# US 8,464,592 B2 · Method and apparatus for determining void volume for a particulate material

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- Number: US 8,464,592 B2
- Document ID: US8464592B2
- Status: Granted
- Kind: B2
- Application number: 12/895,448
- Filed: 2010-09-30
- Published: 2011-04-07
- Granted: 2013-06-18
- Earliest claimed: 2009-10-02
- Assignees: Hitec Luxembourg S.A.
- Applicants: Pierre Hirtt; Yves Leiner
- Inventors: Pierre Hirtt; Yves Leiner
- Web page: https://patentgrep.com/patent/US8464592B2

## CPC

- G01N 3/08: by applying steady tensile or compressive forces (G01N3/28 takes precedence)
- G01N 1/286: {involving mechanical work, e.g. chopping, disintegrating, compacting, homogenising (microtomes G01N1/06; pulverising in general B02C; mixing in general B01F)}
- G01N 9/02: by measuring weight of a known volume
- G01N 33/0091: {Powders}
- G01N 2203/0019: Compressive
- G01N 2203/0284: Bulk material, e.g. powders
- G01N: INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES (measuring or testing apparatus or processes other than immunoassay, involving enzymes or microorganisms C12M, C12Q)

## Abstract

An apparatus for and method of measuring the compressed volume of a particulate material comprising a chamber for containing a particulate material which will be evaluated; a removable, fixed means at one end of said chamber to enclose said chamber and for containing said particulate material within said chamber; a compression means at the other end of said chamber which further encloses and contains said particulate material within said chamber and which provides a linear force on said particulate material so that one end of said particulate material is linearly movable and said compression means will compress the particulate material in said chamber; means to move said moveable piston away from a particulate material placed inside said chamber to decompress the particulate material in said chamber; means for measuring the distance between said movable piston and said fixed means so to measure the thickness of said compressed particulate material; and measuring means on the moveable piston of said chamber for measuring the applied force of said piston to said particulate material when said piston is compressing said particulate material.

## Claims

### Claim 1

An apparatus for measuring the compressed volume of a particulate material comprising
a chamber for containing a particulate material which will be evaluated;
removable, fixed means at one end of said chamber to enclose said chamber and for containing said particulate material within said chamber;
compression means at the other end of said chamber which further encloses and contains said particulate material within said chamber and which provides a linear force on said particulate material so that one end of said particulate material is linearly movable and said compression means will compress the particulate material in said chamber; said compression means comprising a movable piston;
means for measuring the distance between said movable piston and said fixed means so to measure the thickness of said compressed particulate material; and
measuring means on the moveable piston of said chamber for measuring the applied force of said piston to said particulate material when said piston is compressing said particulate material;
further characterized in that
the apparatus includes decompression means to move said moveable piston away from a particulate material placed inside said chamber to decompress the particulate material in said chamber; and
the apparatus includes a means to control the movement of the moveable piston so that the velocity and force can be varied and controlled to be stable during compression up to a pre-set maximum force and during decompression down to full expansion and its movement during compression or decompression is smooth and continuous.

### Claim 2 (depends on 1)

The apparatus of claim 1 wherein said piston has a surface which when in contact with a particulate material placed inside said chamber is linear movable and will compress the particulate material.

### Claim 3 (depends on 1)

The apparatus of claim 1 wherein the compressed volume of said compressed particulate material is determined using the equation:
V(p)=π/4*D2*h(p)
where D is the diameter of the cylindrical chamber, and where h(p) is the thickness of said compressed particulate material at pressure p as measured on said moveable piston, respectively on said fixed end at any stage of the compression or decompression of said particulate material;
the theoretical volume of said particulate material is determined using the equation:
VT=m/p
where m is the mass of said particulate material and p is its true (skeletal) density, which is a specific constant for every material; and
the void volume of said particulate material is determined using the equation:
VV(p)=V(p)/m−VT/m
where VV(p) is such expressed as per mass.

