CN113654952A - A device and method for measuring diffusion coefficient based on right-angle triangular liquid tank - Google Patents
A device and method for measuring diffusion coefficient based on right-angle triangular liquid tank Download PDFInfo
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Abstract
The invention discloses a device and a method for measuring diffusion coefficient based on a right-angle triangular liquid tank, which comprises a line laser, the right-angle triangular liquid tank, an observation white screen, a sampling device and a processor, wherein the line laser is used for generating slender line laser with a horizontal divergence angle far smaller than a vertical divergence angle; the right-angle triangular liquid tank is a hollow triangular column, linear laser emitted by the linear laser penetrates through the right-angle triangular liquid tank to be emitted out, and the right-angle triangular liquid tank stores two kinds of liquid for diffusion; the observation white screen is provided with grid scales, and line laser emitted by the line laser is projected on the observation white screen after being refracted by the right-angle triangular liquid tank; the sampling device shoots the change process of the laser pattern on the observation white screen along with time; the processor obtains the diffusion coefficient from the change of the laser pattern by image processing. On the basis of visualization of the diffusion process, the method effectively avoids errors caused by laser alignment, and can accurately and quantitatively measure the diffusion coefficient.
Description
Technical Field
The invention relates to the field of liquid diffusion coefficient measurement, in particular to a diffusion coefficient measuring device and method based on a right-angle triangular liquid tank.
Background
Diffusion is a phenomenon in which molecules of a substance are transferred from a high concentration region to a low concentration region until they are uniformly distributed, and is a relaxation process that tends to a thermal equilibrium state. The diffusion phenomenon has great research value and application scenes in many fields of biology, chemical engineering, medicine, materials and the like, such as matter exchange of in vivo environment, steel carburization, hemodialysis, semiconductor doping and the like. The diffusion coefficient is important to research of the diffusion process, so that the accurate measurement of the diffusion coefficient has strong practical significance.
Because the average distance between liquid molecules is far smaller than that of gas molecules, and the arrangement between molecules is not as regular as that of solids, the theoretical description and experimental measurement of the liquid diffusion coefficient are more difficult than those of gas and solids, and the data of the liquid diffusion coefficient under different conditions are less. The existing methods for measuring the diffusion coefficient of liquid include a Wiener method, a capillary tube imaging method, a membrane cell method, a Taylor dispersion method, an optical interference method and the like, wherein the former two methods can visualize the diffusion process. Most diffusion processes are very slow, the visualized diffusion coefficient measurement method can help people to know the specific proceeding conditions of diffusion, external interference is eliminated, and meanwhile, the visualization of the diffusion processes enables users to collect data by using high-precision optical instruments, so that the accuracy of measurement results is improved.
The Wiener method uses a point laser to inject into a glass cylinder, generates a fan-shaped light beam to irradiate on a diffusion water tank, and initially presents a bright line similar to an omega shape on an observation white screen. With the progress of diffusion, the shape of the light on the white screen can be observed to change, and the corresponding diffusion coefficient can be measured by observing the area enclosed by the changed light and the original light. The Wiener method is simple in device and can visualize the diffusion process. However, the process of calculating the area of each irregular image is complicated, and the measurement accuracy is not high.
Capillary imaging treats a capillary tube filled with a diffusing liquid and having an annular cross section as a cylindrical lens. After diffusion, gradient distribution of refractive index is formed along the axial direction of the capillary, parallel light is converged into an oblique line on a focal plane after passing through the capillary, and the oblique line and the alignment plane have only one intersection point. A fixed numerical value between the refractive indexes of two diffusion solutions is selected, and the diffusion coefficient can be calculated by observing the clear imaging positions of the refractive index thin layer along the axial direction of the capillary at different moments, namely liquid level boundary points. The capillary imaging method realizes the visualization of the diffusion process to a certain extent, but because the capillary is too thin, the strict coaxiality between the laser beam and the diameter of the capillary is difficult to realize during alignment, astigmatism is easy to generate, the liquid level dividing point is fuzzy, accurate judgment is difficult, and the measurement process is complicated.
