JP6985573B2 - Porous structure evaluation method, structure evaluation device, and structure evaluation program - Google Patents

Description

The present invention relates to structural evaluation of a porous body, particularly evaluation of fluid resistance.

Porous media used in car exhaust gas filters and fuel cells have a catalytic action. Since the reaction of the catalyst proceeds on the surface of the pores in contact with the fluid, the surface area of the pores is important as well as the diameter of the pores as an evaluation item.

Factors that increase the surface area include surface irregularities, the number of flow paths, the number of loops, and the like. In addition, since the exhaust gas filter uses the flow of gas to filter harmful substances in the exhaust gas, it is considered that the properties of the flow also contribute to the filter performance.

Conventionally, a mercury intrusion method or a gas adsorption method has been used for analysis of the communication property of a porous body having a diameter of several nm to several 100 μm. These methods are indirect measurement methods in which mercury or gas is injected into a porous body and the pore size distribution is calculated by a model formula from changes in pressure and flow rate over time.

Further, in Non-Patent Document 1, bone is extracted from a CT (Computed Tomography) image, the morphological characteristics of the bone are calculated, and the network structure and the mechanical strength are evaluated using an electric circuit model. Further, Patent Document 1 also shows that an electric circuit model is used for the flow path of the filter.

Japanese Unexamined Patent Publication No. 2016-97121

Satoshi Nango, Evaluation of Lumbar Vertebra Vulnerability Due to Osteoporosis, Osteoporosis Japan, vol. 16, no. 2, 2008

Here, the mercury intrusion method and the gas adsorption method measure the pressure and flow rate of the fluid, and the flow path network formed by the pores and the distribution of the pressure and flow in the pores cannot be predicted.

Analysis by three-dimensional (3D) fluid simulation is also used. This makes it possible to know the behavior of the fluid in the flow path created by the pores. However, there are problems such as high calculation cost and the model size is not a practical scale.

Methods such as Non-Patent Document 1 and Patent Document 1 can be used to evaluate the flow path network created by pores, but in order to perform analysis such as 3D fluid simulation, improvements that reflect the properties of the fluid are required. is necessary.

The present invention is a method for evaluating the structure of a porous body using a CT image, in which pores are detected from the CT image, and the detected pores are approximated to a model in which elliptical columns are connected. Then, for each elliptical column, Poiseuille Flow was assumed. The flow resistance is defined as the flow rate that divides the pressure difference between both ends of the pipe. This resistance is inversely proportional to the square of the cross-sectional area. The flow path resistance that is inversely proportional to the square of the cross-sectional area is calculated, and the structure of the porous body is evaluated based on the calculated flow path resistance.

（２）始終点間の圧力の合計（始点圧−終点圧）は経路によらず一定である。

Further, the porous body may have an inlet region and an outlet region, apply a pressure difference to the region, and obtain a flow index including the flow rate, the flow velocity, or the power of the fluid in each elliptical column.
Obtain the pressure at the intersection and the flow rate of the branches under the following conditions.
(1) The sum of the flow rates entering and exiting at the intersection is 0.

(2) The total pressure between the start and end points (start point pressure-end point pressure) is constant regardless of the path.

In addition, among the detected pores, the penetration path from the inlet region to the exit region is extracted, and the flow index including any of the power and resistance total, flow rate average, and flow velocity average of the branches constituting the extracted penetration path. You should ask for.

In addition, the extracted penetration path is displayed as a three-dimensional position in the porous body, and one of the obtained flow indexes is selected, and the size of the selected flow index is displayed. Should be displayed in correspondence with.

Further, it is preferable to select the extracted penetration path having a large selected flow index and display only the selected penetration path.

Further, the present invention is a structure evaluation device for a porous body that evaluates the structure of the porous body using a CT image, and is a model in which pores are detected from the CT image and elliptical columns are connected to the detected pores. For each elliptical column, the flow path resistance that is inversely proportional to the square of the cross-sectional area is calculated, and the structure of the porous body is evaluated based on the calculated flow path resistance.

Further, the present invention is a structure evaluation program for a porous body in which a computer is used to evaluate the structure of the porous body using a CT image. The computer is made to detect pores from the CT image, and the detected pores are elliptical columns. For each elliptical column, the flow path resistance that is inversely proportional to the square of the cross-sectional area is calculated, and the structure of the porous body is evaluated based on the calculated flow path resistance.

According to the present invention, the flow path resistance of the fluid of the porous body can be easily calculated by using the shape, and the same result as that of the fluid simulation can be obtained.

