CN111583270B - Method for evaluating mixing effect of immiscible two phases - Google Patents

Method for evaluating mixing effect of immiscible two phases Download PDF

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CN111583270B
CN111583270B CN202010283220.5A CN202010283220A CN111583270B CN 111583270 B CN111583270 B CN 111583270B CN 202010283220 A CN202010283220 A CN 202010283220A CN 111583270 B CN111583270 B CN 111583270B
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徐建新
杨凯
王�华
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Kunming University of Science and Technology
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Abstract

The invention discloses a method for evaluating the mixing effect of two immiscible phases, wherein in the process of mixing materials, a high-speed camera is used for photographing the materials in the mixing process; carrying out binarization processing on the shot picture to obtain an optimal binary image; dividing the optimal binary image into N regions with equal size; calculating the 0 th dimensional Betty number beta of the multiphase mixed fluid mixed pattern in N different areas0Or 1 st wibeth number beta1(ii) a Determining the 0 th dimension Betty number beta of N regions of each optimal binary image0Or 1 st wibeth number beta1Variance of (2)
Figure DDA0002445650230000011
By the formula

Description

Method for evaluating mixing effect of immiscible two phases
Technical Field
The invention relates to the technical fields of chemistry, metallurgical engineering and the like, in particular to a method for evaluating the mixing effect of immiscible two phases.
Background
Mixing is the intermixing of the components of the material under the influence of external forces, which results in a uniform distribution of the particles of the components in any volume. The method is an important link for ensuring the quality of the matched materials and improving the material effect. There are various methods of mixing, such as mechanical mixing, pneumatic mixing, impulse mixing, etc. The industry often encounters the problem of mixing of three phases, gas and liquid or some two of them. The mixing effect is a measure of the degree of homogeneity of the dispersed blend achieved by the mixing of the different components. The degree of mixing is related to the scale under investigation. At present, the mixing degree of the fluid system can be expressed by the following three ways: the degree of leveling is a measure of the uniformity across the entire range of equipment sizes. The average degree of mixing I of a component is the arithmetic mean of the degrees of mixing of a component obtained from several samples in the same tank, and can be used to measure the overall mixing effect of the system, but the number of samples taken must be specified. Separation scale, a measure of the size of the dispersed micelles (e.g., droplets, bubbles, or solid aggregates) in the mixture. Within the range of the separation scale, the substance is homogeneous or only one substance. The smaller the separation dimension, the more uniform the mixing. For immiscible systems, it is not possible to achieve a separation scale on the molecular level. And measuring the separation strength and the uniformity of the mutual soluble system on a small scale. The liquid has mixture micelles of different sizes and different concentrations, and the difference between the concentration of the mixture micelles and the average concentration is the separation strength. The smaller the separation strength, the more thoroughly the material is mixed and the more fuzzy the interface between the micelles is. When the mixed material has reached an ideal mixing state by molecular diffusion, i.e., when the so-called molecular-scale uniformity is achieved, the separation strength is zero, and it is also impossible to achieve a molecular-scale separation scale for immiscible systems.
The evaluation of the mixing effect is crucial in the mixing operation, and although the method can be used for characterizing the fluid mixing degree, the requirements on the working medium in use have certain limitations.
Disclosure of Invention
The invention overcomes the defects of the method, provides a method for evaluating the immiscible two-phase mixing effect with strong applicability and higher reliability, and comprises the following specific steps:
(1) in the process of mixing materials, a high-speed camera photographs the materials in the mixing process;
(2) carrying out binarization processing on the shot picture to obtain an optimal binary image;
(3) dividing the optimal binary image into N regions with equal size;
(4) calculating the 0 th dimensional Betty number beta of the multiphase mixed fluid mixed pattern in N different areas0Or 1 st wibeth number beta1；
(5) Determining the 0 th Betty number beta of each optimal binary image0Or 1 st Betty number beta1Variance of (2)
Figure BDA0002445650210000023
(6) By the formula
Figure BDA0002445650210000022
Calculating λ, where d represents the dimension, in two dimensions, d ═ 2; lambda is more than or equal to 0, which indicates that the mixing effect is random, namely the mixing state is disordered; lambda is more than 0 and less than 1, which indicates that the mixture is in a disordered and super-uniform state, lambda is more than or equal to 1, which indicates that the mixing effect is uniform, namely super-uniform, and the closer lambda is to 0, the stronger the disorder is; the closer λ is to 1, the stronger the uniformity.