The membrane pool method determines the diffusion coefficient by measuring the initial and steady concentrations of the upper and lower parts of the diffusion pool, the measurement result is accurate, but the method is only suitable for measuring the diffusion between solutions with small concentration difference, the membrane pool calibration needs to be carried out in advance, the measurement steps are complex, and the measurement time is long. The optical interference method is used for calculating the diffusion coefficient by measuring interference fringes generated by incident light and reflecting space and time information of the concentration of the diffusion solution, and is wide in measurement range, but has strict requirements on shock resistance, air disturbance resistance, temperature change resistance and the like in an experimental environment and poor in anti-interference capability. The Taylor dispersion method injects trace solute into the flowing solvent in the long capillary, because the molecular diffusion capacity and the convection diffusion capacity among different molecules are different in the flowing phase, the concentration of the solute is changed into a symmetrical Gaussian distribution form, the diffusion coefficient can be calculated by measuring the distribution curves of the concentrations at different moments, the Taylor dispersion method can be used under high temperature and high pressure, the measurement is rapid, and the measurement precision is low. None of the three methods described above can visualize the diffusion process.
The Chinese patent with publication number CN103472507A, published as 12 and 25 in 2013, discloses a method for accurately measuring the refractive index and the liquid phase diffusion coefficient of liquid based on an asymmetric liquid core column lens, and belongs to a method for measuring the refractive index and the liquid phase diffusion coefficient of liquid by using monochromatic light. The invention uses two glass cylindrical surface bodies and a cylindrical cavity filled with a liquid medium to form a monochromatic spherical aberration eliminating variable-focus asymmetric cylindrical lens, applies the principle that monochromatic parallel light can focus on different line positions after passing through the cylindrical lens filled with liquid with different refractive indexes, measures the focal length of the cylindrical lens and calculates the refractive index of the liquid. When two liquids with different refractive indexes are injected into the cylindrical cavity, a diffusion image is shot by utilizing the one-dimensional space resolution of the cylindrical lens to the refractive indexes of the injected liquids along the axial direction, and the diffusion coefficient is calculated according to a formula. The patent cannot realize the precision and visualization of diffusion coefficient measurement at the same time.
Disclosure of Invention
The invention aims to provide a diffusion coefficient measuring device based on a right-angle triangular liquid tank, which effectively avoids errors generated by laser alignment on the basis of visualization of a diffusion process and can accurately and quantitatively measure the diffusion coefficient.
The invention further aims to provide a diffusion coefficient measuring method based on a right-angle triangular liquid tank.
In order to solve the technical problems, the technical scheme of the invention is as follows:
the utility model provides a diffusion coefficient measuring device based on right angle triangle cistern, includes line laser ware, right angle triangle cistern, observes white screen, sampling device and treater, wherein:
the line laser is used for generating elongated line laser with a horizontal divergence angle much smaller than a vertical divergence angle;
the right-angle triangular liquid tank is a hollow triangular column, linear laser emitted by the linear laser penetrates through the right-angle triangular liquid tank to be emitted out, and the right-angle triangular liquid tank stores two kinds of liquid for diffusion;
the observation white screen is provided with grid scales, and line laser emitted by the line laser is projected on the observation white screen after being refracted by the right-angle triangular liquid tank;
the sampling device shoots the change process of the laser pattern on the observation white screen along with time;
the processor obtains the diffusion coefficient from the change of the laser pattern by image processing.
Preferably, the right-angle triangular liquid tank adopts a hollow triangular prism cavity made of glass materials or quartz materials, the cross section of the cavity is in the shape of an isosceles triangle, line laser emitted by the line laser is normally incident on a right-angle side of the right-angle triangular liquid tank, and the upper bottom surface of the right-angle triangular liquid tank is provided with a first port a for exhausting air; the upper bottom surface of the right-angle triangular liquid tank is provided with a second port b for injecting liquid; and a third port c is formed in the side surface of the right-angle triangular liquid tank and used for fixing the right-angle triangular liquid tank.