It is a figure which shows the pore of a porous body, (a) is the one before the pore is extracted using the CT value, and (b) is the thing which binarized the pore. It is explanatory drawing which shows the method of obtaining the maximum diameter of a pore, and the skeleton line. It is a figure which shows the network of the skeleton line. It is a figure which shows the structure of each branch which made up of a pipe in a flow path resistance model. It is a figure which shows the porous body, (a) shows the CT image, (b) shows the skeleton line obtained from the CT image. It is a figure which shows three kinds of analysis results about the pressure distribution of a porous body, (a) shows the analysis result of the fluid simulation, (b) shows the analysis result of the flow path resistance model, and (c) shows the analysis result of the electric circuit model. It is a figure which shows the analysis result of three kinds about the flow velocity distribution of a porous body, (a) shows the analysis result of the fluid simulation, (b) shows the analysis result of the flow path resistance model, and (c) shows the analysis result of the electric circuit model. It is a figure which shows the procedure of selection of a penetration path. FIG. (E) indicates a penetration path having a large power. It is a figure which shows the flow characteristic of the penetration path of Sample 1 with small permeability, the flow path resistance model, and the penetration path in an electric circuit model. It is a figure which shows the curve ratio of a penetration path, (a) shows Sample1 and (b) shows Sample2. It is a figure which shows the pore diameter distribution of a porous body, (a) shows Sample1 and (b) shows Sample2. It is a figure which shows the pore diameter histogram, and shows (a) Sample1 and (b) Sample2. It is a figure which shows the pressure of a penetration path, (a) shows Sample1 and (b) shows Sample2. It is a figure which shows the flow rate of a penetration path, (a) shows Sample1 and (b) shows Sample2. It is a figure which shows the equal potential surface, the current, the power consumption on the flow path by the electric circuit model, (a) (b) (c) are the equal potential surface, the current, the power consumption on the flow path of Sample1 by the electric circuit model, (a) (b) (c). d) (e) (f) indicate the equipotential surface, the current, and the power consumption on the flow path of Sample2. It is a flowchart which shows the process by the computer of the structure evaluation which concerns on this embodiment.

Hereinafter, embodiments of the present invention will be described with reference to the drawings. The present invention is not limited to the embodiments described here.

"System configuration"
The method for evaluating the structure of a porous body in the present embodiment is carried out by an apparatus (system) for that purpose, and the structural evaluation device for the porous body is an apparatus for executing a structural evaluation program for the porous body, and is a general-purpose apparatus. Computer is fine. Further, the program may be an application program that runs on various operating systems (OS) as long as it can be executed on a computer. Such an application program may be provided in the form of a DVD or the like, may be provided by downloading via a network, or may be pre-installed on a computer.

"Porous medium"
Three-dimensional porous structures produced by various methods can be evaluated. Such a porous body is used, for example, as a gas filter, a liquid filter, an electrode material of a fuel cell, or a building material.

In this embodiment, a porous body having pores having a diameter of several nm to several 100 μm is adopted as a target. Such pores can be formed by mixing a foaming agent with a solvent and vaporizing it at a high temperature to create bubbles, mixing a molten material such as ice with a base material and melting and removing it by heat treatment, or forming pores together with a scaffold material. The agent is made into a zel and freeze-dried to remove the pore-forming material, or the molten material is removed from the high-porosity zel.

<Creation of analysis model>
In this embodiment, a model is created from an X-ray CT image. If the shape of the pores in the porous body can be expressed, a model may be formed based on other data. For example, it is possible to create a model from three-dimensional images of FIB SEM (Focused Ion Beam Scanning Electron Microscope) and TEM (Transmission Electron Microscopy).

<Extraction of pores>
Since the pores are filled with a substance having a small air density as compared with the base material, the pores are extracted using the CT value. FIG. 1 is a diagram showing pores of a porous body, and FIG. 1A is a CT value image. The pores are extracted using this image. (B) is the one obtained by extracting the pores and binarizing them. Here, in FIG. 1 (a), black indicates pores (pores), and in FIG. 1 (b), white indicates pores.

<Pore diameter and skeletal line>
FIG. 2 is an explanatory diagram showing how to obtain the maximum diameter of the pores and the skeleton line. In this way, the spheres are packed in the pores, and the pore diameter is determined as the maximum diameter of the spheres contained in the pores. Further, the locus of the center point of the sphere is used as the skeleton line of the pores.

