Method of and an apparatus for determining particle size distributions by measuring the spectral light extinction during sedimentation
OwnerReiner Weichertinventor
Life of this patent
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Abstract
A method of determining particle size distributions in the range of from about 0.03 to 10 .mu.m by measuring the spectral light extinction during sedimentation of particles suspended in a transparent liquid in a centrifugal field. The light transmissions through the suspension of light of different wavelengths are measured in response to the settling time and the particle size distribution is determined from the light transmissions measured. No knowledge of the optical data of the particles is needed. The integral equation to be solved for that purpose is given. A wide particle size range can be covered precisely within short times of analysis.
Claims11
A particle size determination method comprising the steps of:
- placing a quantity of a transparent liquid containing suspended particles in a device for sedimenting said particles by application of a centrifugal field;
- subjecting said transparent liquid and said particles to said centrifugal field and simultaneously exposing said transparent liquid to light of different wave lengths .lambda..sub.i (i=1, 2, . . . );
- measuring the spectral light extinction by measuring the respective light transmissions (T) through the transparent liquid in response to the settling time (t) and calculating the particle size distribution q.sub.e (x) from the light transmissions measured;
- storing the respective light transmissions (T) measurements in a memory;
- and
- determining q.sub.3 (x) with the following integral equation for the light wave lengths .lambda..sub.i (i=1, 2, . . . ) used and the stored light transmissions values T ##EQU8## whereupon ##EQU9## from .PHI.(.lambda..sub.i,x) with i=1, 2, . . . is determined from
- .PHI.(.lambda..sub.i, x)=K(.pi.x/.lambda..sub.i)q.sub.3 (x)
- K(.alpha.=.pi.x/.lambda..sub.i) and q.sub.3 (x) with i=1, 2, . . .
- by means of ##EQU10## with K(.alpha.) from the Fraunhofer approximation, wherein K(.pi.x/.lambda.) is the extinction function dependent on the material,
- Pf is the density of the suspension liquid,
- .eta. is the viscosity of the suspension liquid,
- Ps is the density of the solids particles,
- c is a constant,
- .omega. is the number of revolutions of the centrifuge per unit of time,
- r is the inner radius of the cuvette, and
- R is the radius at which the transmission measurement is made.
A particle size determination apparatus comprising:
- at least one transparent measuring cuvette means for containing a suspension of particles in a transparent liquid;
- photocentrifuge means adapted to receive said at least one measuring cuvette means;
- an illumination means for transilluminating said cuvette means with bundles of light beams of different wave lengths .lambda..sub.i (i=1, 2, . . . );
- at least one photodetector means positioned adjacent said cuvette for measuring the respective light transmissions T (.lambda.,t) during sedimentation;
- and
- an analyzer means for computing the particle size distribution q.sub.3 (x) from the transmission measurements T, by means of separate numerical solutions of the following integral equation for the light wave lengths .lambda..sub.i (i=1, 2, . . . ) used (method of weighted singular value decomposition) ##EQU11## whereupon ##EQU12## from .PHI.(.lambda..sub.i,x) with i=1, 2, . . . is determined from
- .PHI.(.lambda..sub.i, x)=K(.pi.x/.lambda..sub.i)q.sub.3 (x)
- K(.alpha.=.pi.x/.lambda..sub.i) and q.sub.3 (x) with i=1, 2, . . .
- by means of ##EQU13## with K(.alpha.) from the Fraunhofer approximation, wherein K(.pi.x/.lambda.) is the extinction function dependent on the material,
- Pf is the density of the suspension liquid,
- .eta. is the viscosity of the suspension liquid,
- Ps is the density of the solids particles,
- c is a constant,
- .omega. is the number of revolutions of the centrifuge per unit of time,
- r is the inner radius of the cuvette, and
- R is the radius at which the transmission measurement is made.
Dependencies are inferred from the claim text.