A diffusion coefficient measuring method based on a right-angle triangular liquid tank is applied to the measuring device and comprises the following steps:
s1: sequentially placing and installing the measuring devices according to the light path;
s2: preparing a plurality of aqueous solutions of liquid to be detected with concentration gradients, respectively measuring the refractive indexes of the aqueous solutions, and fitting to obtain a functional relation between the concentration and the refractive index of the liquid to be detected;
s3: measuring and calculating relevant parameters in the device, wherein the parameters comprise a distance L from an emergent surface of a right-angle triangular liquid tank to an observation white screen, a distance d between an upper inner bottom and a lower inner bottom of the liquid tank, an included angle parameter cot alpha between the incident surface and the emergent surface of the liquid tank, and an incident angle parameter sini;
s4: keeping the incident angle unchanged, injecting water into the cavity of the right-angle triangular liquid tank through the second port b, then injecting liquid to be detected into the same port, and starting diffusion, wherein the diffusion time t is 0 when the diffusion starts;
s5: shooting the laser pattern on the observation white screen by using a sampling device with fixed position and angle, and shooting a plurality of pictures at each time;
s6: calibrating according to the grid scales on the white screen to obtain the transformation relation between the pixel coordinates and the real coordinates;
s7: and measuring the diffusion coefficient of the liquid to be measured by measuring the change of the offset of a certain position in the laser pattern along with time or measuring the distribution of the offset relative to the position of the liquid tank at a certain moment and utilizing Fick's law linear fitting.
Preferably, the method for measuring the included angle parameter cot α and the incident angle parameter sini in step S3 specifically includes:
injecting a proper amount of pure water and liquid to be detected with a certain concentration gradient into the right-angle triangular liquid tank cavity through the second port b respectively, keeping an incident angle unchanged during each injection, measuring the offset of the pure water and the liquid corresponding to the laser pattern on the observation white screen, and obtaining cot alpha and sini by utilizing the following fitting formula:
wherein N is refractive index, y is offset, L is distance between the observation white screen and the right-angle triangular liquid tank, i is incident angle of the vertical plane of the right-angle side of the line laser incident liquid tank, and alpha is included angle between the incident plane and the emergent plane of the right-angle triangular liquid tank, which is a fixed value.
Preferably, the method for keeping the incident angle constant in steps S3 and S4 is specifically:
a reflector is fixed on a platform fixed on a right-angle triangular liquid tank, a calibration white screen with scale marks is placed behind a line laser, partial light of the line laser is reflected by the reflector to be imaged on the calibration white screen, and the position of the image on the calibration white screen is adjusted to be consistent when liquid is injected each time.
Preferably, in step S6, the calibration is performed according to the grid scale on the white screen to obtain the transformation relationship between the pixel coordinate and the real coordinate, which specifically includes:
and observing the real distance between the air refracted ray and the water refracted ray on the white screen when the liquid level is measured to be stable, and calculating the pixel distance between the air refracted ray and the water refracted ray in the picture to obtain the transformation relation between the pixel coordinate and the real coordinate.
