JPH0746075B2 - Particle size distribution measuring device - Google Patents

Description

TECHNICAL FIELD The present invention relates to a particle size distribution measuring device, and more particularly to a particle size distribution measuring device using a sedimentation method.

<Background of the Invention> Generally, the biggest problem in expressing the size of a particle is that the shape of the particle is complicated and is not regular such as a sphere, a cube, a disk, or a prism. Due to this, the meaning of the obtained particle size differs due to the difference in the principle of the particle size measuring method.

In the particle size measurement method applying the sedimentation method, as described later,
To measure the particle diameter called Stokes diameter based on the definition "particle diameter equal to the diameter of a sphere having the same density and the same settling velocity as the particles to be measured settling in an arbitrary medium used for measurement". Become. That is, in the particle size measured by the sedimentation method, the shape of the sample particles is assumed to be a sphere, and the difference in this shape is not taken into consideration.

On the other hand, a microscope method that measures the major axis, minor axis, area, etc. based on the projected image of particles, a screening method that uses passage if the maximum width and maximum temperature of particles are smaller than the opening of the filter, or flow In a measurement method such as a pore passing method in which the major axis diameter is measured with the long axis along the direction of, the particle size distribution measurement result is greatly affected by the particle shape.

Therefore, when the measurement result obtained by the sedimentation method is compared with the result measured by another principle, there is a problem that they do not match.

The present invention has been made to solve such a problem, and despite the sedimentation method as the measurement principle, it is possible to reflect the difference in particle shape in the obtained particle size distribution measurement result, Therefore, it is an object of the present invention to provide a particle size distribution measuring device that can obtain a measurement result that is more consistent with the measurement result obtained by a measuring device based on another principle.

<Principle of the Invention> In measuring the particle size by the sedimentation method, the Stokes equation (10) shown below is used.

Considering the sedimentation motion of a single particle suspended in an arbitrary medium, the particle undergoes a sedimentation motion in the weight direction due to the difference between gravity and the buoyancy received from the medium. Receives a resistance force R in the opposite direction from
The equation of motion is expressed as follows.

Where u is the sedimentation velocity of the particles (cm / s), t is the time (S), m
Is the mass of the particle (g), m'is the buoyancy (g), g
Is the acceleration of gravity (cm / s ² ), R is the resistance force of the fluid, C is the resistance coefficient, and A is the projected area of the particle (c
m ² ) and ρ are fluid densities (g / cm ³ ).

From (1) and (2), let ρ _p be the particle density (g / cm ³ ). If the particles are spherical and their diameter is D _p (cm), Therefore, equation (3) is Will be transformed. Than this, It is represented by.

The target in particle size measurement is the range in which the resistance force acting on the particles complies with Stokes's law of resistance. In this range, the resistance coefficient C is μ as the viscosity coefficient of fluid (g / cm ·
s), Here, Re is the Reynolds number, It is represented by.

From (7) and (8), This is the Stokes equation for the sedimentation of particles, which is the basic equation for particle size measurement by the sedimentation method.

In the actual particle size measurement, the particles are separated by the distance h during the time t.
Is settled, u = h / t 11), and from (10) and (11), The particle size D _P is calculated by

As is clear from the above description, the particle diameter D _P calculated here is, as described above, “settling in any medium used for measurement, having the same density and the same sedimentation velocity as the particles to be measured. The particle diameter is equal to the diameter of the sphere ", which is called the Stokes diameter.

As is clear from the above, according to the Stokes equation, the sedimentation motion is explained assuming that the particles are spherical, and the difference in particle shape is not taken into consideration.
Taking this into consideration, in order to obtain a more realistic particle size, it is necessary to replace the terminal velocity u _{m in} equation (10) with the actual terminal velocity of the particles to be measured. That is, when the terminal velocity in the Stokes equation is u _m and the actual velocity (or corrected terminal velocity) is u _mc , The final velocity in the Stokes equation by
By correcting u _m , it is possible to make the measurement result of the particle size by the sedimentation method more realistic.

Regarding the above correction method, various proposals have been mainly made based on experimental results, but Pettyjohn et al.
With the sphericity Ψ of the particle as a parameter, Is leading. The sphericity Ψ is For example, a regular shaped particle is defined as a cube 0.
806, regular tetrahedron 0.671, cylinder (equal in diameter and height) 0.877
Take the values such as.

Heywood also calculates the terminal velocity of non-spherical particles by using the average equi-shadow diameter D _H and Heywood's volumetric shape factor k ′. That is, the particle volume is defined by k'D _H3 (16), and the method of calculating the sedimentation velocity is shown when k'can be experimentally obtained. in this way, On the right side and by calculating calculates the CRe ^2, Re of the spherical particles
Re is obtained from the known relationship between C and C, and And the logR obtained by experiment from the above k'value
The e correction value is calculated, the previously obtained Re is corrected, and the corrected method Re is used to calculate the sedimentation method velocity u in equation (9).

<Example> An example of the present invention will be described below with reference to the drawings.

FIG. 1 is a block diagram showing the configuration of the embodiment of the present invention.

This example shows a case where the present invention is applied to a centrifugal sedimentation type particle size distribution measuring apparatus to which a light transmission method is applied.

