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The specific mechanisms by which settling occurs in this case must be determined - refer to the 'Recommendations' section below for a discussion of the possible scientific principles at work, and how they may be used to optimize the design. | The specific mechanisms by which settling occurs in this case must be determined - refer to the 'Recommendations' section below for a discussion of the possible scientific principles at work, and how they may be used to optimize the design. | ||
=== Engineering principles === | |||
It has yet to be determined which settling mechanisms are at work in this design. One of two types of particle settling may be at work: Type I (discrete particle settling), or Type II (flocculating particle settling). In Type I settling, particle size, shape and density do not change with time but rather, stay as independent bodies - particle settling velocity remains constant. In Type II settling, particles coalesce with other particles and change in size, shape and density as they move downwards - as a result, the particle settling velocity also changes. <ref name = "Droste">R.H. Droste, ''Theory and Practice of Water and Wastewater Treatment'', John Wily & Sons, Toronto, 1997.</ref> If Type I is the case, then the settling of the clay particles must be induced by the settling of the larger, denser sand particles, but each remains discrete. If Type II is at work, then particle flocculation would be due to the negative charge of the clay particles being attracted to the positive charge of the larger sand particles. It is likely that settling in this case occurred according to Type II. | |||
For Type I settling, the terminal settling velocity of discrete particles in a column of water is given by the Stokes Equation: | |||
<math>V_t=\frac{g(\rho_p-\rho_w)d^2}{18\mu}</math> <ref name="Droste"/><br> | |||
where ''g'' is acceleration due to gravity; <math>\rho_p</math> and <math>\rho_w</math> are particle and water density, respectively; ''d'' is particle diameter, and <math>\mu</math> is fluid viscosity. | |||
The mass fraction of particles remaining with settling velocity <math>V_x<\frac{Z_o}{t_x}</math>, where <math>Z_o</math> is the column depth and <math>t_x</math> is the time step is: | |||
<math>X_i=\frac{C_i}{C_o}</math> <ref name="Droste"/><br> | |||
where <math>C_i</math> is the concentration of particles in a sample of water drawn off at that time and <math>C_o</math> is the initial concentration of particles. | |||
Optimization of settling based on Type I settling occurs by analyzing the terminal settling velocity of the particles and designing a settling basin of idealized geometry to remove particles of a given size. In this case this is not practical, as the design settling column - i.e., effluent collection container - would be governed by the discrete particle settling velocity, which would therefore limit which materials could be used. | |||
The more likely Type II settling occurs similarly, but analysis of settling velocity must be adjusted to account for the change in particle size and density as it flows downwards. Once this is done, settling time can be reduced by determining the optimal concentration of sand particles relative to clay particles required to cause settling. | |||
== Treatment process == | == Treatment process == | ||