The Ultrapyc 5000 at the MCL measures the density of samples varying from 0.25 cc to 135 cc in volume, allowing for a wide variety of samples to be tested, including powders, solids, and slurries. Slurries are a suspension of solid in some liquid and are used in a variety of applications including cement construction, coal waste slurry, wood pulp slurry (used to make paper), solid / fluid transportation, and ceramic manufacturing. Accurately knowing the density and composition of a slurry is useful to many areas of research. Using the Ultrapyc 5000, various aspects of the slurry can be measured and/or calculated.

## Gas pycnometry

A gas pycnometer works by utilizing the ideal gas law, written as PV = nRT. The pycnometer contains two chambers: one chamber, called the reference chamber, is empty. The other one, appropriately called the sample chamber, holds the sample. Both chambers are of known (and usually identical) volume. The reference chamber is first filled to a certain pressure and the amount of gas added is measured. The sample chamber is then filled with an equal amount of gas, and the pressure of the chamber is measured.

Referring back to the ideal gas law for this measurement, the number of moles of gas (n) is the same, R is the gas constant, and the temperature (T) is held constant. Therefore, the pressure (P) and volume (V) are the only two variables that change. By looking over the equation

Psample Vsample = Preference Vreference,

only one variable is unknown: the volume taken up by the gas in the sample chamber. Therefore, we can solve for the volume taken up by the gas via

Vsample = Preference Vreference / Psample.

The machine solves for the volume taken up by the sample by subtracting the original chamber volume by the volume taken up by the gas. If we know the mass of the sample, the density can then be calculated by dividing the mass by the volume of the sample.

## Unknown slurry analysis

If given an unknown slurry, the density of the slurry, density of the solid, and weight percent of the solid in the slurry can all be measured while the density of the liquid must be calculated using the other three variables. The procedure for analyzing an unknown slurry is as follows:

1. Measure out a specific volume of the slurry (10-15mL is sufficient for the Ultrapyc 5000) and record the weight of the slurry.
2. Measure the density of the slurry using the pycnometer.
1. First calibrate the pycnometer using the appropriate calibration sphere (if using the medium cell, you will be prompted to insert the medium calibration sphere, etc.)
2. Enter the weight of the slurry.
3. Set up pycnometer with the following parameters for ideal accuracy:
1. Cell size: medium or large
2. Target pressure: 18psi (set He regulator to 20psi)
3. Flow direction mode: Reference first
4. Equilibration: Pressure
5. Flow mode: Monolith
6. Preparation mode: Flow, 1min
7. End mode / finish criteria: Better than 0.01%
8. Max runs: 15
9. Runs to average: 5
3. Dry the slurry by keeping it at an elevated temperature to ensure that as much moisture as possible has evaporated from the mixture.
4. Weigh the dry solids left over.
5. Find the density of the solid using the pycnometer. If it is a powder, follow these criteria for the pycnometer setup.
1. Cell size: medium
2. Target pressure: 10 psi (set He regulator to 12 psi)
3. Flow direction: Reference first
4. Equilibration mode: Pressure and Temperature
5. Flow mode: Fine powder
6. Preparation mode: Pulse (9 pulses)
7. End mode / finish criteria: Better than 0.01%
8. Max runs: 15
9. Runs to average: 5
6. Calculate the weight percent of solid in the slurry using the slurry calculator spreadsheet at the bottom of this post or by simply dividing the dry weight of the solid part by the total wet weight of the slurry.
7. Calculate the density of the liquid component using the slurry calculator spreadsheet or by plugging in the relevant numbers into this equation:

$\rho_{l}=\frac{(c_{w}-100)\rho\rho_{s}}{c_{w}\rho-100\rho_{s}}$

Where $\rho_{s}$ is the density of the solid component, $c_{w}$ is the weight percent of the solid component, and $\rho$ is the density of the slurry.

In fact, if at least 3 of the variables above can be calculated or measured, then you can solve for the fourth with simple algebraic manipulation, or by plugging in the equation to a solver such as Wolfram Alpha or into the slurry calculator spreadsheet.

## Verification of concept

I have personally tested this method using the Ultrapyc 5000 with slurries, and it worked with very little error. My method was to create a slurry using a known mass of mica powder and a known volume of water. I measured the densities of the mica powder, then measured the density of the slurry. This allowed me to calculate the density of water (a known constant at around 20° C) with great accuracy. I conducted 2 trials to confirm this. My first trial returned the density of water as 999.052 kg/m3, which is a percent error of .0948%. The second trial resulted in a density of 1000.398 kg/m3, for a percent error of only .0398%. While it isn’t exactly the same as being given an unknown slurry and is rather idealistic, it still demonstrates the remarkable accuracy that the Ultrapyc 5000 can give you in dealing with unknown mixtures.