<Communication hole network>
When a skeletal line is obtained, connect it to obtain a communication hole network. FIG. 3 is a diagram showing a network of skeleton lines. First, one region of the porous body (for example, one surface of a polygon) is defined as an inlet region, the other region is defined as an outlet region, and the end of the skeleton line located here is defined as an inlet In and an outlet Out (Ct). .. Further, the intersection of the skeleton lines is the node Node (Nd), and the end point other than the node Nd is the terminal Tm. Nd: Nd, Nd: Tm, Nd: In, Nd: Out and the like are called branches. Then, let L be the length between the end points of the branches.

Then, the cross section orthogonal to the skeleton line is approximated by an ellipse for each branch. That is, the short side length is defined as the thickness (Th), and the long side length is defined as the width (Wd). L, Th, and Wd are calculated from the binarized pore image. The cross-sectional area S is S = π (Th / 2) · (Wd / 2).

In this way, it is possible to create a communication hole network consisting of branches of elliptical columns as shown in FIG.

Here, the ellipse of the branch can be determined by the cross section orthogonal to the skeleton line of the branch. For example, it gradually moves inward (for example, by a predetermined distance) from its periphery (outer circumference of the pore) in a direction orthogonal to the tangent of each point. By repeating such an operation, points that have moved from opposite directions come into contact with each other at any point near the center. Therefore, the minor axis is specified at the point of first contact. Then, in the direction orthogonal to the minor axis, the operation is repeated and the outer peripherals from the opposite directions come into contact with each other to specify the major axis.

In this way, an approximate ellipse at one point in the length L direction can be specified. By specifying an ellipse in the entire length direction of a branch (between nodes), an elliptical column for each branch can be specified as shown in FIG. For one branch, both ends may be approximated to an ellipse and these may be connected to form an elliptical column.

<Flower resistance model>
In this way, if an elliptical column can be defined for each branch, the flow path resistance for these branches is specified. In the present embodiment, the resistance is inversely proportional to the square of the cross-sectional area, which is the resistance that realizes Poiseuille Flow (flow path resistance model).

FIG. 4 is a diagram showing the configuration of each branch in the flow path resistance model. In this way, the branch of the elliptical pillar described above is used as a hollow pipe, and the flow of Poiseuille in each pipe is analyzed.

If the Poiseuil flow resistance Rf is used,
Rf = 8πμL / S ²
Will be. Here, S: cross-sectional area, L: pipe length, μ: viscosity (Pa · s). Note that S changes in the L direction.

Thus, the flow path resistance depends only on the shape of the flow path, except for the viscosity μ of the fluid. This flow path resistance is used as the resistance of the communication hole flow path. This method assumes a steady flow of laminar flow in the pipe. This makes it possible to analyze the fluid flow that strongly depends on the pore size. After the resistance is defined, the analysis is performed by solving the circuit equation in the same way as the equation of the electric circuit model in which the pressure difference between the input and output is the voltage.

<Electric circuit model>
Assuming that the pores (branches) are filled with an electric conductive material, the resistance reflecting the cross-sectional area and length of the pores in the structure is defined, and an electric circuit network is created from the pore network. That is, one branch is replaced with one electric resistance, and the electric resistance is connected at the node to form an electric circuit network. A potential difference is given to the inlet and outlet to obtain the voltage and current at each point on the network. We weaken the properties of the flow and perform a simulation that emphasizes the shape and connection of the pores.

Electrical resistance R _E of the pores (branch) is expressed as follows.
_RE = ρ ・ L / S
Here, S: cross-sectional area, L: length, ρ: volume resistivity (Ω · m).

Table 1 shows the correspondence between the models that reflect the resistance equation. Here, the electric resistance is inversely proportional to the cross-sectional area, and the flow path resistance of the flow path resistance model is inversely proportional to the square of the cross-sectional area. Both models differ in this respect.

<Others>
Other main flow path structure evaluation indexes include "star volume" and "number of loops (number of one-dimensional Betti numbers)".

The star volume is the area volume connected by a straight line around the point. It is possible to express the local expanse of the flow path and the base material. There is a flow path star volume and a base material star volume. When the bend of the flow path is large, the flow path star volume takes a small value. It becomes a large value when it is straight. The large star volume of the base metal indicates the deviation of the flow path. Small indicates that the flow paths are uniformly dispersed.

The one-dimensional Betti number is the number of connected loops in the pore network. Represents network connectivity. A large number of loops (one-dimensional Betti number) indicates that the flow paths are connected.

