Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids

The overall goal of this procedure is to measure the terminal settling velocities of spherical particles in unbounded and bounded surfactant based viscoelastic fluids of varying ology. This is accomplished by preparing surfactant based viscoelastic fluids of different concentrations to obtain a wide range of real logical properties. The second step is to measure the settling velocities of particles in unbounded fluids in beakers of diameter, much larger than the particle over a wide range of fluid radiological properties.

Next, the settling velocity of the particles is measured in the presence of parallel walls in a parallel plate experimental cell made of plexiglass. The final step is to measure the radiological properties of the fluids. Using a ter, the properties are correlated with the settling velocities of particles.

Ultimately, the experiment helps in measuring the settling velocities in unbounded and bounded viscoelastic surfactant fluids as a function of their real logical properties. The data can be the basis for quantifying the influence of fluid elasticity on settling velocities. Visual demonstration of this method is essential to ensure that other labs can reproduce what we are demonstrating in our experiments.

It is extremely important to get good accuracy in these measurements for many practical applications such as hydraulic fracturing, manufacturing in the pharmaceutical industry, semiconductor processing and and so on. Accurate experimental results for particle settling and viscoelastic fluids can further form the basis for validating numerical simulations that calculate the effect of elasticity on the drag on particles. As a first step, prepare the two component optically transparent viscoelastic fluids that will be used in this experiment.

One component is an onic surfactant, sodium xylene sulfonate. The other component is a onic surfactant, NNN trimethyl one Okta de ammonium chloride. Use distilled water to vary the surfactant, concentrations, and span a range of viscosities.

Begin by adding the onic surfactant to the required amount of distilled water. After mixing, add the cationic surfactant to this mixture and mix for an additional two to three minutes. Once a mixture is prepared, allow it to rest for two to six hours to release air bubbles for the measurement, obtain glass spheres with diameters ranging from one to five millimeters.

Use a high resolution microscope to measure the diameters of the spheres and ensure that they are smooth and near perfect. To minimize the effect of the confining walls on the settling velocities of the beads. Deposit the viscoelastic fluid in a glass container with a diameter at least 25 times the diameter of the spheres to be used.

Record the room temperature and the fluid temperature with a lab thermometer mount a meter stick along the side of the container. Use a high resolution camera mounted on a tripod to record motion of the particle in the fluid. Gently immerse a glass sphere in the liquid and release it as it settles.

Record the process once the recording is complete. Use an image analysis program to track the position of the sphere at different times. Plot the vertical position of the sphere as a function of time.

Then calculate the terminal settling velocity from the slope of the line. Repeat the experiment under the same conditions with the same sphere at least three times. Then repeat the steps for spheres of different diameters.

Use the data collected to plot the settling velocities versus the sphere diameter, as in this example, the error bars suggest the variability in the three measurements for each sphere. Note the settling velocity increases with the sphere diameter parameter. For this measurement, construct a cell of smooth plexiglass with walls that are perfectly parallel to each other and access ports on the top and bottom.

This cell has a gap of eight millimeters between the walls, the ratio of the gap and the horizontal length should be small. Seal one of the access ports and fill the cell with viscoelastic fluid. Record the room temperature and the fluid temperature using a laboratory thermometer with the high resolution camera ready to record, place the cell on its side.

Gently release a glass bead in the cell through the port and seal the port with a rubber stopper. Allow the sphere to settle and reach the middle of the cell. Rotate the cell so that it is vertical and the sphere can settle.

Place a meter. Stick along the record the sphere of motion using the high resolution video camera. Use the image analysis program to determine the settling velocity as before.

To characterize the fluid, use a TER to measure its viscosity as a function of sheer rate. First, make sure the temperature of the cup is the same as the measured temperature during the experiment. Then vary the sheer rate from 0.1 per second to 800 per second.

Take at least 10 measurements per decade for the fluid and spheres in the settling experiments. Calculate the surface averaged particle shear rate defined here. V is the settling velocity and DP is the sphere diameter.

Next, define a power lock curve in the shear rate for the viscosity. With K being the flow consistency index and N being the flow behavior index. Fit this curve to the viscosity versus shear rate plot for values near the calculated shear rate.

Continue with the characterization by performing dynamic oscillatory. Sheer measurements over the range of frequencies. 0.1 rad per second to 100 rad per second.

Measure the elastic modulus and the viscous modulus at 10 points per decade minimum then fit the ratio of the mod I to a Maxwell model to determine the relaxation time of the fluid. Begin investigating the influence of fluid elasticity by finding the settling viscosity in an unconfined inelastic fluid. Do this by using K and n from the characterization studies, the fluid density and the Reynolds number.

For a sphere falling in a power law fluid continue by calculating the velocity ratio defined as the experimental settling velocity in an unbounded fluid over the settling velocity based on the power law viscosity. Using the k and n values plot the velocity ratio as a function of sphere diameter for different fluids. In this case, smaller spheres experience a drag reduction and larger spheres experience.

A drag enhancement determine the wall factor for a given diameter sphere by dividing the settling velocity in the presence of walls by the settling velocity in the unbounded fluid. For a given fluid plot, the wall factors as a function of the sphere diameter to wall spacing ratio R as shown here. These data show that wall factors decrease with increase of the value of R.This suggests that wall retardation effects increase as the sphere diameters become comparable to wall spacing.

Observe that the wall factor is not unique at a value of R unlike Newtonian fluids and is dependent on the wall spacing. While attempting this procedure, it is important to remember that the fluid radiology is a strong function of temperature. The temperature at which the experiment is performed should be accurately recorded, and the fluid ology should be measured at the same temperature.

It is very important for the experimentalist to check the accuracy and the repeatability of the measurements by doing these experiments on some model systems such as the settling of particles in an unbounded fluid in solutions such as glycerol that are well understood. It is also important to repeat these measurements three or four times so that you can get an idea of what the repeatability of the measurements and the precision of the measurements is.