CN110044777A - A method of utilizing transient images rapid survey various concentration Liquid Diffusion Coefficient - Google Patents
A method of utilizing transient images rapid survey various concentration Liquid Diffusion Coefficient Download PDFInfo
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Abstract
The present invention relates to a kind of methods using transient images rapid survey various concentration Liquid Diffusion Coefficient.The advantages of spherical aberration can be controlled in wider ranges of indices of refraction using biliquid stem lens, measures the Liquid Diffusion Coefficient changed with concentration using Bolzmann-Matano method and Sauer-Freise method according to width transient state diffusion.The Liquid Diffusion Coefficient of various concentration is finally obtained according to the concentration space distribution that the relationship between picture traverse and refractive index, concentration obtains entire transient state diffusion image.This method only needs a width transient state diffusion image that the Liquid Diffusion Coefficient of various concentration can be obtained, the measurement process of the Liquid Diffusion Coefficient changed with concentration can be greatly shortened from tens hours of conventional method or even for more time to the time of one width transient state diffusion image of shooting, really realize the instantaneous measurement to Liquid Diffusion Coefficient.The present invention can substantially shorten the time of measuring of Liquid Diffusion Coefficient, reduce measurement workload.
Description
Technical field
The present invention relates to liquid phase measuring technical fields, utilize transient images rapid survey various concentration more particularly to a kind of
The method of Liquid Diffusion Coefficient.
Background technique
Liquid Diffusion Coefficient is research mass transport process, calculates the important foundation number of mass transfer rate and Chemical Engineering Design and exploitation
According to being widely used in the emerging industries such as biology, chemical industry, medicine and environmental protection.Liquid Diffusion Coefficient is the function of solution concentration, with
The variation of dispersion solutions concentration and change.Currently, Liquid Diffusion Coefficient rely primarily on experimental method acquisition, by measurement solution by
In the concentration that diffusion process is formed with the distribution of room and time, liquid phase is calculated according to the Fick law of description diffusion process and is expanded
Dissipate coefficient.
Wherein, membrane cisterna method (Stoke R.H., An improved diaphragm-cell for diffusion
Studies, and some tests of the method, J.Am.Chem.Soc., 72:763-767 (1950)), light it is dry
Relate to method (Zhao Changwei, Li Jiding, Ma Peisheng, Xia Shuqian, Measurement of Liquid Diffusion Coefficients
of Aqueous Solutions of Glycine,L-Alanine,L-Valine and L-Isoleucine by
Holographic Interferometry,Chinese Journal of Chemical Engineering,13(2):285-
290 (2005)) and " Taylor's dispersion method " (CottetH., Biron J.P., MartinM., Taylor dispersion
Analysis of mixtures, Anal.Chem., 79 (23): 9066-9073 (2007)) it is three kinds of main traditional measurement sides
Method.But these three conventional methods there are devices it is complicated, stability is insufficient, result low precision the problems such as.
To solve the problems, such as that conventional method exists, Chinese invention patent ZL201610436334.2 discloses a kind of measurement liquid
The varifocal biliquid stem lens of the aplanasia of phase diffusion coefficient, can it discloses a high refractive index measurement capability, system spherical aberration
The biliquid stem lens of tune, while academic paper " Double liquid-core cylindr ical lens utilized
To measure liquid diffusion coefficient, " (Optics Express, 25 (5): 5626,2017) also sends out
The table biliquid stem lens.Based on the biliquid stem lens, occur three kinds at present based on wick-containing cylindrical lens focal plane imaging
The method of method measurement Liquid Diffusion Coefficient: a kind of method be " a kind of method and device for measuring Liquid Diffusion Coefficient " (Li Qiang, it is general
Cloudling, Sun Licun, Li Yu, Chinese invention patent ZL201110283339.3) and " with the measurement liquid phase diffusion of capillary imaging method
The refractive index thin layer such as coefficient-measurement method " (Acta Physica Sinica, 62 (9): academic paper 094206,2013)；A kind of method is
" method based on asymmetric wick-containing cylindrical lens precise measurement liquid refractivity and Liquid Diffusion Coefficient " (Sun Licun, general cloudling, Meng
Big east, Li Qiang, Chinese invention patent ZL201310412166.X) and " Asymmetric liquid-core cylindrica
l lens used to measure liquid diffusion coefficient”(Applied Optics,55(8):
2011-2017,2016), the resolution capability of measuring refractive indexes of liquid can be improved in this method, and reduces the spherical aberration of system imaging；
A kind of method be " with the method for the instantaneous refractive index spatial distribution measuring Liquid Diffusion Coefficient of wick-containing cylindrical lens " (Meng Weidong, it is general
Cloudling, Sun Licun, Yang Ruifen, Zhai Ying, Chinese invention patent 201410440938.5) and " Ne w method to
Measure liquid diffusivity by analyzing an instantaneous diffusion image, "
(Optics Express, 2015,23 (18), 23155~23166), this method can shorten time of measuring, improve measurement effect
Rate.
