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PhD defence Varghese Mathai

Varghese Mathai is a PhD student in the MESA+ research group Physics of Fluids (PoF). His supervisors are Detlef Lohse and Chao Sun.

Buoyant particles and fluid turbulence 

The ubiquity of particle-laden turbulent flows in nature and technology makes it important to study them. This thesis covers mainly the broad topic of buoyant particles in turbulent flows. These particles rise through the carrier fluid, and their rising motion can lead to a variety of interesting physical phenomena. We have carried out experiments in a unique large-scale turbulence facility: the Twente Water Tunnel (TWT), which is part of the European High-performance Infrastructures in Turbulence (EuHIT) consortium.


We first addressed the acceleration statistics of small buoyant particles in turbulence (Chapter 2). To this end, we injected microbubbles (diameter ≥ 100μm) in the Twente Water Tunnel flow and tracked their motion using a moving camera setup. We compared the accelerations of the microbubbles to that of similar sized neutrally buoyant tracer particles. This provided the first evidence that tiny bubbles do not necessarily behave like fluid tracers, when it comes to the statistics of acceleration. Using numerics and theory, we showed that the deviations from neutrally buoyant tracers occur due to the finite drift velocity of these bubbles through the turbulent flow. We obtained quantitative predictions for the variance, time-correlation, and intermittency of acceleration. This has provided the first demonstration of the effects of crossing trajectories on the acceleration statistics of buoyant particles in turbulence.

As a next step, we studied the dynamics of finite-sized buoyant particles in a turbulent water flow (Chapter 3), i.e. particles having a diameter larger that the smallest length scale of the flow, and with a density that is lower than that of water. We found that the larger the size of the particle, the more intense are the accelerations it experiences. This appears to be in contradiction to inertial range scaling predictions, which suggest that with increasing size, the acceleration variance ought to decrease as dp-2/3, where dp is the particle diameter. We showed that the apparent reversal of trend occurs due to the wake-induced forces on the particles. With increasing particle size, while the forces due to turbulence decrease, the unsteady wake-induced forces on the particle increase. The latter outweighs the contribution from turbulence, resulting in an overall increase in the particle’s acceleration variance.

In Chapter 3, we obtained the three dimensional trajectories of spheres moving in a turbulent flow. However, a full description of particle motion requires knowledge of their rotation as well. In Chapter 4, we described a method to obtain the three degrees of rotation of the spherical particle. The method employs a minimization algorithm to obtain the orientation from the 2D projection of an analytically prescribed pattern drawn onto the surface of the sphere. This method has been used to track the translation and rotation of buoyant spheres in turbulence in Chapter 5. Here, we showed that tuning the rotational inertia of a buoyant sphere can change its overall dynamics. A low moment of inertia sphere experiences intense accelerations when compared to a high moment of inertia sphere. We reveal that this occurs due to the in- creased rotational motion, which presumably changes the wake-induced forces on the sphere. This highlights the particle moment of inertia as an important control parameter governing the dynamics of buoyant spherical particles in flows. In Chapter 6, motivated by our observations from Chapter 5, we have conducted a numerical study on the effect of mass and moment of inertia on the two-dimensional motion and wakes of freely rising/falling circular cylinders. Here again, we found that both mass and moment of inertia control the dynamics of buoyant cylinders. Changing the moment of inertia affects the rotation of the particle. This has provided the first evidence that auto-rotation can significantly influence the trajectories and wakes of freely rising isotropic bodies.

In Chapter 7, we studied the dynamics of buoyant and heavy cylindrical pendulums undergoing large amplitude oscillations in water. By accounting for the fluid forces due to buoyancy, added mass, and (non-linear) drag, we are able to obtain a fair agreement with the experimental measurements of the pendulum motion.

Chapters 2­­-7 had addressed the dynamics of rigid buoyant particles. In Chapter 8, we moved from rigid to deformable light particles, i.e. a swarm of 2-4 mm diameter air bubbles rising within an incident turbulent flow. The bubbles have a strong wake, and the liquid agitation induced by them is significant at the studied volume fractions (≥ 1%). We have used the bubblance parameter b to characterize the turbulent bubbly flow. The bubblance parameter b measures the ratio of the bubble-induced kinetic energy to the kinetic energy of the incident turbulent flow. Further, through conditional measurements of the velocity downstream of the bubbles, we have disentangled three regions of the flow: the primary wake, the secondary wake, and the far field. These have specific statistical properties. The overall agitation in the turbulent bubbly flow is the result of these three contributions.