<Morphological features>
Here, by extracting the pores from the CT image, information (structural index) about the morphology of the flow path (communication hole network) composed of the pores can be obtained. Therefore, the following structural index of the porous body can be obtained.

"Porosity (porosity)", "channel branch dimensions: thickness, width, length", "pore diameter distribution", "minimum pore diameter of through path", "number of loops (number of one-dimensional vetches)" "," Channel particle division, particle size distribution (mainly used for evaluation of channel formation by foaming agent) "," Bulk specific surface area: Expresses the ratio of the surface area to the bulk volume of the base metal in the catalytic reaction layer, etc. " , "Total length of channel network, number of branch points, average branch length", "Number of inlet nodes, average inlet cross-sectional area", "Number of exit nodes, average cross-sectional area of exit", "Channel star volume (straight line of channel) (Indicating sex) "," Base material star volume (indicating bias in the flow path) ".

<Indicator of flow>
Further, the following flow indexes are obtained for each branch according to the calculation result of the flow path resistance.
"Pressure (Pa), pressure loss (Pa)", "flow velocity (m / sec)", "flow ^{velocity (m 3} / sec) (= flow velocity x cross-sectional area)", "energy consumption (N / (sec / m)) ) ”,“ Viscous resistance (Pa / (m ³ / sec)) ”
In addition, it is possible to calculate the flow rate, flow velocity, pressure loss, etc. when the defined inlet to outlet are considered as one flow path.

<Penetration path morphology feature amount>
By giving the resistance of the holes and the pressure difference between the inlet and the outlet, it is possible to extract a continuous flow path from the inlet to the outlet. This is called a penetration path. It is possible to express the characteristics of the porous body by the penetration path.

Search for all paths from the inlet to the exit of the channel and select the most suitable path in that order. Since the number of paths is innumerable, the sum of the energy consumption of the branches that make up the path is defined as the energy consumption of the path, and the energy consumption is taken out in descending order. Duplicate paths are not counted for penetrating paths.

<Penetration path measurement>
A continuous flow path from the entrance to the exit is called a penetration path. Search every path from the inlet to the exit and select the best path for the fluid to flow. Since the number of paths is innumerable, the sum of the powers (energy consumption) of the branches that make up the paths is defined as the power of the paths, and the power is taken out in descending order.

Here, in order to prevent the number of paths from becoming enormous, paths with a small contribution to the overall flow are excluded.

Further, a path having a large turnover rate, an overlapping path in which most of the branches are included in the selected path may be excluded, or the number of measured paths may be limited.

The following items are measured for each penetration path, and the average of the entire penetration path is used as the feature amount of the porous body.
-Morphological features: number of through passes, minimum pore diameter, curvature ratio / flow index: total viscous resistance, total power, average flow velocity, average flow rate

<Penetration pass coverage>
The ratio of the total of the penetration paths covering the entire porous body is calculated. The obtained ratio was multiplied by 100 and displayed as%.
・ Pore volume ratio = {Σ [through path constituent branches] (branch length x cross-sectional area) / (Σ [all branches] (branch length x cross-sectional area))

The vacancy volume ratio is 100, which is obtained by dividing the total vacancy volume (branch length x cross-sectional area) of the branches constituting the through path by the total vacancy volume (branch length x cross-sectional area) of all branches. It is a multiplication.

-Flow rate ratio The flow rate ratio is the value obtained by dividing the total flow rate for the penetration path by the total flow rate flowing from the inlet to the outlet.

-Power ratio The power ratio is the value obtained by dividing the total power (energy consumption) for the flow of the penetration path by the total power for the entire flow flowing from the inlet to the outlet.

In this way, by selecting a penetration path, obtaining an index of the flow for each penetration path, and displaying this, it is possible to easily display the characteristics of the porous body. Here, the flow velocity of all the branches can be indicated by color, but the number of branches is too large to grasp the tendency. For example, if you select a penetration path and display the pressure for each penetration path, you can see the pressure trend as a whole. In particular, the penetrating path is responsible for much of the overall flow, and the pressure of dead-end branches is hidden, making it easier to see the overall trend. Furthermore, by limiting the penetration path to be displayed by selecting the one with high power, it is possible to make the display easier to see.

<Analysis result>
Using a porous body (building material) with relatively high permeability, flow analysis and fluid simulation were performed using the flow path resistance model and electric circuit model according to this embodiment.