Three kinds newly have compared with conventional method from method and are significantly improved, but no matter are surveyed with above-mentioned any method
The Liquid Diffusion Coefficient that changes with concentration is measured, is required to prepare a large amount of various concentrations, and " solution to " of concentration comparable, passes through survey
The Liquid Diffusion Coefficient of these " solution to " is measured, Liquid Diffusion Coefficient change with solution concentration is obtained, and then finds out diffusion and is
Several correlations with solution concentration.The Liquid Diffusion Coefficient that change with concentration is measured, then time-consuming, heavy workload is asked for presence
Topic.
Summary of the invention
Expanded the invention mainly solves the technical problem of providing a kind of using transient images rapid survey various concentration liquid phase
The method for dissipating coefficient can substantially shorten time of measuring, reduce workload.
In order to solve the above technical problems, one technical scheme adopted by the invention is that: it provides a kind of fast using transient images
The method of speed measurement various concentration Liquid Diffusion Coefficient, comprising: inject two kinds of liquid in the preceding wick-containing of biliquid stem lens, adopt
The liquid lamella for being incident on biliquid stem lens with monochromatic collimated light, and being formed after spreading to two kinds of liquid carries out Image Acquisition
Obtain diffusion image, wherein the rear wick-containing of biliquid stem lens is injected with the liquid of predetermined refraction, to eliminate system spherical aberration；
The width transient state diffusion image for selecting t moment shooting, measures width and the position of the transient state diffusion image, obtains width and position
The distribution relation set, is expressed as (Zi, Σi), wherein ΣiIt indicates away from image boundary ZiThe width of distance, i are positive integer；According to
Relationship between the width and refractive index of known liquid is to (Zi, Σi) converted, the distribution for obtaining refractive index and position is closed
System, is expressed as (Zi, ni), wherein niIt indicates away from image boundary ZiThe refractive index of distance；According to the refractive index of known liquid and
Relationship between concentration is to (Zi, ni) converted, the distribution relation of concentration and position is obtained, (Z is expressed asi, Ci), wherein Ci
It indicates away from image boundary ZiThe concentration of distance；Using least square method to (Zi, Ci) linear fit is carried out, concentration is obtained with position
The concentration profile of variation is expressed as C (Z)；According toOrIt calculates dense on C (Z)
Spend the Liquid Diffusion Coefficient at A point, whereinIndicate the inverse of concentration slope at A point on C (Z),Table
Show from C1To CAIntegral, Y (CA)=(CA-C1)/(C2-C1), C1And C2Indicate two asymptotes of C (Z), and C1< C2。
Preferably, the basisLiquid phase of the concentration at A point on C (Z) is calculated to expand
The step of dissipating coefficient specifically includes: Matano plane is found on C (Z), and using Matano plane position as co-ordinate zero point
C (Z) is coordinately transformed, wherein the area of the closed figure of the Matano plane left side and C (Z) composition and the right and C (Z)
The area equation of the closed figure of composition；Linear Quasi is re-started to the C (Z) after coordinate transform using least square method
It closes；According toCalculate Liquid Diffusion Coefficient of the concentration at A point on C (Z).