The capture rate of the high-speed camera in the step (1) is 250 frames/second.
And (2) finding out the optimal threshold value of image binarization by using an iterative method to obtain an optimal binary image.
And (3) N is more than or equal to 3, and the N areas are circular or rectangular.
Step (4) 0 th wibeth number beta0Or 1 st wibeth number beta1Is calculated by the Chom International Rabbit fee software.
And (4) during gas-liquid mixing and liquid-liquid mixing, calculating the 1 st dimensional Betty number beta of the multiphase mixed fluid mixing pattern in N different areas by using the optimal binary image1(ii) a When mixing solid and liquid, it is calculated by the optimal binary imageCalculating the 0 th dimensional Betty number beta of the multiphase fluid mixture pattern in N different areas0。
In algebraic topology, the Betty number β of the topological space0，β1，β2.., is a family of important invariant, taking on non-negative integers or infinity. Viewed visually,. beta.0Is the number of connected components, beta1Beta is a maximum number of clipping times, higher order, which cuts the space along the closed curve to maintain the connectionkCan be defined by the group of homology, wherein β0The number of the 0-dimensional Betty represents the number of connected components in the region, namely the number of blocks in the region; beta is a1Representing the number of holes in the area. The invention relates to a method for evaluating the disorder and the super-uniformity of a multiphase mixed topology by using a 0-dimensional Betty number or a 1-dimensional Betty number, which adopts a statistical method to carry out binarization processing on a picture captured by a high-speed camera in the multiphase mixing process and then calculates the 0-dimensional Betty number beta of a multiphase mixed pattern by using a binary picture0Or 1 st wibeth number beta1. Specifically, the mixed pattern is divided into N regions of equal size, and the 0 th wibeki number β of each region is calculated0Or 1 st wibeth number beta1Further, the variance is obtained by the formula
Figure BDA0002445650210000021
Calculating to obtain lambda, reflecting the mixing uniformity, wherein lambda is more than or equal to 0 to indicate that the mixing effect is random; lambda is more than or equal to 1, the mixing effect is ultra-uniform like crystals; 0 < lambda < 1 indicates that the mixture is in a disordered and ultra-homogeneous state.
The method is simple and reliable, is suitable for all the representations related to the immiscible two-phase mixing effect, can be applied to various fields such as chemical industry and metallurgy, for example, can be used for researching the leaching and stirring process of hydrometallurgy, can also be used for researching the water model research of pyrometallurgy, particularly relates to the multiphase stirring and mixing effect evaluation in the fields of metallurgy and chemical industry, and has high practical value.
When the material is judged to be disordered and super-uniform, when lambda is more than 0 and less than 1, the size of lambda represents the strength of the disordered and super-uniform state, and the smaller the lambda is, the stronger the disorder is; the larger the lambda is, the stronger the uniformity is, and the multiphase mixing state of the working medium is divided into three types: random, disordered and super-uniform, super-uniform (or uniform), and strong discriminability and applicability.
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FIG. 1 is an optimal binary diagram of example 1.
Detailed Description
The method of the present invention is further illustrated with reference to the accompanying drawings and specific examples.
