Observations of coagulation in isotropic turbulence

Abstract

Turbulent-shear-induced coagulation of monodisperse particles was examined experimentally in the nearly isotropic, spatially decaying turbulence generated by an oscillating grid. The 3.9 μm polystyrene microspheres used in the experiments were made neutrally buoyant and unstable by suspending them in a density-matched saline solution. In this way, particle settling, double-layer repulsion and particle inertia were negligible and the effect of turbulent shear was isolated. The coagulation rate was measured by monitoring the loss of singlet particles as a function of time and reactor turbulence intensity. By restricting consideration to experimental conditions where the singlet concentration was in excess, the effect of higher-order aggregate (i.e. triplet) formation was negligible and nonlinear regression using an integral rate expression that included terms for doublet formation and breakup was used to obtain the turbulent coagulation rate constant. The strength of the van der Waals attractions was characterized with the Hamaker constant obtained from Brownian coagulation experiments. Since particle bulk mixing was fast compared to the coagulation rate, the observed coagulation rate constants were averages over the local coagulation rates within the grid-stirred reactor. Knowledge of the spatial variation of turbulence within the reactor was necessary for quantitative prediction of the experiments because model predictions for the coagulation rate are nonlinear functions of shear rate. The investigation was conducted with particles smaller than the length scales of turbulence and since the smallest turbulent length scales, the Kolmogorov scales, have the highest shear rate they controlled the rate of particle aggregation. The distribution of the Kolmogorov shear rate at various grid oscillation frequencies was obtained by measuring the turbulent kinetic energy (E) using acoustic Doppler velocimetry and relating E to the Kolmogorov shear rate using scaling arguments. The experimentally measured turbulent coagulation rate constants were significantly lower than theoretical predictions that neglect interparticle interactions; however, simulations that included particle interactions showed excellent agreement with the experimental results. The favourable comparison provides evidence that the computer simulations capture the important physics of turbulent coagulation. That is, particle transport on length scales comparable to the particle radius controls the rate of turbulent shear coagulation and particle interactions are significant.

Population balance modeling of aggregation and breakage in turbulent Taylor–Couette flow

“…On the other hand, Saffman and Turner [38] obtained a similar value of the prefactor, equal to 1.293, for turbulent-flow conditions and spherical droplets. As was shown by Bäbler et al [39] once the hydrodynamic interactions of the particle on the surrounding fluid are incorporated in the trajectory analysis the value of aggregation rate prefactor reduces significantly, in agreement with experimentally determined values (see, e.g., [32,33,[40][41][42]). The reason for such differences from simple theoretical models is that the theoretical derivations did not include effects of particle interactions, such as hydrodynamic interactions, van der Waals attraction, surface chemistry, etc.…”

“…Since its dependency on the shear rate can be measured experimentally [32,33] it is possible to separate shear-rate dependency from other mentioned parameters and write it in the following form: [30,[34][35][36] and experimental measurements [32,33] for large primary particles confirmed that the aggregation rate prefactor α SA ij (G) in Eq. (4) is weakly dependent on the shear rate.…”

Modelling turbulent collision rates of inertial particles

“…We restrict the consideration to the channel core where the nearly homogeneous and isotropic flow conditions allow the application of the collision model developed. The particles are regarded as a mono-size suspension, and, consequently, the droplet size growth is treated as a sequence of the formation of doublets due to the loss of singlets (e.g., see Brunk et al, 1998). This simple coalescence model gives a rather crude approximation to the real agglomeration process and it may be solely used for estimating the droplet mean size.…”

Effects of phytoplankton physiology on export flux

“…The observed rate of coagulation can be compared to theoretical models of physically based coagulation processes to estimate the mean sticking efficiency in the natural system. While this method of estimating sticking efficiency has been successfully tested for clay particles (Hunt 1982) and colloids (Brunk et al 1998), it has yet to be tested for systems containing algal cells.…”