Preferably, the basisConcentration is in A point in calculating C (Z)
The step of Liquid Diffusion Coefficient at place, specifically includes: introducing mathematics and changes Y (CA)=(CA-C1)/(C2-C1), C1And C2Indicate C
(Z) two asymptotes, and C1< C2, substituting into calculation formula can be obtained the Liquid Diffusion Coefficient at A point.
It is in contrast to the prior art, the beneficial effects of the present invention are: the present invention expands in the liquid phase of measurement various concentration
There is good effect when dissipating coefficient, it is only necessary to carve obtain a width transient state diffusion image in due course, by the image analysis processing
The Liquid Diffusion Coefficient changed with concentration can be quickly obtained, when measurement so as to substantially shorten Liquid Diffusion Coefficient
Between, reduce measurement workload, working efficiency can be improved significantly, time of measuring theoretically can substantially foreshorten to Millisecond
Not, the specific time-consuming time for one width transient state diffusion image of shooting.
Detailed description of the invention
Fig. 1 is used by the method for the Liquid Diffusion Coefficient of the rapid survey various concentration of the embodiment of the present invention based on double
The structural schematic diagram of the experimental provision of wick-containing cylindrical lens.
Fig. 2 is the structural schematic diagram of biliquid stem lens shown in FIG. 1.
Fig. 3 is imaging schematic diagram when injecting different refractivity liquid in biliquid stem lens.
Fig. 4 is the geometry schematic diagram that concentration profile is obtained using Boltzmann-Matano method.
Fig. 5 is the geometry schematic diagram that concentration profile is obtained using Sauer-Freise method.
Fig. 6 is spherical aberration curve synoptic diagram of the biliquid stem lens in KCl system.
Fig. 7 is collected diffusion image when different moments KCl aqueous solution is spread in water.
Fig. 8 is transient state diffusion image of the 3.00Mol/L KCl in pure water in moment t=4800s shooting.
Fig. 9 is the concentration profile for carrying out the KCl aqueous solution obtained after linear fit.
Figure 10 is KCl aqueous solution in the refractive index of the diffusion image of t=4800s and the gradient distribution relationship of position.
Figure 11 is KCl aqueous solution in the concentration of the diffusion image of t=4800s and the gradient distribution relationship of position.
Figure 12 is concentration profile of diffusion image of the KCl aqueous solution in t=4800s after coordinate transform.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that the described embodiments are merely a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
The method of the Liquid Diffusion Coefficient of the rapid survey various concentration of the embodiment of the present invention the following steps are included:
Two kinds of liquid are injected in the preceding wick-containing of biliquid stem lens, and biliquid stem lens are incident on using monochromatic collimated light
On, and the liquid lamella formed after spreading to two kinds of liquid carries out Image Acquisition and obtains diffusion image, wherein biliquid stem lens
Rear wick-containing be injected with the liquid of predetermined refraction, to eliminate system spherical aberration；
A width transient state diffusion image of t moment shooting is selected, width and the position of transient state diffusion image is measured, obtains width
With the distribution relation of position, it is expressed as (Zi, Σi), wherein ΣiIt indicates away from image boundary ZiThe width of distance, i are positive integer；
According to the relationship between the width and refractive index of known liquid to (Zi, Σi) converted, obtain refractive index with
The distribution relation of position, is expressed as (Zi, ni), wherein niIt indicates away from image boundary ZiThe refractive index of distance；
According to the relationship between the refractive index and concentration of known liquid to (Zi, ni) converted, obtain concentration and position
Distribution relation, be expressed as (Zi, Ci), wherein CiIt indicates away from image boundary ZiThe concentration of distance；
Using least square method to (Zi, Ci) linear fit is carried out, obtain concentration with the concentration profile of change in location,
It is expressed as C (Z)；
According toOrIt calculates dense on C (Z)
Spend the Liquid Diffusion Coefficient at A point, whereinIndicate the inverse of concentration slope at A point on C (Z),Table
Show from C1To CAIntegral, Y (CA)=(CA-C1)/(C2-C1), C1And C2Indicate two asymptotes of C (Z), and C1< C2。
Wherein, the method for the present embodiment use the experimental provision based on biliquid stem lens, structure as shown in Figure 1,
Including laser 1, attenuator 2, microcobjective 3, aperture 4, collimation lens 5, slit plate 6, biliquid stem lens 7, CMOS (CCD)
Image capturing system 8 and Image Acquisition display system 9.The laser of 1 output wavelength λ=589.0nm of laser, laser is through overdamping
Device 2 is decayed, and the monochromatic collimated light successively generated after microcobjective 3, aperture 4, collimation lens 5, monochromatic collimated light is through slit
Impinged perpendicularly on after 6 limit for width of plate on biliquid stem lens 7, CMOS (CCD) image capturing system 8 acquire transient state diffusion image after by
9 real-time display of Image Acquisition display system.