Example 1
The method for evaluating the incompatible gas-liquid mixing effect comprises the following specific steps:
the first step is as follows: direct contact heat exchange behavior research of a refrigerant pentafluoropropane (gas) and medium-low temperature synthetic heat transfer oil (liquid) in a direct contact heat exchanger is carried out, a high-speed camera photographs the mixing process of the refrigerant pentafluoropropane (gas) and the medium-low temperature synthetic heat transfer oil (liquid), and the capturing rate of the high-speed camera is 250 frames/second;
secondly, performing binarization processing on the shot picture, and finding out the optimal threshold value of image binarization by using an iterative method to obtain an optimal binary image;
the third step: dividing the optimal binary image into 3 regions with equal size, wherein the regions are rectangular;
the fourth step: the 1 st dimensional Betty number beta in 3 different areas is calculated and obtained by the Chom international rabbit fee software1，β1Represents the number of "channels" in the mixed binary pattern, i.e., the number of "holes" -bubbles generated in the binary pattern, resulting in 3 sets of bubble numbers;
the fifth step: finding the beta of each optimal binary image1Variance of (2), variance for
Figure BDA0002445650210000031
Represents;
and a sixth step: by variance
Figure BDA0002445650210000032
In a correlation system
Figure BDA0002445650210000033
To reflect the mixing uniformity, i.e. by formula
Figure BDA0002445650210000034
Determining λ, where d represents the dimension, and in two dimensions, d is 2 and N is 3;
the seventh step: analyzing a lambda value, wherein lambda is less than or equal to 0 to indicate that the mixing effect is random, namely the mixing state is disordered; lambda is more than or equal to 1, which indicates that the mixing effect is uniform, namely ultra-uniform; the lambda is more than 0 and less than 1, which indicates that the mixture is in a disordered and super-uniform state, particularly, when the lambda is more than 0 and less than 1, the size of the lambda can qualitatively describe the strength of the disordered and super-uniform state, and the closer the lambda is to 0, the stronger the disorder is; the closer λ is to 1, the stronger the uniformity.
Performing the above processing on the picture taken at 1 min to obtain an optimal binary image, as shown in FIG. 1, wherein 3 represents the ordinal number of the selected region, white is bubble and black is liquid, and determining β of the three regions according to the above method1Has a variance of
Figure BDA0002445650210000041
Will be provided with
Figure BDA0002445650210000042
d. N is respectively substituted into
Figure BDA0002445650210000043
Lambda-0.56 was obtained, i.e. the mixing process achieved at this time point was a chaotic process.
The above-described processing was performed on the picture taken at a time of 1.5 minutes, and β of the three regions was obtained according to the above-described method1Has a variance of
Figure BDA0002445650210000044
Will be provided with
Figure BDA0002445650210000045
d. N is respectively substituted into
Figure BDA0002445650210000046
Lambda is 0.33, i.e. the mixing process is disordered and ultra-uniform。
The pictures taken at 3 minutes were processed as described above to determine β for the three regions1Has a variance of
Figure BDA0002445650210000047
Will be provided with
Figure BDA0002445650210000048
d. N is respectively substituted into
Figure BDA0002445650210000049
λ 2.33 was obtained, i.e. the mixing process was homogeneous.
From the above analysis, it can be seen that when the mixing time is 1 minute, the mixing is in disorder and not uniformly mixed; when the mixing time is 1.5 minutes, the process is disordered and super-uniform, and the mixture is not uniformly mixed; when the mixing time is 3 minutes, the process is a uniform mixing process, the time point of lambda being 1 can be found out between 1.5 and 3 minutes, the optimal mixing time is obtained, and the time can be uniformly mixed and saves the cost.
Comparative example 1
The first step is as follows: in the research of the direct contact heat exchange behavior of refrigerant pentafluoropropane (gas) and medium and low temperature synthetic heat transfer oil (liquid) in a direct contact heat exchanger, a high-speed camera photographs the mixing process of the refrigerant pentafluoropropane (gas) and the medium and low temperature synthetic heat transfer oil (liquid), and the capture rate of the high-speed camera is 250 frames/second;
performing binarization processing on the shot picture, and finding out the optimal threshold value of image binarization by using an iterative method to obtain an optimal binary image;
the third step: dividing the optimal binary image into 3 regions with equal size, wherein the regions are rectangular;
the fourth step: calculated beta in 3 different regions by the Chom International Rabbit fee software0And beta1The above-described processing is performed on the picture taken at a time of 1 minute to obtain an optimal binary image, as shown in fig. 1, β0Representing the number of connected branches in a mixed binary pattern, i.e. "block" - "notThe amount of aggregate liquid distribution participating in mixing, in solid-liquid mixing, of0Larger means better mixing; beta is a1Denotes the number of "channels" in the mixed binary pattern, i.e. the number of "holes" -bubbles produced in the binary pattern, in the gas-liquid reaction, β1The larger the size, the better the mixing effect, but if there are 99 bubbles in the area 1, 0 bubble in the area 2 and 0 bubble in the area 3, the mixing uniformity evaluation by such a method is not accurate, and neither the optimum mixing time nor the overall mixing effect can be evaluated.