Preferably, the diffusion coefficient of the liquid to be measured is obtained by measuring the change of the offset of a certain position in the laser pattern with time, specifically:
s701: determining the position of the water liquid interface, namely z is 0, taking a series of discrete points of the laser pattern acquired for the first time after the liquid to be detected is injected, fitting the series of discrete points, taking the inflection point of a fitting curve as the position of the water liquid interface, and making the origin of the coordinate system be the lower end of the laser pattern, so that the pixel coordinate mark of the water liquid interface is x0And measuring the distance x between the upper and lower pixels of the laser patterndThe real distance z of the water interface relative to the inner bottom of the liquid tank is calculated by the following formula0：
The concentration distribution of the liquid region which is not reached by diffusion is constant, so that the corresponding laser pattern is a parallel straight line segment, namely the diffusion does not reach the region, points are taken from the uppermost end of the laser pattern to form a point set, linear fitting and point taking iteration are carried out on the point set, and goodness of fit R obtained by fitting the point sets after two adjacent point taking is carried out2For comparison, if R2If the change is obvious, the change is the upper boundary of diffusion, and the lower boundary is determined in the same way;
s702: binarizing and median filtering the picture shot by the sampling device, calculating the offset of the light ray at a certain position by utilizing the transformation relation between the pixel coordinate and the real coordinate obtained in the step S6, selecting the middle point of the light ray as a target point for calculating the offset, and obtaining the accurate position of the light ray by using the following two methods:
firstly, filling up incomplete light spots by generating a confrontation network to obtain laser patterns with uniform width, and then calculating a central line;
acquiring the coordinate of the effective part of the light or the coordinate of one side of the effective part of the light, and reading the offset of the target position on a fitting curve through function fitting;
the selection of the binarization threshold value is divided into two conditions:
if the gray level distribution frequency histogram of the picture shows two discrete peaks, selecting a value at the valley bottom between the two peaks as a threshold value;
if the gray frequency distribution histogram of the picture does not meet the conditions, manually adjusting the threshold value from large to small, wherein the reasonable criterion for adjusting the threshold value is that the optical line width is minimum under the condition of ensuring the light continuity;
s703: calculating the diffusion coefficient D by linear fitting by using the following formula and the relation between the refractive index and the concentration of the liquid to be measured obtained in the step S2:
where t is the diffusion time, z is a position in the bath cavity, erfiv (x) is the inverse of the Gaussian error function, C2Is the initial concentration of the liquid to be measured and u (z, t) represents the concentration at the diffusion time t at the z position.
Preferably, after one or more calibration objects are arranged in the right-angle triangular liquid tank, the calibration objects block a part of emergent light of the right-angle triangular liquid tank, so that the laser pattern on the white screen is observed to generate straight and thin breaks, a plurality of diffusion coefficients can be calculated by a plurality of markers, and the average value of the diffusion coefficients is used as the final measurement result.
Preferably, the diffusion coefficient of the liquid to be measured is obtained by measuring the distribution of the offset with respect to the position of the liquid tank at a certain time, and specifically:
s711: carrying out binarization and median filtering on a photo shot at a certain time t, taking points of a laser pattern, fitting by using a Boltzmann function, wherein the fitting function is B (x), the independent variable is the pixel coordinate x of the laser pattern in the vertical direction, the dependent variable is the pixel offset of the laser pattern, the inflection point of the fitting function is the position where z is 0, and the position of a water liquid interface on a liquid tank is determined by the following formula:
s712: measuring the length d of the laser pattern in the vertical direction2Then, a position z on the laser pattern corresponding to the position on the liquid bath is calculated by the following formula:
wherein, Deltax is the pixel distance between a certain position on the laser pattern and the lower end of the laser pattern;
s713: using B (x), the transformation relation between the pixel coordinates and the real coordinates in step S6, and the position z obtained in step S712, the distribution of the offset amount with respect to the liquid tank position can be calculated;
s714: d is calculated by linear fitting using the following equation, the relationship between the refractive index and the concentration obtained in step S2, and the distribution of the amount of displacement with respect to the liquid tank position in step S713:
where t is the diffusion time, z is a position in the bath cavity, erfiv (x) is the inverse of the Gaussian error function, C2Is the initial concentration of the liquid to be measured and u (z, t) represents the concentration at the diffusion time t at the z position.
Preferably, measuring the laser spot at different times allows to calculate a plurality of diffusion coefficients, which are averaged as a final result of the diffusion coefficients.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
the invention eliminates the errors of astigmatism, spot distortion and the like caused by the fact that laser cannot be aligned strictly, the difference of the alignment positions of the laser only enables the laser pattern to generate bias without changing the shape and the longitudinal relative position of the pattern, calibration and measurement of the incident angle are carried out in each experiment, and the laser does not need to be aligned strictly in the experiment. The physical quantity measured by the method is the light spot offset, and compared with the method for measuring and calculating the area of an irregular pattern and determining a diffusion interface through the light spots, the method is easy to measure and high in measurement accuracy. The invention also realizes the visualization of the diffusion process which is difficult to be observed by naked eyes by observing the white screen, and can observe the progress of diffusion and determine the boundary of diffusion.
