CN111583270A - 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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CN111583270A
CN111583270A CN202010283220.5A CN202010283220A CN111583270A CN 111583270 A CN111583270 A CN 111583270A CN 202010283220 A CN202010283220 A CN 202010283220A CN 111583270 A CN111583270 A CN 111583270A
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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 an immiscible two-phase mixing effect, which comprises the steps of photographing materials in a mixing process by a high-speed camera in the material mixing process, carrying out binarization processing on the photographed images to obtain an optimal binary image, dividing the optimal binary image into N regions with equal size, and calculating the 0-dimensional Betty number β of a multiphase mixed fluid mixed pattern in the N different regions0Or 1 st wibeki number β1Determining the 0 th dimension Betty number β of N regions of each optimal binary image0Or 1 st wibeki number β1Variance 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 a 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 during the mixing operation, and although the method can be used for characterizing the fluid mixing degree, the requirement on the working medium during the use has certain limitation.
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 β of the multiphase mixed fluid mixing pattern in the N different regions0Or 1 st wibeki number β1；
(5) Determine the 0 th dimension Betty number β of each optimal binary image0Or 1 st wibeki number β1Variance 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.
N in the step (3) is more than or equal to 3, and the N areas are circular or rectangular.
Step (4) 0 th wibeki number β0Or 1 st wibeki number β1Is calculated by the Chom International Rabbit fee software.
And (4) during gas-liquid mixing and liquid-liquid mixing, calculating multiphase in N different areas by using the optimal binary image1 st wibeki number of mixed fluid mixture β1When mixing solid and liquid, the 0 th dimension Betty number β of the multiphase mixed fluid mixing pattern in N different areas is calculated by the optimal binary image0。
In algebraic topology, the Betty number of the topological space β0，β1，β2.., is a family of important invariant, the value is nonnegative integer or infinity, intuitively, β0Is the number of connected components, β1β of the maximum number of cuts, higher order, that cuts through the space along a closed curve to maintain continuitykCan be defined by a coherent group, wherein β0β is the 0 th Betty number representing the number of connected components in the region, which is simply the number of blocks in the region1The invention relates to a method for evaluating multiphase mixed topology disorder and super-uniformity by using 0-dimension or 1-dimension Betty number, which is characterized in that pictures captured by a high-speed camera in a multiphase mixing process are subjected to binarization processing by adopting a statistical method, and then the 0-dimension Betty number β of a multiphase mixing pattern is calculated by a binary image0Or 1 st wibeki number β1Specifically, the mixed pattern is divided into N regions of equal size, and the 0 th-dimensional Betty number β of each region is calculated0Or 1 st wibeki number β1Further, 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: the direct contact heat exchange behavior research of refrigerant pentafluoropropane (gas) and medium and low temperature synthetic heat transfer oil (liquid) in a direct contact heat exchanger is carried out, a high-speed camera is used for photographing the mixing process of the refrigerant pentafluoropropane (gas) and the medium and 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;
fourthly, calculating and obtaining the 1 st dimensional Betty number β in 3 different areas through 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 is to find β 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 pictures taken at 1.5 minutes were processed as described above to obtain β for the three regions as described above1Has a variance of
Figure BDA0002445650210000044
Will be provided with
Figure BDA0002445650210000045
d. N is respectively substituted into
Figure BDA0002445650210000046
λ ═ 0.33 was obtained, i.e. the mixing process was disordered and ultra-homogeneous.
The pictures taken at 3 minutes were processed as described above to obtain β of 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;
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;
fourthly, β in 3 different areas are obtained through calculation by the Chom international rabbit fee software0And β1The picture taken at 1 minute is processed to obtain the optimal second pictureValue map, as shown in FIG. 1, β0Representing the number of connected branches in a mixed binary pattern, i.e. "block" -the number of aggregated liquid distributions not participating in mixing, in solid-liquid mixing, β0Greater indicates better mixing, β1Representing the number of "channels" in the mixed binary pattern, i.e. the number of "holes" -bubbles produced in the binary pattern, in a 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;
fourthly, calculating and obtaining 0-dimensional Betty number β in 4 different areas through 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 is to find β of each optimal binary image0Variance of (2), variance for
Figure BDA0002445650210000051
Represents;
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;
fourthly, the 1 st dimensional Betty number β in 5 different areas is obtained through calculation 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 is to find β 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 at 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 of the mixed pattern in N different regions β0Or 1 st wibeki number β1；
(5) Determine the 0 th dimension Betty number β of each optimal binary image0Or 1 st wibeki number β1Variance 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 Betty number β in the step (4)0Or 1 st wibeki number β1Is 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 mixing pattern is calculated during the gas-liquid mixing and the liquid-liquid mixing in step (4)1When mixing solid and liquid, the 0 th dimension Betty number β of the mixed pattern is calculated0。
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CN112669268A (en) * 2020-12-21 2021-04-16 昆明理工大学 Method, system and terminal for evaluating distribution uniformity of multiphase mixed concentration field
CN112669268B (en) * 2020-12-21 2023-06-06 昆明理工大学 Multiphase mixed concentration field distribution uniformity evaluation method, system and terminal

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