Example 2
The method for evaluating the incompatible solid-liquid mixing effect comprises the following specific steps:
the first step is as follows: during the process of mixing materials, such as the mixing of solid particles in liquid (water), the materials in the mixing process are photographed by a high-speed camera, and the capture rate of the high-speed camera is 250 frames/second;
the second step is that: carrying out binarization processing on the shot picture, and finding out the optimal threshold value of image binarization by using an iterative method to obtain an optimal binary image, wherein white in the binary image is liquid, and black in the binary image is solid;
the third step: dividing the binary image of the mixed image into 4 regions with equal size, wherein the shape of the regions is rectangular;
the fourth step: the 0-dimensional Betty number beta in 4 different areas is calculated and obtained by the Chom international rabbit fee software0，β0Representing the number of connected branches in the mixed binary pattern, i.e. "block" — the number of solid distributions; obtaining 4 sets of solid distribution quantities, wherein 4 represents the ordinal number of the selected region;
the fifth step: finding the beta of each optimal binary image0Variance of (2), variance for
Figure BDA0002445650210000051
Representing;
and a sixth step: by variance
Figure BDA0002445650210000052
In a correlation system
Figure BDA0002445650210000053
To reflect the mixing uniformity, i.e. by formula
Figure BDA0002445650210000054
Determining λ, where d represents the dimension, and in two dimensions, d is 2;
the seventh step: analyzing a lambda value, wherein lambda is less than or equal to 0 to indicate that the mixing effect is random, namely the mixing state is disordered; lambda is more than or equal to 1, which means that the mixing effect is uniform, namely ultra-uniform; the lambda is more than 0 and less than 1, the mixture is in a disordered and super-uniform state, particularly, when the lambda is more than 0 and less than 1, the size of the lambda can qualitatively describe the strength of the disordered and super-uniform state, and the closer the lambda is to 0, the stronger the disorder is; the closer λ is to 1, the stronger the uniformity, and the optimum mixing time is obtained by calculating the mixing time at λ ═ 1.
Verifying the optimal mixing time obtained in the example 2, selecting different slurry type stirrers in a biological fermentation tank to enable each area in the tank to achieve solid-liquid suspension and uniform mixing, improving fermentation yield and reducing energy consumption, selecting two non-optimal times according to the optimal mixing time t obtained in the example 2, wherein the three times are (t-3) minutes, t minutes and (t +3) minutes respectively, detecting the final fermentation yield, the fermentation yield obtained in the t-3) minutes is not as good as that obtained in the t minutes, and the difference between the fermentation yield obtained in the t +3) minutes and the fermentation yield obtained in the t minutes is not large, so that the optimal mixing time obtained in the example 2 is correct, the optimal mixing time of the stirrers with different slurry types is compared, and the most appropriate stirrer and stirring duration are selected.
