such systems are notoriously difficult to model. There is a fundamental discrepancy between theoretical calculations and empirical observations, where standard theory predicts substantially slower growth of small particles than observed. This lack of understanding of a very fundamental process is commonly referred to as the bottleneck problem.

We have identified four key questions that must be understood in order to solve the bottleneck problem. The applicants have recently developed experimental and numerical methods as well as analytical approximation schemes that will allow us to address these questions. Therefore we believe that this concerted effort will finally lead to a solution of the bottleneck problem.

First, turbulence induces relative motion between the suspended particles. Despite several decades of research there is no statistical or numerical model that reliably predicts at which rates the suspended particles are thrown at each other by the turbulence. But recent model calculations have identified universal aspects of this problem that will allow us to quantitatively model the relative velocities of the aerosol particles (Mehlig, Johansen). Preliminary results are promising, but many factors (neglected so far) must be taken into account: the size dispersion of the particles, forcing terms in addition to Stokes force and gravity, asymmetry of solid particles, and the effect of the back reaction of the moving particles on the fluid (Brandenburg, Mitra, Johansen, Mehlig). The Göttingen group will measure the distribution of relative velocities of droplets in their crystal-ball experiment (Bewley, Bodenschatz). The results will be compared to model calculations (Mehlig) and simulations (Brandenburg, Mitra, Johansen). The dynamics of asymmetric solid particles in shear flows will be studied in Gothenburg (Hanstorp, Mehlig).

Second, very little is known about collision and coalescence efficiencies. In the literature widely different values are quoted, indicating that these efficiencies fluctuate substantially. To solve the bottleneck problem it is necessary to formulate a statistical model of the empirically and numerically observed fluctuations. We will perform numerical simulations (Brandenburg, Mitra, Johansen) and measure collision and coalescence efficiencies of individual droplets by optically trapping and releasing them (Hanstorp).

Third, once we have a reliable model of collision velocities and efficiencies the question is: what are the likely collision outcomes? Will fragmentation, aggregation, or erosion occur? This depends crucially on the material properties of the colliding particles (droplets, silicate particles, ice-coated particles). We will perform collision experiments with microscopic particles (Hansen) and will compare the results with static and dynamic fragmentation models (Johansen, Mehlig).

These steps will take several years. The final and fourth key step is synergetic: to formulate simplified models for the dynamics of the particle-size distribution in turbulent aerosols that show how and under which circumstances the bottleneck is overcome, taking into account the results of the three questions mentioned above (all applicants). For planet formation it will be necessary to investigate the effects of possible instabilities caused by the back reaction of the particles on the fluid flow, experimentally (Bodenschatz, Xu) as well as theoretically (Johansen).

We have identified four key questions that must be understood in order to solve the bottleneck problem. The applicants have recently developed experimental and numerical methods as well as analytical approximation schemes that will allow us to address these questions. Therefore we believe that this concerted effort will finally lead to a solution of the bottleneck problem.

First, turbulence induces relative motion between the suspended particles. Despite several decades of research there is no statistical or numerical model that reliably predicts at which rates the suspended particles are thrown at each other by the turbulence. But recent model calculations have identified universal aspects of this problem that will allow us to quantitatively model the relative velocities of the aerosol particles (Mehlig, Johansen). Preliminary results are promising, but many factors (neglected so far) must be taken into account: the size dispersion of the particles, forcing terms in addition to Stokes force and gravity, asymmetry of solid particles, and the effect of the back reaction of the moving particles on the fluid (Brandenburg, Mitra, Johansen, Mehlig). The Göttingen group will measure the distribution of relative velocities of droplets in their crystal-ball experiment (Bewley, Bodenschatz). The results will be compared to model calculations (Mehlig) and simulations (Brandenburg, Mitra, Johansen). The dynamics of asymmetric solid particles in shear flows will be studied in Gothenburg (Hanstorp, Mehlig).

Second, very little is known about collision and coalescence efficiencies. In the literature widely different values are quoted, indicating that these efficiencies fluctuate substantially. To solve the bottleneck problem it is necessary to formulate a statistical model of the empirically and numerically observed fluctuations. We will perform numerical simulations (Brandenburg, Mitra, Johansen) and measure collision and coalescence efficiencies of individual droplets by optically trapping and releasing them (Hanstorp).

Third, once we have a reliable model of collision velocities and efficiencies the question is: what are the likely collision outcomes? Will fragmentation, aggregation, or erosion occur? This depends crucially on the material properties of the colliding particles (droplets, silicate particles, ice-coated particles). We will perform collision experiments with microscopic particles (Hansen) and will compare the results with static and dynamic fragmentation models (Johansen, Mehlig).

These steps will take several years. The final and fourth key step is synergetic: to formulate simplified models for the dynamics of the particle-size distribution in turbulent aerosols that show how and under which circumstances the bottleneck is overcome, taking into account the results of the three questions mentioned above (all applicants). For planet formation it will be necessary to investigate the effects of possible instabilities caused by the back reaction of the particles on the fluid flow, experimentally (Bodenschatz, Xu) as well as theoretically (Johansen).

Status | Active |
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Effective start/end date | 2015/07/01 → 2020/06/30 |