Drawings
Fig. 1 is a schematic diagram of the optical path of the device of the present invention.
FIG. 2 is a schematic flow chart of the method of the present invention.
Fig. 3 is a schematic diagram of the optical path of the device for keeping the incident angle consistent in the embodiment.
FIG. 4 is a schematic view of a laser pattern of a liquid column during diffusion according to an embodiment.
FIG. 5 is a graph of the deviation of light from the white screen at a point observed according to the example of the present invention as a function of the refractive index.
Fig. 6 is a fitted image of the laser pattern in the example.
In the figure, 1 is a line laser, 2 is a sampling device, 3 is a right-angle triangular liquid tank, 4 is an observation white screen, 5 is a marker, 6 is a reflector, 7 is a calibration white screen, and 8 and 9 are approximate straight line parts in a laser pattern.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the patent;
for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product;
it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
Example 1
The present embodiment provides a diffusion coefficient measuring device based on a right-angle triangular liquid tank 3, as shown in fig. 1, including a line laser 1, a right-angle triangular liquid tank 3, an observation white screen 4, a sampling device 2 and a processor, wherein: the line laser 1 is used for generating elongated line laser light with a horizontal divergence angle much smaller than a vertical divergence angle;
the right-angle triangular liquid tank 3 is a hollow triangular column, the linear laser emitted by the linear laser 1 penetrates through the right-angle triangular liquid tank 3 and is emitted out, and the right-angle triangular liquid tank 3 stores two liquids for diffusion;
the observation white screen 4 is provided with grid scales, and line laser emitted by the line laser 1 is refracted by the right-angle triangular liquid tank 3 and then is projected onto the observation white screen 4;
the sampling device 2 shoots the change process of the laser pattern on the observation white screen 4 along with time;
the processor obtains the diffusion coefficient from the change of the laser pattern by image processing.
The right-angle triangular liquid tank 3 is a hollow triangular prism cavity made of glass materials or quartz materials, the cross section of the right-angle triangular liquid tank is in the shape of an isosceles triangle, line laser emitted by the line laser 1 is normally incident on a right-angle side of the right-angle triangular liquid tank 3, and the upper bottom surface of the right-angle triangular liquid tank 3 is provided with a first port a for discharging air; the upper bottom surface of the right-angle triangular liquid tank 3 is provided with a second port b for injecting liquid; the side surface of the right-angle triangular liquid tank 3 is provided with a third port c for fixing the right-angle triangular liquid tank 3, and light is normally incident from a right-angle side without the port and is emergent from a bevel edge during measurement.
The sampling device 2 adopts a single lens reflex camera, so that the influence caused by accidental errors is prevented, the sampling needs to be repeated for many times during each sampling, and each time point is sampled for three times in the example.
The observation white screen 4 is made of a hard material such as acrylic plate, and grid lines are drawn on the observation white screen, and the interval can be 5mm if the interval is large.
When the diffusion coefficient is measured, water is injected into the cavity of the liquid tank through the second port b, and then liquid to be measured is injected into the same port. After the two liquids contact each other in the cavity and begin to diffuse, the concentration of the solution at each position in the liquid groove changes along with the time, and the change of the concentration further causes the change of the refractive index of the solution. At the moment, the line laser is lightened to vertically enter a vertical face corresponding to one of the right-angle sides of the liquid tank, and the linear direction of the laser spot is parallel to the axis of the cavity in the liquid tank. The line laser is refracted on the inner and outer surfaces of the vertical surface of the incident right-angle side of the liquid tank and the inner and outer surfaces of the vertical surface of the bevel edge of the liquid tank in sequence, and is received by the observation white screen 4 after being emitted. Because the water and the liquid to be detected in the liquid tank have refractive index difference, under the diffusion action, a water-liquid to be detected mixing area is formed between the area of the liquid to be detected which is not permeated by water and the area of the liquid to be detected which is not permeated by the liquid to be detected, and the refractive index gradually changes, so that the light spot of the line laser on the observation white screen 4 is not a straight line segment any more, but is in an approximate S shape of 90-degree turnover. The refractive index change caused by diffusion is reflected as the gradual change of the light spot offset on the observation white screen 4, so that the visualization of the diffusion process can be realized by observing the offset and the evolution of the light spots. If the change of the offset of a certain position along with time or the distribution of the offset relative to the position of the liquid tank at a certain time is measured, the diffusion coefficient of the liquid to be measured can be measured by combining the Fick's law linear fitting.
