Settling velocity aggregates

Alldredge AL, Gotschalk CC (1989) Direct observations of the mass flocculation of diatom blooms characteristics, settling velocities and formation of diatom aggregates. Deep-Sea Re-serach 36 1959-171... 

With hydraulic residence times ranging from months to years, lakes are efficient settling basins for particles. Lacustrine sediments are sinks for nutrients and for pollutants such as heavy metals and synthetic organic compounds that associate with settling particles. Natural aggregation (coagulation) increases particle sizes and thus particle settling velocities (Eq. 7.1) and accelerates particle removal to the bottom sediments and decreases particle concentrations in the water column. 

The case of impermeable spherical aggregates has been analyzed by Johnson el al. (Johnson et al., 1996). In this work, the settling velocity of aggregates in liquids using Stoke s law has been studied and a modified Stoke s law has been introduced. The difference from the classical Stoke s law is that the density difference is expressed in terms of the aggregate density. 

Sternberg, R.W., Berhane, I., and Ogston, A.S. (1999) Measurement of size and settling velocity of suspended aggregates on the northern California continental shelf. Mar. Geol. 154, 43-53. 

Imafuku et al. (1968) estimated the effective settling velocity of a particle in the presence of gas. They found that the settling velocity of the particles in the presence of gas was always larger than the hindered setthng velocity. They attributed the increase in settling velocity in the presence of gas to the formation of aggregates. They proposed the correlation (for 1.3 < ys < 27.2mm/s)... 

Observation of sedimentation behavior (wetting of particles, formation of aggregates, settling velocity, density of sediment)... 

Jahmhch, S., Lund-Hansen, L. C., Leipe, T., 2002. Enhanced settling velocities and vertical transport of particulate matter by aggregation in the benthic boundary layer. Geografisk Tidskrift, Danish Journal of Geography, 102, 37 9. 

Here nh np and nk are the number concentrations of particles of sizes i, j, and k in the epilimnion and nfc in is the number concentration of fc-size particles in river inflows. The term X(i,j)s incorporates most of the effects of physical processes on the rate at which particles of size i and j come into close proximity. The subscript S is used to indicate that Smoluchowski s approach (1917) to the kinetics of particle transport has been adopted. Smoluchowski did not consider hydro-dynamic retardation in his early analysis, and it has not been included here in Mi,j)s. A more rigorous approach is possible (Valiolis and List, 1984a, b). The term a(i J)s incorporates chemical factors that retard the kinetics of aggregation between particles of size i and j and also those aspects of the kinetics of particle transport that are not included in Smoluchowski s analysis. The Stokes settling velocity of a particle of size k is denoted as vk the mean depth of the epilimnion is zc qin and qoul refer to river flows into and out of the lake expressed as volume of water per unit of lake surface area and time (the sum of such inflows or outflows is also termed the areal hydraulic loading of the lake). The symbol W refers to all processes of production or destruction of particles in the epilimnion it can include a variety of chemical and biological processes. 

The constants A and B describe characteristic properties of the aggregating suspension A is a measure of the mean settling velocity and B reflects the degree of dispersion (analogous to the standard deviation). The constants are determined by regression analysis from experimental data. 

Figure 3. A typical variation of settling velocity distribution of a natural suspension underlying aggregating phenomena in a flowing system. Data are observed with a photosedimentometer in an aggregating kaolinite suspension, where the suspending medium was a water sample from a river, upstream (A) and downstream (O) from a waste discharge.

For larger particles or nanoparticle aggregates, SMPS measurements can be coupled with an aerodynamic particle sizer (APS). For spherical particles, it is easy to relate the measured diameters from the SMPS and APS because no corrections need to be made for shape and volume, but for irregularly shaped particles the APS reports an aerodynamic diameter. Da, by comparing the settling velocity to a spherical particle with a density of 1 g cm to compute the particle size. A volume equivalent diameter, D g, which is defined as the volume of a sphere with the same volume as a particle with an irregular shape, is used to relate the aerodynamic diameter from the APS with mobility diameter, D , from the SMPS (46) ... 

Looking at the meaning of Qc in another way, if the hydrodynamic radius of an aggregate is the radius of a sphere that has the same settling velocity and drag force as the aggregate in question, then S2e can be shown to relate the radius of collision to... 

These kinds of experiments are without exception carried out in a column of fluid, usually of the same composition as that from which the aggregates were sampled. The aggregates are introduced into the top of the column and one or more microscopes are used to measure the settling velocity. Farrow and Warren describe a floe density analyser [69] which may be used to determine the fractal dimension. Nobbs et al. [70] review many of the practical aspects involved in performing this type of experimental investigation. 

Physical properties, such as floe densities, settling velocities or the diffusion of compounds inside aggregates and floes, depend on their fractal dimensions, which have to be calculated. The floe fractal dimensions can be determined directly from simulation, since each monomer and particle position is repeatedly computed during a simulation, allowing the mathematical definition of a fractal to be applied directly. 

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