An Explicit Full-Range Settling Velocity Equation for Mud Flocs

Abstract

Abstract A simple explicit model for calculating the settling velocity of mud flocs in both the viscous and inertial settling range is presented. The model is based on a nondimensional settling velocity and floc diameter, and the basic structure of the model follows that of Ferguson and Church (2004) with modifications for the fractal structure of flocculated sediment. The explicit form of the equation simplifies settling-velocity calculations and makes it easier to code into larger computational models of river plume sedimentation and morphodynamics. Input parameters needed for calculating settling velocity include: the floc size, the size of the primary particles, the fractal dimension of the floc, the specific gravity of the sediment, and values for two coefficients which incorporate effects due to floc shape, permeability, and flow separation on drag. The behavior of the model using a constant and variable fractal dimension over a range of parameter space is presented. The model is also compared to historic settling-velocity data from in situ measurements and laboratory settling-column data. For much of the field and laboratory data examined, floc settling remained viscous and is best described with a constant fractal dimension. Flocs with fractal dimensions equal to and greater than 2.5 are interpreted as impermeable aggregates, and calculated drag coefficients are larger than those of a smooth solid sphere of equivalent-volumetric diameter. It is suggested that the increased drag is due to the increased surface area of a floc in contact with the fluid relative to a smooth sphere of equivalent diameter. For flocs with fractal dimensions less than 2, calculated drag coefficients are on the order of those for a solid particle of equivalent diameter, even though it is likely that flocs have a larger relative surface area; this phenomenon is interpreted as being the outcome of flow passing through the more permeable flocs as they settle. Estimates of settling-velocity model coefficients are given for these two broad sets of floc settling behavior, and a recommended methodology for using measured settling velocity data to calibrate the model is presented.