When the distance between the observation white screen 4 and the right-angle triangular liquid tank 3 is far larger than the optical path of the line laser passing through the liquid tank, the relationship between the light ray offset and the refractive index of a certain point on the observation white screen 4 is determined by the following formula;
wherein, N is the refractive index, y is the offset, L is the distance between the observation white screen 4 and the right-angle triangular liquid tank 3, i is the incident angle of the vertical plane of the right-angle side of the line laser incident liquid tank, and alpha is the included angle between the incident plane and the emergent plane of the right-angle triangular liquid tank 3, which is a fixed value.
Fick's law is the following equation:
d is a diffusion coefficient, u is concentration, z is a certain position in the liquid tank cavity, z is 0 which is the boundary position of water and the liquid to be measured at the initial moment, and t is diffusion time. The boundary condition is set to an unbounded condition, whose solution is:
wherein C is2Is the initial concentration of the liquid to be measured, and erf (x) is a gaussian error function, which can be expressed as:
where erfiv (x) is the inverse of the gaussian error function, equation (4) contains the variables z and t, and fixed z or fixed t, and linear fitting is performed, and the diffusion coefficient D can be calculated from the slope obtained by fitting.
Example 2
The present embodiment provides a method for measuring diffusion coefficient based on a right-angle triangular liquid tank 3, as shown in fig. 2, the method is applied to the measuring apparatus described in embodiment 1, and includes the following steps:
s1: sequentially placing and installing the measuring devices according to the light path;
s2: preparing a plurality of aqueous solutions of liquid to be detected with concentration gradients, respectively measuring the refractive indexes of the aqueous solutions, and fitting to obtain a functional relation between the concentration and the refractive index of the liquid to be detected;
s3: measuring and calculating relevant parameters in the device, wherein the parameters comprise a distance L from an emergent surface of a right-angle triangular liquid tank 3 to an observation white screen 4, a distance d between an upper inner bottom and a lower inner bottom of the liquid tank, an included angle parameter cot alpha between an incident surface and the emergent surface of the liquid tank, and an incident angle parameter sini;
s4: keeping the incident angle unchanged, injecting water into the cavity of the right-angle triangular liquid tank 3 through the second port b, then injecting liquid to be measured into the same port, and starting diffusion, wherein the diffusion time t is 0 when the diffusion starts; in this embodiment, water is injected into the cavity of the right-angled triangular liquid tank 3 through the second port b, and then 5.5mol/L of glycerin solution is injected into the same port, so that the diffusion starts, and the diffusion time t is 0 at the beginning of the diffusion
S5: the laser patterns on the white screen 4 are observed by shooting through the sampling device 2 at a fixed position and at a fixed angle, a plurality of pictures are shot at each time, the shooting interval time of the sampling device 2 is fixed, and the fixed interval time can be adjusted according to the viscosity coefficient of the liquid to be measured. A more viscous liquid to be measured may be preferred for a longer time interval. In this embodiment, the liquid to be measured is glycerol, so the time interval is 30 minutes;
s6: calibrating according to the grid scales on the observation white screen 4 to obtain the transformation relation between the pixel coordinates and the real coordinates;
s7: and measuring the diffusion coefficient of the liquid to be measured by measuring the change of the offset of a certain position in the laser pattern along with time or measuring the distribution of the offset relative to the position of the liquid tank at a certain moment and utilizing Fick's law linear fitting.
