Settling

Settling is an important operation in many applications, such as mining, wastewater and drinking water treatment, biological science, space propellant reignition,[1] and scooping.

For dilute suspensions, Stokes' law predicts the settling velocity of small spheres in fluid, either air or water.

Stokes' law finds many applications in the natural sciences, and is given by: where w is the settling velocity, ρ is density (the subscripts p and f indicate particle and fluid respectively), g is the acceleration due to gravity, r is the radius of the particle and μ is the dynamic viscosity of the fluid.

Subsequently, semi-analytic or empirical solutions may be used to perform meaningful hindered settling calculations.

The solid-gas flow systems are present in many industrial applications, as dry, catalytic reactors, settling tanks, pneumatic conveying of solids, among others.

Obviously, in industrial operations the drag rule is not simple as a single sphere settling in a stationary fluid.

However, this knowledge indicates how drag behaves in more complex systems, which are designed and studied by engineers applying empirical and more sophisticated tools.

The standard Imhoff cone of transparent glass or plastic holds one liter of liquid and has calibrated markings to measure the volume of solids accumulated in the bottom of the conical container after settling for one hour.

A standardized Imhoff cone procedure is commonly used to measure suspended solids in wastewater or stormwater runoff.

To numerically gauge the stability of suspended solids and predict agglomeration and sedimentation events, zeta potential is commonly analyzed.

This parameter indicates the electrostatic repulsion between solid particles and can be used to predict whether aggregation and settling will occur over time.

The sampling bucket is vigorously stirred to uniformly re-suspend all collected solids immediately before pouring the volume required to fill the cone.

The rack should be located away from heating sources, including direct sunlight, which might cause currents within the cone from thermal density changes of the liquid contents.

Accumulated sediment is observed and measured fifteen minutes later, after one hour of total settling time.

Settling pond for iron particles at water works
Creeping flow past a sphere: streamlines , drag force F d and force by gravity F g .
Dimensionless force versus Reynolds number for spherical particles
The linear model derived from Stokes’ Law is accurate for small particles with low Reynolds numbers. Parameterized terminal velocity from Clift, Grace & Weber (1978) deviates from the Stokes Model when larger particles are impacted by Transition Drag and Newtonian Drag.
Deviation from the Stokes' Model from increased fluid drag as a particle increases in size.