Particle calculation from turbidity

The other state variables are the fugacity of dissolved methane in the bulk of the liquid water phase (fb) and the zero, first and second moment of the particle size distribution (p0, Pi, l )- The initial value for the fugacity, fb° is equal to the three phase equilibrium fugacity feq. The initial number of particles, p , or nuclei initially formed was calculated from a mass balance of the amount of gas consumed at the turbidity point. The explanation of the other variables and parameters as well as the initial conditions are described in detail in the reference. The equations are given to illustrate the nature of this parameter estimation problem with five ODEs, one kinetic parameter (K ) and only one measured state variable. 

For dilute suspensions of particles smaller than 0.04 pm in diameter, the turbidity can be calculated from the equation ... 

Once the optical constant was known, the turbidity of the flocculated suspension calculated from Equation 11, using the known particle size distribution, could be compared with the experimentally measured turbidity. Correlations were made between particle size distributions and turbidity readings as the PEI molecular weight and dose were varied. The velocity gradient in the stirrer-reactor was held constant at G = 20 sec Other experiments indicate that the influence of varying the velocity gradient in the range G = 20 to 60 sec" on either turbidity or particle size distribution was minor. 

Silt Density Index (SDI) It is an empirical measurement ASTM Standard D-4189-82, 1987) used for measuring the colloidal fouling potential of RO/NF feed water. It is not a direct measure of the particle concentration, which is more properly measured by turbidity. The SDI value is based on the time required to filter a volume of feed water throu a 0.45 pm filter pad at a feed pressure of 2.1 bar g. The SDI value is calculated from the formula ... 

The calculated turbidities for a wide variety of particle size distributions with aggregates ranging from 1 to 18 pm in diameter were within 20% of the experimentally measured turbidities, that is ... 

Numerical calculations by Mic s theory for model gamma distribution of particles and experiments with bimodal latex suspensions have shown (Khlebtsov and Mel nikov, 1992) the mean particle size determined by the turbidity spectrum method from n(r) calibrations for monodisperse particles to correspond to the relationship... 

As another example of a stoichiometric calculation by the mole ratio method, consider the reaction of iron(III) sulfate, Fe(S04)3, with calcium hydroxide, Ca(OH>2. This reaction is used in water treatment processes for the preparation of gelatinous iron(III) hydroxide, Fe(OH)3, which settles in the water, carrying solid particles with it. The iron(III) hydroxide acts to remove suspended matter (turbidity) from water. The Ca(OH)2 (slaked lime) is added as a base (source of OH ion) to react with iron(III) sulfate. The reaction is... 

If the mass of particles contains two sizes, then two transmitted lights will be detected, when light passes through the mass. Let us say that L is the distance from the top surface of the suspension at which the light source is located. The plot of turbidity versus time is shown in Figure 12.11. The turbidity is expressed in terms of nephelometric turbidity units (NTu). The instrument nephelometer measures the turbidity in terms of the reflected light from the passing particles. The time of travel is obtained from the plot and is used to calculate the terminal velocity. 

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