The method is limited by the manufacturing process, the cross section of the right-angle triangular liquid tank 3 is not a strict isosceles right triangle, so the included angle α between the light incident surface and the light emergent surface is to be measured, in this embodiment, the included angle parameter cot α and the incident angle parameter sini in the step S3 are calculated by measuring the laser offset of water and pure glycerin and looking up the corresponding refractive indexes thereof and substituting into the following formula to solve the equation:
injecting a proper amount of pure water and liquid to be measured with a certain concentration gradient into the right-angle triangular liquid tank 3 cavity through the second port b respectively, keeping the incident angle unchanged during each injection, measuring the offset of the pure water and the liquid corresponding to the laser pattern on the observation white screen 4, and obtaining cot alpha and sini by utilizing the following fitting formula:
wherein, N is refractive index, y is offset, L is distance between the observation white screen 4 and the right-angle triangular liquid tank 3, i is incident angle of the right-angle side elevation of the line laser incident liquid tank, and alpha is the included angle between the incident surface and the emergent surface of the right-angle triangular liquid tank 3, which is a fixed value. In this embodiment, the diffusion liquid selected is glycerol, i.e., glycerin. At room temperature, the refractive indices of pure glycerol and water are about 1.4746 and 1.3330, respectively, which is a difference of 0.1416. The refractive index difference is large enough that a significant deflection phenomenon can be observed during the experiment.
In this example, the measured incident angle parameter sini is 0.01075 ± 0.0098, and the measured liquid bath angle parameter cot α is 1.02022 ± 0.01998, and the image is fitted as shown in fig. 5.
The relationship between the concentration of the glycerol aqueous solution and the refractive index obtained in the present example is as follows:
u＝99.40n-132.6
the method for keeping the incident angle unchanged in step S3 and step S4, as shown in fig. 3, specifically includes:
a reflector 6 is fixed on a platform fixed on a right-angle triangular liquid tank 3, a calibration white screen 7 with scale marks is placed behind a line laser 1, partial light of the line laser 1 is reflected by the reflector 6 to form an image on the calibration white screen 7, and the position of the image on the platform to the calibration white screen 7 is adjusted to be consistent when liquid is injected at each time, so that the incident angle is guaranteed to be unchanged.
In step S6, calibration is performed according to the grid scale on the observation white screen 4 to obtain a transformation relationship between the pixel coordinate and the real coordinate, which specifically includes:
and observing the real distance between the air refracted ray and the water refracted ray on the white screen 4 when the liquid level is measured to be stable, and calculating the pixel distance between the air refracted ray and the water refracted ray in the picture to obtain the transformation relation between the pixel coordinate and the real coordinate.
The diffusion coefficient of the liquid to be measured is obtained by measuring the change of the offset of a certain position in the laser pattern along with time, and the method specifically comprises the following steps:
s701: determining the position of water interface (z is 0), fitting a series of discrete points of the laser pattern acquired for the first time after injecting the liquid to be measured, and taking the inflection point of the fitting curve as the water interface (shown in FIG. 4)When the origin of the coordinate system is the lower end of the laser pattern, the coordinate of the water interface pixel is marked as x0And measuring the distance x between the upper and lower pixels of the laser patterndThe real distance z of the water interface relative to the inner bottom of the liquid tank is calculated by the following formula0：
Since the liquid diffusion near z-0 occurs first and the light shift is significant, the position of this region is preferably selected as the measurement position. The z coordinate value of the position can be obtained by subtracting the zi from the z 0.