The sample particles w to be measured are uniformly dispersed in the medium solution and are accommodated in the sample cell 1 as a suspension. The sample cell 1 is fixed to a rotating disc 2 and is rotated by a motor 3. In the centrifugal force field due to this rotation, the sedimentation of particles is promoted and the measurement time is shortened.

The change in the concentration of the suspension due to the settling of the particles is measured by an optical system composed of a light source 4 and a light receiving element 5 provided at a fixed distance from the center of rotation of the rotating disk 2. That is, when the sample cell 1 arrives at the center of the optical axis of this optical system, the switch 7 is closed by the output signal from the rotational position detector 6. The output signal of the light receiving element 5 when the switch 7 is closed becomes a signal representing the absorbance of the suspension, and is arithmetically controlled via the amplifier 8 and the AD converter 9 as the detection value of the suspension concentration. Adopted in Part 10.

The arithmetic and control unit 10 is mainly composed of a micro computer composed of a CPU 11, a ROM 12, a RAM 13, etc.
In addition to the 14, CRT 15 and printer 16, the motor 3 described above
An inverter 17, which controls the CPU based on a command from the CPU 11,
Also, the analysis calculation unit 23 is connected via the serial interface 24.

The analysis / calculation unit 23 (for example, trade name; Shimadzu Bosch Lom image analysis device Omnicon FAS-II) takes in an image pickup signal from the TV camera 22 attached to the microscope 21 as image data, and based on the image data, The sphericity Ψ can be determined. That is, by placing the sample particles under the field of view of the microscope 21 and capturing the image with the TV camera 22, the analysis calculation section 23 obtains the geometric information of the sample particles from the image pickup signal and recognizes the particle shape, and the recognition thereof. The sphericity Ψ of the sample particle is determined based on the result. The determination of the sphericity Ψ is performed before the sample particles are accommodated in the sample cell 1 and subjected to centrifugal sedimentation, and the sphericity Ψ thus determined is sent to the arithmetic control unit 10 via the serial interface 22. Supplied.

A measurement program for calculating the particle size distribution of the sample particles based on the above-described Stokes equation from the time-series detection value of the concentration of the suspension in the sample cell 1 is written in the ROM 12, but here, The terminal velocity u _m in the Stokes equation is calculated by Pettyjohn et al. (13), (1
Correction using equation 4) is added. As the sphericity Ψ in the equation (14), the sphericity Ψ supplied from the above-described analysis calculation unit 23 before the sedimentation measurement is used.

As a result, the obtained particle size distribution takes into consideration the shape of the sample particles.

Note that other measurement conditions and the like are input from the keyboard 14 in an interactive form with the CRT 15. If most of the particles settle down, the measurement is terminated and the measurement conditions and the measurement results are output to the printer 16.

Further, the correction of the terminal velocity u _m may be performed by the Heywood method instead of the Pettyjohn et al. Method, or another method may be used.

Furthermore, the present invention can be universally applied to a particle size distribution measuring device by a sedimentation method, and can be applied to a measuring device by a natural sedimentation method in addition to the centrifugal sedimentation method, and the concentration can be detected by a light transmission method. Of course, it is not limited to.

<Effects of the Invention> As described above, according to the present invention, an image capturing unit for capturing an image of a sample particle, and an image analyzing unit for capturing image data from the image capturing unit and outputting data relating to the shape of the sample particle. And a correction calculation means for correcting the sedimentation velocity in the process of calculating the particle size distribution by the Stokes equation using the data from the image analysis means, and correcting the terminal velocity of sedimentation in the Stokes equation to obtain the particle size. With this configuration, it is possible to directly obtain the particle size distribution measurement result that reflects the difference in the shape of the sample particles, that is, more suitable for the actual state of the particle shape. As a result, the measurement result by the particle size distribution measuring apparatus using the sedimentation method of the present invention is, for example, the microscopic method, the screening method, or the pore passing method, and the measurement results by other measurement methods susceptible to the particle shape. It becomes possible to directly compare with, and it is possible to relax the peculiarity of the measurement result based on the sedimentation method and make it more universal.

On the contrary, by determining the input value of the data relating to the shape of the particles so as to match the data obtained by another method, it can be applied to applications such as obtaining the correlation between the sedimentation method and another method.

[Brief description of drawings]

 FIG. 1 is a block diagram showing the configuration of the embodiment of the present invention. 1 …… Sample cell 2 …… Rotating disk 4 …… Light source 5 …… Light receiving element 10 …… Computer control unit 11 …… CPU 12 …… ROM 13 …… RAM 21 …… Microscope 22 …… TV camera 23 …… Analysis Arithmetic unit 24 …… Serial interface

Claims (1)

[Claims] 1. A sample container for holding a suspension in which sample particles are dispersed in a medium solution, and detection for detecting a change in the concentration of the suspension caused by sedimentation of the sample particles in the sample container. In the device having a means and a calculating means for calculating the particle size distribution of the sample particles by using the Stokes equation from the detection signal of the concentration change, an imaging means for imaging the sample particles and the image data from the imaging means are captured. Image analysis means for outputting data relating to the shape of the sample particles,
A particle size distribution measuring device comprising a correction calculation means for correcting the sedimentation velocity in the process of calculating the particle size distribution by the Stokes equation using the data from the image analysis means.