The fluid simulation was performed by constructing a three-dimensional structure from the CT image of the porous body and using the obtained flow path. The software Flowsquare (trade name) (Nora Scientific) used for the fluid simulation.

5A and 5B are views showing a porous body, where FIG. 5A shows a CT image and FIG. 5B shows a skeleton line obtained from a CT image. In the flow path resistance model, the skeleton line as shown in FIG. 5 (b) is obtained based on the CT image of FIG. 5 (a), and based on this, the flow path model (flow path resistance model) consisting of the above-mentioned elliptical columns is obtained. To build. Then, analysis was performed based on this flow path resistance model. That is, a pressure difference was applied between the inlet and the outlet of the flow path, and all the flow paths were approximated by the Poiseuille flow to obtain a flow index. The electric circuit model was formed by replacing the skeleton line with an electric resistance for each branch, and the circuit was analyzed by applying a voltage corresponding to the pressure.

The correlation between the analysis results of the flow path resistance model and the electric circuit model with the fluid simulation was investigated.

In the porous flow path model (flow path resistance model), the analysis results were obtained by extracting the values on the skeleton line, and the fluid simulation results were obtained by extracting and comparing the average values on the plane orthogonal to the skeleton line.

First, the pressure and flow velocity by the flow path resistance model were compared with the fluid simulation. The pressure was ^{correlated with R 2} = 0.9 (p <0.00) and the flow velocity was ^{correlated with R 2} = 0.73 (p <0.00). Here, R ² is the variance and p is the significance probability.

The fluid simulation result and the communication hole measurement result by the flow path resistance model showed that the regression line passes through the origin and is directly proportional to both the pressure and the flow velocity.

The electrical circuit model correlated with the fluid simulation. In the analysis result by the electric circuit model in which the pores are approximated by the electric circuit resistance, the pressure is R ² = 0.72 (p <0.00), the flow velocity is R ² = 0.82 (p <0.00), and the fluid is fluid. Correlates with simulation results. However, neither the pressure nor the flow velocity showed a proportional relationship because the regression line did not pass through the origin.

FIG. 6 is a diagram showing three types of analysis results for the pressure distribution of the porous body, (a) shows the results of fluid simulation, (b) shows the results of flow path resistance model analysis, and (c) shows the results of electric circuit model analysis. .. Also in this display, the place where the pressure is high is shown in red, the place where the pressure is low is shown in blue, and the middle part is shown in orange, green, and yellow. FIG. 6 is black and white, and the brightness is relatively high in the middle. From the shading in FIG. 6, it can be seen that the result of the flow path resistance model for the pressure is close to the result of the fluid simulation.

FIG. 7 is a diagram showing three types of analysis results for the flow velocity distribution of the porous body, (a) is a fluid simulation, (b) is an analysis of a flow path resistance model, and (c) is an analysis result of an electric circuit model. show. Also in this display, the place where the flow velocity is high is shown in red, the place where the flow velocity is low is shown in blue, and the middle part is shown in orange, green, and yellow. FIG. 7 is black and white, and the brightness is relatively high in the middle. From the shading in FIG. 6, it can be seen that the result of the flow velocity resistance model is close to the result of the fluid simulation for the flow velocity distribution.

Thus, the flow path resistance model correlates with the fluid simulation.

<Measurement of flow path resistance model penetration path>
As described above, a penetration path was selected, and the penetration path was analyzed by a flow path resistance model. FIG. 8 is a diagram showing a procedure for selecting a penetration path, where (a) is a CT image of a porous body, (b) is a pore in the porous body, (c) is a skeleton line of a hole, and (d) each penetration path. The power of (e) indicates a penetration path having a large power.

First, FIG. 8A is a CT image of the target porous body, and blue (gray in the figure) indicates pores. In FIG. 8B, only the holes are shown in blue (black in the figure). As described above, there are many holes, and it is difficult to judge the shape of the holes from this display. The upper end is the entrance and the lower end is the exit.

FIG. 8 (c) shows the extracted skeleton lines of the vacancies. Displaying the skeleton line makes it easier to see the shape of the holes. Each branch is defined by approximating the holes on each point of the skeleton line on the cross section in the direction perpendicular to the skeleton line with an ellipse having a short axis and a long axis. Then, the flow path resistance of each branch can be calculated, and the pressure, flow velocity, flow path resistance, power, etc. of each branch can be calculated.

