[1] A new equation was developed to relate the size and settling velocity of particulate matter commonly recurring in aqueous ecosystems. This equation explicitly balanced the gravitational, buoyancy, viscous, and inertial forces as in Rubey (1933) but was amended to describe in one instance both individual particles and granular aggregates with an internal fractal architecture. This approach allowed for an algebraic solution of the settling velocity, thus overcoming earlier approaches that required iterative numerical solutions. The equation was tested with mineral, biomineral, and biological suspended particles and granular aggregates from 52 existing experimental data sets, and resulted in average correlation coefficients R between 71% and 93.9%, and normilized residuals between 14.3% and 24.8% over Reynolds numbers ranging within 10−7 and 102. Accuracy of these results was generally better than for the Stokes' law, the Stokes' law modified with the Schiller-Naumann drag coefficient, and Rubey's equation. Estimated parameters ranged within observed ones, thus suggesting that the equation was robust. An analysis of the drag showed that inertial force was negligible only for biological cells (isolated cysts), whereas it contributed by not less than 5% to the drag on large mineral particles and up to 20% for biomineral and biological aggregates. Finally, a correlation was found between the organic matter content and fractal properties of granular aggregates, which were described by empirical equations proposed here for the first time. The hypothesis that the settling velocity is a function of linear and nonlinear drag, and is ultimately determined by physical characteristics as much as biological composition and internal aggregate geometry, is supported here by quantitative analyses.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/jgrc.20086

The settling velocity of mineral, biomineral, and biological particles and aggregates in water

The preparation and characterization of a controlled-release multicomponent (NPK) fertilizer with the coating layer consisting of a biodegradable copolymer of poly(butylene succinate) and a butylen...

Controlled-Release Fertilizer Prepared Using a Biodegradable Aliphatic Copolyester of Poly(butylene succinate) and Dimerized Fatty Acid

Review of the empirical correlations for the drag coefficient of rigid spheres

Laminar forced convection of a nanofluid in a microchannel: Effect of flow inertia and external forces on heat transfer and fluid flow characteristics

Degraded plastic debris has been found in nearly all waters within and nearby urban developments as well as in the open oceans. Natural removal of suspended microplastics (MPs) by deposition is often limited by their excess buoyancy relative to water, but this can change with the attachment of biological matter. The extent to which the attached biological ballast affects MP dynamics is still not well characterised. Here, we experimentally demonstrate using a novel OMCEC (Optical Measurement of CEll colonisation) system that the biological fraction of MP aggregates has substantial control over their size, shape and, most importantly, their settling velocity. Polyurethane MP aggregates made of 80% biological ballast had an average size almost twice of those containing 5% biological ballast, and sank about two times slower. Based on our experiments, we introduce a settling velocity equation that accounts for different biological content as well as the irregular fractal structure of MP aggregates. This equation can capture the settling velocity of both virgin MPs and microbial-associated MP aggregates in our experiment with 7% error and can be used as a preliminary tool to estimate the vertical transport of MP aggregates made of different polymers and types of microbial ballast.

Sinking of microbial-associated microplastics in natural waters.

This article, which is largely a review, deals with the drag force and drag coefficient for rigid spherical and deformable particles in ordinary and non-Newtonian fluids. The most important theoretical formulas for small Reynolds numbers of Re ≪ 1 and semiempirical formulas for the drag coefficient in a wide Re range up to 106 are presented. The deformation of drops and bubbles and its effect on the drag coefficient are considered.

Drag coefficients of variously shaped solid particles, drops, and bubbles

The construction of a complex model for the granulation of powdered materials in drum-type granulators is considered, taking into account structure anisotropy and layering on a surface. It is noted that granulation proceeds in several stages depending on the relaxation time of nucleation. The graphical interpretation of the layering of powder on the surface is given using the model. A rheological model for the consolidation of granules under the effect of external deforming stresses is presented that makes it possible to estimate the variation of porosity and density with the residence time. A comparison between calculated and experimental results is given.

Modeling the granulation of powdered materials by rolling

A generalized viscosity equation has been proposed for structured disperse systems with their peculiar rheological properties. Some characteristic features of the viscosity curve have been revealed at the beginning of structuration. Different variants of viscosity equations for structured disperse systems have been considered, and their comparison with the experimental data has been performed. The possibilities of estimating the porosity and shear viscosity of structured media with a fixed layer of particles have been demonstrated.

Viscosity of Structured Disperse Systems

The possibilities of improving the quality of superphosphate fertilizers by using intensifying additives (MnO and Al2O3 with NH4OH) that decrease the porosity and enhance the strength of granules are considered. The mass-exchange problem of granule moistening is solved, and the dependence of the moistening thickness and granule strength on the granule porosity is determined.

Experimental study and calculation of the effect of intensifying additives on the strength of superphosphate granules

The problems of the rheology of oil disperse systems, which are accompanied by asphaltene particles being set into nanoaggregates and clusters of nanoaggregates and viscoelastic framework have been analyzed. The models of the coagulation of asphaltene particles and the calculation of the nanoaggregate size have been suggested. The conditions of the destruction of the structure have been considered and the rheological models of the filtration of oil disperse systems have been considered with the assumption of the Maxwell equation and model of the change of viscosity and mobility. The results have been compared with the experimental data.

G. I. Kelbaliyev

Papers

Drag coefficients of variously shaped solid particles, drops, and bubbles

Modeling the granulation of powdered materials by rolling

Viscosity of Structured Disperse Systems

Experimental study and calculation of the effect of intensifying additives on the strength of superphosphate granules

Rheology of structural oil disperse systems