### Claim 4 (depends on 2)

The apparatus of claim 2 further including a means located at the fixed end of said chamber for measuring the transmitted force on said particulate material when said piston is compressing a particulate material.

### Claim 5 (depends on 1)

The apparatus of claim 1 wherein the chamber is a cylinder and the diameter of the cylindrical chamber is more than 12.7 mm (0.5 inches) and less than 76.2 mm (3 inches).

### Claim 6 (depends on 1)

The apparatus of claim 1 wherein the chamber is a cylinder and the diameter of said cylindrical chamber is more than 20 mm (0.78 inches) and less then 30 mm (1.18 inches).

### Claim 7 (depends on 1)

The apparatus of claim 1 wherein the chamber is a cylinder and the diameter of said cylindrical chamber is about 25 mm (about 1 inch).

### Claim 8 (depends on 1)

The apparatus of claim 1 wherein the compressed volume of said compressed particulate material is determined using the equation:
V(p)=π/4*D2*h(p)
where D is the diameter of the cylindrical chamber, and where h(p) is the thickness of said compressed particulate material at pressure p as measured on said moveable piston, respectively on said fixed end at any stage of the compression or decompression of said particulate material.

### Claim 9

A method of measuring the void volume of a particulate additive material comprising
A. providing a cylindrical chamber for containing a particulate material which will be evaluated;
B. providing a fixed means at one end of said chamber for containing said particulate material;
C. providing a movable piston at the other end of said chamber which piston is linearly movable to compress the particulate material in said chamber;
D. providing a measuring means for measuring the force of compression of said particulate material when said piston is compressing said particulate material;
E. providing a measuring means for measuring the thickness of the compressed particulate material;
F. providing a measuring means for measuring the force of decompression of said particulate material after the release of said piston from the compressed state;
G. providing a particulate material for measurement;
H. compressing the particulate material to measure the force of compression of the particulate mass;
I. allowing the particulate material to decompress and measuring the decompression value;
J. measuring the thickness of the compressed and the decompressed material; and
K. determining the void volume of said particulate material;
wherein said particulate material is characterized as a continuous set of data points for the void volume as a function of the pressure during compression and a second set of data points for the void volume as a function of the pressure during decompression;
wherein the decompression curve is plotted using the following exponential equation:
p=a*exp(b*VV)+c
wherein p is the pressure, VV is the void volume and a, b and c are the fit parameters, which are determined by using least squares nonlinear regression analysis on the data points for the void volume as a function of the pressure during decompression, with void volume as the independent variable.

### Claim 10 (depends on 9)

The method of claim 9 wherein the data points of void volume and pressure, from pressure 10 MPa down to the end of the measurement are used for the nonlinear regression, on a system that is set to calculate pressure in MPa and void volume in cm3/100 g.

### Claim 11 (depends on 9)

The method of claim 9 wherein the goodness of the fit is quantified by the coefficient of determination (the R-squared value R2) as returned by the least squares nonlinear regression analysis.

### Claim 12 (depends on 11)

The method of claim 11 wherein a fit is accepted as sufficiently good if its coefficient of determination (R-squared value R2) is at least 0.98.

### Claim 13 (depends on 9)

The method of claim 9 wherein the residual void volume is calculated using the following equation:
VVres=1/b*log(q/a)
where q is a selected threshold from c, q must be kept constant when comparing different materials.

### Claim 14 (depends on 13)

The method of claim 13 wherein the threshold q is set to 0.1 MPa on a system that is set to calculate pressure in MPa and void volume in cm3/100 g.

### Claim 15 (depends on 9)

The method of claim 9 wherein the energy (or work) that the moving piston puts into the sample during a full compression and decompression cycle can be calculated using the following equation:
w=∫p∂VV
and is the integral of the product of pressure p and void volume VV over the full cycle.

### Claim 16 (depends on 15)

The method of claim 15 wherein said integral can be numerically solved by using the following calculation:
W=ΣpΔVV
And the sum of the products of pressure p and void volume increment ΔVV, wherein the void volume increment is positive during compression and negative during decompression.