Then, by integrating these flow indexes for each penetration path, the flow index for each penetration path can be calculated. FIG. 8D shows the power for each through pass, and the difference in the total power for each through pass can be recognized by the difference in gradation. Although it is displayed in black and white in this figure, in the actual display, the power for each penetration path is shown in color. This makes it possible to recognize the large and small powers for each penetration path. Also, assuming black-and-white display, it is possible to make the brightness correspond to the power. That is, by associating display attributes such as hue, lightness, saturation, and hatching with the flow index, it is possible to display the size of the flow index for branches, penetration paths, and the like.

FIG. 8 (e) shows an example in which a path having a large power is taken out and displayed so that the total power of the penetration path is 80% or more. By limiting the penetration path to be displayed in this way, the display becomes easier to see. In this example, the total power of the penetration path shown in FIG. 8 (e) covers 80% of the total power of all the flow paths, and the communication hole network is based on the display of FIG. 8 (e). Can be evaluated.

<Selection path of flow path resistance model and electric circuit model>
FIG. 9A is a diagram showing a penetration path of Sample 1 having a small permeability. Here, the penetration path selected as the one with high power is shown, green (light gray) is the selection path of the electric circuit model, red (dark gray) is the selection path of the flow path resistance model, and yellow (white) is the selection path of the electric circuit model. The route common to both is shown.
(B) is a diagram showing the minimum cross-sectional area of the penetration path in the order of power large → small. The flow path resistance model (red: flow) selects a path with the smallest cross-sectional area compared to the electric circuit model (green: electricity).
(C) is a diagram about the curve ratio of the penetration path. In the electric circuit model (green: electricity), the flow path resistance model (red: flow) selects a route with a relatively small curve ratio.
(D) is a diagram showing the relationship between the through-pass flow rate and the minimum cross-sectional area in the flow path resistance model. Both are ^{positively correlated at (R 2} = 0.52, p <0.00).
(E) is a diagram showing the relationship between the flow rate and the curve ratio in the flow path resistance model. The flow path resistance model flow rate does not correlate with the curve ratio.
(F) is a diagram showing the correlation between the electric circuit model current and the minimum cross-sectional area. Both are ^{positively correlated at (R 2} = 0.58, p <0.00).
(G) is a figure which shows the curve ratio dependence of the flow rate in an electric circuit model. The current and curvature were negatively correlated (R ² = 0.39, p <0.00).
From (d) to (g), the flow path resistance flow depends on the minimum cross-sectional area of the path, the dependence on the curve ratio is small, and the flow of the electric circuit model depends on both the minimum cross-sectional area and the curve ratio. It can be seen that it shows sex.

As a result of analyzing the minimum cross-sectional area and the curved path ratio of the selected path, the flow path resistance model selects the path having the minimum cross-sectional area larger than that of the electric circuit model, and the electric solution circuit model is the curved path. It turned out that the route with a low rate was selected.

Furthermore, the correlation between the through-pass flow rate and the minimum cross-sectional area and the curve ratio was investigated. As a result, it was found that the flow depends on the minimum cross-sectional area of the path, and the dependence on the curve ratio is small. From this, it was found that the flow path resistance model is more suitable than the electric circuit model in the flow analysis.

<Structural index>
Table 2 shows a comparison of the analysis results for S1 having low permeability and Sample2 having high permeability.

Compared to 1, there was no big difference in porosity, pore size (thickness, width), number of branch points of the flow path (N.NdNd), and flow path length (TSL / TV), but the number of loops was In Sample2, 1/2 of Sample1 and V * tr showed more than twice the value. It can be seen that Sample 2 is composed of a path having many straight flow paths. The water retention capacity of Sample2 was lower than that of Sample1, suggesting that the drainage was good.

10A and 10B are diagrams showing the curvature ratio of the penetration path, where FIG. 10A is Sample1 and FIG. 10B is Sample2. In the original figure, the curve ratio is shown by color, but this figure is black and white, and the blacker the curve ratio, the larger the curve ratio. I understand. It can also be seen that Sample2 has a relatively straight path.

11A and 11B are views showing the distribution of the pore size of the porous body, in which FIG. 11A is Sample1 and FIG. 11B is Sample2. In the original figure, the pore diameter is shown by color, but this figure is black and white, and the blacker the pore diameter, the smaller the pore diameter. Therefore, it can be seen that Sample 1 has more channels with smaller pore diameters than Sample 2. Further, in the display in which the colors can be identified, it can be seen that the flow path having a smaller pore diameter than that of the Sample 2 exists in the middle of the path in the Sample 1. That is, by the display of FIG. 11, it is possible to grasp the distribution of pores, such as what kind of pores are in what position.

