Particle Beads

Turbid water is created by colloidal particles and flocs of varying sizes and densities. Unless all the sizes and densities are predetermined, theoretical settling velocity values cannot be calculated. Especially, in the case of flocs, the exact fractal dimension will be needed for this calculation, but unfortunately, the fractal dimension is still unknown. Therefore, any random fluid cannot be used to calculate theoretical values of settling velocity; since the specifications of most of the particles and flocs are unknown and the variation is too wide, the determination of the sedimentation velocities solely through mathematical calculations is close to impossible.

To make this calculation possible, the Tube Floc team will be creating a particular mixture with a predetermined turbidity created only by known particles. This mixture will consist of pure, distilled water and latex particle beads of known sizes and densities. None of these beads will be flocculated; the sizes of the particles in the water should not be altered. Since this influent mixture solely involves the particle beads, FReTA will be measuring the settling velocities for these individual beads only.

Determining the Dimensions of the Beads

In order to decide on the optimal sizes of particle beads for this experiment, the Tube Floc team first chose two sedimentation times that will make the task of data comparison simple and highly successful. The team chose two different times of 5 minutes and 20 minutes; the two times should have a significant difference to clearly show the trend resulting from the sedimentation of particles of different size.

From the basic definition of velocity, an estimate settling velocity of the particles can be expressed as a function of displacement (z) divided by time (t):
(EQUATION: Vs=z/t) (1.1)
In the case of this experiment, z will be the maximum distance between the bottom of the ball valve and the measurement volume of the turbidimeter: 16 cm. With the two settling times already chosen as 5 and 20 minutes, estimate settling velocities of 0.533 mm/s and 0.133 mm/s were calculated.

Settling velocity can also expressed in terms of gravity (g), particle diameter (D), particle density (ρbead in this case), water density (ρH2O), and the kinematic viscosity of water (ν):

***EQUATION

The density of the beads given when purchased was 1.05 g/cm3 and the water density and kinematic viscosity are already known to be 1000 kg/m3 and 1.004e-6 m2/s. Relating equation 1.1 and 1.2, the diameters of the two beads were found to be about 140.159 μm and 70.014μm.

The available latex bead diameters that came closest to the desired values found above were 150 μm and 60 μm. Re-calculating the sedimentation velocities corresponding to these new diameters using equation 1.2, the resulting values were 0.61 mm/s (D = 150 μm) and 0.098 mm/s (D = 60 μm).

Determining How Much Bead is Needed

The desired influent turbidity for this experiment is 10 NTU (10 mg/L); to create this turbidity, the amount of beads that will be mixed in the water also needs to be specified. Knowing that the volume of the whole apparatus is about 231 mL, through dimensional analysis, the following equation was found:
(Equation 1.3: Bead needed=NTU*Volume/ρbead)
where NTUdesired is the desired influent turbidity (10 mg/L), V is the volume of the apparatus (231 mL), and ρbead is the density of bead(1.05 g/cm3).

Using equation 1.3, the volume of the desired amount of beads was calculated to be 2.2e-3 mL (~2.31e-6 kg) within the whole apparatus.