Example 3
The method for evaluating the mixing effect of the incompatible liquid comprises the following specific steps:
the first step is as follows: in the process of mixing materials, the materials in the mixing process are photographed by a high-speed camera in the process of mixing the two immiscible liquids, and the capturing speed of the high-speed camera is 250 frames/second;
the second step is that: carrying out binarization processing on the shot picture, and finding out the optimal threshold value of image binarization by using an iterative method to obtain an optimal binary image; when the two liquids are mixed, the physical properties are different, after binarization treatment, the different liquids are in different colors, and in the process of mixing and diffusing the two liquids, one liquid is white in a binary image, and the other liquid is black;
the third step: dividing the binary image of the mixed image into 5 regions with equal size, wherein the shape of the regions is circular;
the fourth step: the 1 st dimensional Betty number beta in 5 different areas is calculated and obtained by the Chom international rabbit fee software1，β1Represents the number of "channels" in the mixed binary pattern, i.e., "holes" generated in the binary pattern-the number of small liquid accumulations, yielding 5 sets of liquid accumulation numbers;
the fifth step: finding the beta of each optimal binary image1Variance of (2), variance for
Figure BDA0002445650210000061
Represents;
and a sixth step: by variance
Figure BDA0002445650210000062
In a correlation system
Figure BDA0002445650210000063
To reflect the mixing uniformity, i.e. by formula
Figure BDA0002445650210000064
Determining λ, where d represents the dimension, and in two dimensions, d is 2;
the seventh step: analyzing a lambda value, wherein lambda is less than or equal to 0 to indicate that the mixing effect is random, namely the mixing state is disordered; lambda is more than or equal to 1, which means that the mixing effect is uniform, namely ultra-uniform; the lambda is more than 0 and less than 1, the mixture is in a disordered and super-uniform state, particularly, when the lambda is more than 0 and less than 1, the size of the lambda can qualitatively describe the strength of the disordered and super-uniform state, and the closer the lambda is to 0, the stronger the disorder is; the closer λ is to 1, the stronger the uniformity, and the optimum mixing time is obtained by calculating the mixing time with λ ═ 1.
The optimum mixing time obtained in example 3 was verified: in agricultural production, in order to reasonably use pesticides, water-insoluble liquid is usually prepared into emulsion (taking oil-water mixing as an example) for spraying crops suffering from diseases and insect pests, so that pesticide liquid is less in loss and more in attachment to leaf surfaces, two non-optimal times are selected according to the optimal mixing time t obtained in example 3 in the mixing process of two liquids (the volume ratio is 1: 1), the three times are respectively (t-10) minutes, t minutes and (t +10) minutes for mixing, and conductivity monitoring is carried out, the t minutes are matched with the time for achieving stable fluctuation, and the optimal mixing time obtained in example 3 is correct.

Claims (6)

1. A method for evaluating the mixing effect of two immiscible phases is characterized by comprising the following specific steps:
(1) in the process of mixing materials, a high-speed camera photographs the materials in the mixing process;
(2) carrying out binarization processing on the shot picture to obtain an optimal binary image;
(3) dividing the optimal binary image into N regions with equal size;
(4) calculating the 0 th dimension Betty number beta of mixed patterns in N different regions0Or 1 st Betty number beta1；
(5) Finding the 0 th Betty number beta of each optimal binary image0Or 1 st wibeth number beta1Variance of (2)
Figure FDA0002445650200000012
(6) By the formula
Figure FDA0002445650200000011
Calculating λ, where d represents the dimension, in two dimensions, d ═ 2; if lambda is less than or equal to 0, representing the mixed state disorder; if lambda is more than 0 and less than 1, the mixture is in a disordered and super-uniform state; if lambda is more than or equal to 1, the mixing effect is uniform.
2. The method for evaluating the effect of immiscible two-phase mixing according to claim 1, wherein the capturing rate of the high speed camera of step (1) is 250 frames/sec.
3. The method for evaluating the immiscible two-phase mixing effect according to claim 1, wherein the step (2) uses an iterative method to find the optimal threshold value for image binarization, so as to obtain the optimal binary image.
4. The method for evaluating the effect of mixing two immiscible phases according to claim 1 wherein N.gtoreq.3 in step (3).
5. The method for evaluating the effect of immiscible two phases in accordance with claim 1, wherein the 0 th dimension beta is the Betty number β in the step (4)0Or 1 st wibeth number beta1Is calculated by the Chom International Rabbit fee software.
6. The method for evaluating the effect of immiscible two phases as claimed in claim 1, wherein the 1 st wibeki number β of the mixture pattern is calculated during the gas-liquid mixing and the liquid-liquid mixing in the step (4)1(ii) a When solid and liquid are mixed, the 0 th dimension Betty number beta of the mixed pattern is calculated0。
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