FIG. 12 is a diagram showing a pore size histogram, showing (a) Sample1 and (b) Sample2. As described above, it can be seen that the channels having a large pore diameter are widely distributed in Sample 2 and the channels having a small pore diameter are widely distributed in Sample 1.

<Indicator of flow>
Table 3 is an index of the flow calculated by the flow path resistance model. From the flow index, in many indexes indicating that the flow rate is easy to flow, Sample 2 is significantly larger than Sample 1. That is, it can be seen that Sample 2 has a smaller resistance than Sample 1 and has a good flow.

13A and 13B are views showing the pressure of the penetration path, where FIG. 13A shows Sample1 and FIG. 13B shows Sample2. In the original figure, the flow pressure for the penetration path is shown in color, but in FIG. 13, it is shown in black and white. In the figure, the black (red) at the top shows the branches with high pressure, and the black (blue) at the bottom shows the branches with low pressure. As described above, it can be seen that in Sample 1, the isobaric surface is relatively close to the horizontal plane and the flow is uniform. On the other hand, in Sample2, the isobaric surface is curved upwardly and downwardly, and the flow rate is mixed.

14A and 14B are views showing the flow rate of the penetration path, where FIG. 14A shows Sample1 and FIG. 14B shows Sample2. The number of Sample 2 is larger than that of Sample 1, and the flow rate of the pass is also large. In the figure, it is not possible to distinguish between a path with a large flow rate and a path with a small flow rate, but it can be seen that the number of paths is large.

In this way, the properties of the porous body can be displayed by displaying the three-dimensional position of the penetrating path and displaying the flow index such as flow rate, flow velocity, pressure, and power for each penetrating path by color and brightness. Can be done. Therefore, based on this analysis result, it becomes possible to optimize the method for producing a porous body and the like.

<Equal potential surface, current>
FIG. 15 is a diagram showing the equipotential surface, current, and power consumption on the flow path according to the electric circuit model, and (a), (b), and (c) are the equal potential surface, current, and on the flow path of Sample 1 according to the electric circuit model. , (D), (e), and (f) indicate the equipotential surface, current, and power consumption on the flow path of Single2. The original figure is a color display, but the figure is a black and white display, and the difference can be seen depending on the brightness. From this, it can be seen that the sample 2 has a non-parallel equipotential surface as compared with the sample 1, the sample 1 has a uniform flow, and the sample 2 has a flow that changes depending on the location. The currents (b) and (e) and the power consumption (c) and (f) tended to be small in Sample 1 and large in Sample 2. It is considered to be a reflection of the fact that Sample2 is connected by a straight pore network. In FIGS. 15 (c) and 15 (f), a path having a power of 0.2 mW or more is selected and displayed.

In this way, by appropriately using both the flow path resistance model and the electric circuit model, it is possible to obtain more demanding information.

<Processing flow>
FIG. 16 is a flowchart showing a computer-based process of structural evaluation according to the present embodiment. First, a CT image of the target porous body is acquired (S11). As described above, the CT image is not necessarily limited to the CT image, but the CT image is an appropriate image when evaluating an actual porous body. Pore is detected from the acquired CT image (S12). Normally, the base material is a solid and the pores are air, and the pores can be detected from the CT value. The skeletal line is detected by connecting the centers of the pores (S13). A skeletal line network is obtained by the continuation of skeletal lines.

Next, in the simulation using the flow path resistance model, each branch of the skeleton line is approximated to an elliptical column. By connecting these elliptical columns, a flow path resistance model that expresses pores as a network connecting the elliptical columns is constructed (S15). Here, the flow path resistance is inversely proportional to the square of the cross-sectional area of the flow path. Then, a simulation is performed using the flow path resistance model (S16), and a flow index when a fluid flows between the inlet and outlet is calculated. Further, based on the obtained flow index, a penetrating path penetrating between the inlet and the outlet is detected, and a penetrating path having a large power is selected from the detected penetrating paths.

On the other hand, in the case of the simulation using the electric circuit model, it is assumed that the pores obtained in S14 are filled with the electric material, each branch is replaced with the electric resistance, and the electric resistance is connected to the electric circuit. Build a model (S17). Here, the electrical resistance is inversely proportional to the cross-sectional area of the pores. Then, a simulation is performed using the electric circuit model (S18), and flow indexes such as current density and power between the inlet and outlet are calculated. Further, based on the obtained flow index, a penetrating path penetrating between the inlet and the outlet is detected, and a penetrating path having a large power is selected from the detected penetrating paths.