The concentration distribution of the liquid region which is not reached by diffusion is constant, so that the corresponding laser pattern is a parallel straight line segment, namely the diffusion does not reach the region, as shown in fig. 4, the regions 8 and 9 in the laser pattern are similar to a straight line, namely the diffusion does not reach the region, points are taken from the uppermost end of the laser pattern to form a point set, linear fitting and point taking iteration are carried out on the point set, and the goodness of fit R obtained by fitting the point sets after two adjacent point taking is obtained2For comparison, if R2If the change is obvious, the change is the upper boundary of diffusion, and the lower boundary is determined in the same way;
s702: binarizing and median filtering the picture shot by the sampling device 2, calculating the offset of light at a certain position by utilizing the transformation relation between the pixel coordinate and the real coordinate obtained in the step S6, selecting the middle point of the light as a target point for calculating the offset, and observing laser spots on the white screen 4 possibly with defects due to the influences of camera performance, shooting environment limitation, liquid disturbance and the like, wherein the defects are not complete curves with uniform width, and the accurate position of the light central line can be obtained by the following two methods:
firstly, filling up incomplete light spots by generating a confrontation network to obtain laser patterns with uniform width, and then calculating a central line;
acquiring the coordinate of the effective part of the light or the coordinate of one side of the effective part of the light, and reading the offset of the target position on a fitting curve through function fitting;
the selection of the binarization threshold value is divided into two conditions:
if the gray level distribution frequency histogram of the picture shows two discrete peaks, selecting a value at the valley bottom between the two peaks as a threshold value;
if the image is limited by shooting equipment or a shooting environment, the gray frequency distribution histogram of the image does not meet the conditions, the threshold value is manually adjusted from large to small, and the reasonable criterion for adjusting the threshold value is that the width of the light line is the minimum under the condition of ensuring the light continuity;
s703: calculating the diffusion coefficient D by linear fitting by using the following formula and the relation between the refractive index and the concentration of the liquid to be measured obtained in the step S2:
where t is the diffusion time, z is a position in the bath cavity, erfiv (x) is the inverse of the Gaussian error function, C2Is the initial concentration of the liquid to be measured and u (z, t) represents the concentration at the diffusion time t at the z position.
After one or more calibration objects 5 are arranged in the right-angle triangular liquid tank 3, the calibration objects 5 block a part of emergent light of the right-angle triangular liquid tank 3, so that the laser pattern on the white screen 4 is observed to generate straight and thin breaks, a plurality of diffusion coefficients can be calculated by the calibration objects 5, and the average value of the diffusion coefficients is used as a final measurement result. In the embodiment, two identical thin rods are pasted on different positions on the bevel edge of the right-angle triangular liquid groove 3 in parallel, light rays are emitted from the bevel edge, the calibration object 5 can block a small part of the emitted light rays, so that two thin and straight broken parts can be generated at a certain fixed position by the light rays on the observation white screen 4, and the same position can be determined for each picture during image processing. Since the diffusion process is performed first near the interface between water and glycerin and the light beam is significantly deflected, it is preferable that the calibration object 5 is placed near the interface.
The diffusion coefficient of the liquid to be measured is obtained by measuring the distribution of the offset relative to the position of the liquid tank at a certain time, and the method specifically comprises the following steps:
s711: carrying out binarization and median filtering on a photo shot at a certain time t, taking points of a laser pattern, fitting by using a boltzmann function, wherein the fitting function is B (x), the fitting image is shown as figure 6, the independent variable is the pixel coordinate x of the laser pattern in the vertical direction, the dependent variable is the pixel offset of the laser pattern, the inflection point of the fitting function is the position where z is 0, and the position of a water liquid interface on the liquid tank is determined by the following formula:
s712: measuring the length d of the laser pattern in the vertical direction2Then, a position z on the laser pattern corresponding to the position on the liquid bath is calculated by the following formula:
wherein, Deltax is the pixel distance between a certain position on the laser pattern and the lower end of the laser pattern;
s713: using B (x), the transformation relation between the pixel coordinates and the real coordinates in step S6, and the position z obtained in step S712, the distribution of the offset amount with respect to the liquid tank position can be calculated;
s714: d is calculated by linear fitting using the following equation, the relationship between the refractive index and the concentration obtained in step S2, and the distribution of the amount of displacement with respect to the liquid tank position in step S713:
in the formula, t is diffusionTime, z is a position in the fluid bath cavity, erfiv (x) is the inverse of the Gaussian error function, C2Is the initial concentration of the liquid to be measured and u (z, t) represents the concentration at the diffusion time t at the z position.
Measuring the laser spot at different times allows to calculate a plurality of diffusion coefficients, which are averaged as a final result of the diffusion coefficients.
The same or similar reference numerals correspond to the same or similar parts;
the terms describing positional relationships in the drawings are for illustrative purposes only and are not to be construed as limiting the patent;
it should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
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