Then, the result of the simulation is output (S19). For example, the power, flow velocity, flow rate, etc. of the obtained penetration path are displayed by the color, brightness, etc. of each penetration path in the three-dimensional display of the penetration path. As described above, various types of result outputs can be adopted.

<Summary>
In the present embodiment, first, the pores that can be visualized by X-ray CT were measured for a porous sample having a diameter of several nm to several 100 μm. Next, the image contrast was discriminated from the X-ray CT image by the threshold value, the pore structure was extracted, and the structural index was calculated. The actual pore structure was approximated by a pipe, and pressure and flow simulations were performed.

In particular, in the simulation, the structural indexes of both the flow path of the porous material and the carrier are calculated from the CT image. Then, an inlet and an outlet are given to the porous structure, a flow path resistance is defined for the pores, a pressure difference is given between the inlet and the outlet, and the flow in the pores is simulated three-dimensionally. According to this embodiment, it is possible to accurately obtain an index of the structure and flow of a porous body within a practical time for a porous body model of a practical size by using an approximate model of a fluid. According to this embodiment, it is possible to simulate a porous body having a wide pore diameter of 50 nm to 10 mm.

According to this embodiment, pores can be extracted by gradation (= density) using an X-ray CT image of a macroscopic pore structure. Therefore, it is possible to measure structural indexes such as the cross-sectional area distribution of the pore structure and the connected network from the three-dimensional image of the pores.

Also, by defining resistance in the pore network, it is possible to analyze the flow in the pore structure. Using the flow path resistance model, it is possible to simulate the pressure and flow velocity at each point in the pore structure depending on the pressure difference between the inlet and outlet. The results in the flow path resistance model are proportional to the fluid simulation results. Therefore, an approximate solution of the three-dimensional fluid simulation can be easily obtained by analysis using the flow path resistance model. It is considered to be effective for analysis of pores using the properties of flow such as exhaust gas filters. On the other hand, in the simulation given the electric circuit model, the effect of the resistance element of the flow was weakened, and the characteristics of the flow path reflecting the communication and structural characteristics were obtained. It is suggested to be effective for analysis of catalysts and biomaterials.

Claims (7)

It is a structural evaluation method for a porous body that evaluates the structure of the porous body using a CT image.
Detecting pores from CT images,
For the detected pores, approximate the model in which the elliptical columns are connected,
For each elliptical column, calculate the flow path resistance that is inversely proportional to the square of the cross-sectional area.
Evaluate the structure of the porous body based on the calculated flow path resistance,
A method for evaluating the structure of a porous body. The method for evaluating the structure of a porous body according to claim 1.
The porous body has an inlet region and an outlet region.
Applying a pressure difference between the inlet and outlet regions to determine the flow index, including the flow rate, flow rate, or power of the fluid in each elliptical column.
A method for evaluating the structure of a porous body. The method for evaluating the structure of a porous body according to claim 2.
In the detected pores, the penetration path from the inlet region to the exit region is extracted.
Obtain a flow index that includes either flow rate, flow velocity, or power for the extracted penetration path.
A method for evaluating the structure of a porous body. The method for evaluating the structure of a porous body according to claim 3.
The extracted penetration path is displayed as a three-dimensional position in the porous body, and is displayed.
Select one of the obtained flow indexes and display the size of the selected flow index in correspondence with the display attribute of the penetrating path to be displayed.
A method for evaluating the structure of a porous body. The method for evaluating the structure of a porous body according to claim 4.
For the extracted penetration paths, select the one with the larger selected flow index and display only the selected penetration paths.
A method for evaluating the structure of a porous body. It is a structure evaluation device for a porous body that evaluates the structure of the porous body using a CT image.
Detecting pores from CT images,
For the detected pores, approximate the model in which the elliptical columns are connected,
For each elliptical column, calculate the flow path resistance that is inversely proportional to the square of the cross-sectional area.
Evaluate the structure of the porous body based on the calculated flow path resistance,
Structure evaluation device for porous materials. This is a structure evaluation program for porous bodies that allows a computer to evaluate the structure of the porous body using CT images.
On the computer
The pores are detected from the CT image,
Approximate the detected pores to a model in which elliptical columns are connected,
For each elliptical column, calculate the flow path resistance that is inversely proportional to the square of the cross-sectional area.
To evaluate the structure of the porous body based on the calculated flow path resistance,
Porous structure evaluation program.

Images