As shown in Fig. 2, biliquid stem lens 2 are made of symmetric lens, 1 plano-convex lens the concave-convex lens of 2 crescent
The liquid composition of specific refractive index, is six face formula biliquid stem lens of three pieces, radius of curvature is respectively R between lens1=R4=
45.0mm、R2=R3=27.9mm, R5=21.5mm, lens thickness and spacing are respectively d1=d4=4.0mm, d2=d3=
3.0mm、d5=1.0mm, d6=12.0mm, d7=8.3mm, d8=3.7mm, height 2h=20.0mm, O are in lens system
The heart, O1、O2、O3、O4、O5The center of circle of respectively first to the 5th curved surface, the length L=50.0mm of lens, lens material are folding
Penetrate rate n0=1.5163 K9 glass.Wick-containing had not only been used as liquid phase diffusion cell but also had been used as image-forming component before biliquid stem lens, rear liquid
Core is for improving refractive index sensitivity and reducing spherical aberration.Since the rear wick-containing of biliquid stem lens is injected with the liquid of predetermined refraction
Body can eliminate system spherical aberration, can change the meeting of the 4th, the 5th curved surface by liquid refractivity in wick-containing after changing
Cumulative power, so as to adjust the spherical aberration of system.
It is spherical aberration curve synoptic diagram of the biliquid stem lens in KCl system referring to Fig. 6.It to be reflected in entire diffusion system
Spherical aberration is controlled within the scope of rate and reaches minimum, injects the best liquid of elimination system spherical aberration in wick-containing after biliquid stem lens
Body, after being selected with the method when wick-containing refractive index, so that it is controlled spherical aberration minimum in entire ranges of indices of refraction can make to expand in this way
Scattered image Reaction-diffusion terms information as precisely as possible.By taking the KCl diffusion system of 0-3mol/L as an example, in n=1.3330-
In 1.3600 ranges, every 0.0002 refraction index changing cause the sum of the spherical aberration of system then in wick-containing liquid refractivity change
Change curve, after Fig. 6 expression in wick-containing the liquid (n'=1.3992) of the sum of injection spherical aberration minimum refractive index afterwards system spherical aberration with preceding
The change curve of wick-containing.
Imaging when injecting different refractivity liquid before biliquid stem lens in wick-containing is different, as shown in figure 3, in biliquid core
After the liquid that wick-containing injection refractive index is n' after cylindrical lens, injection refractive index is n in wick-containing before biliquid stem lens1Single liquid
When body, wick-containing cylindrical lens along the different location of Z axis be to the refracting power of directional light it is the same, when cmos image acquisition system 8
When positioned at the focal plane of biliquid stem lens, the image received on CMOS is a wide thin sharp bright line, such as Fig. 3 (a)
It is shown；When injecting two different liquid before biliquid stem lens in wick-containing, when two kinds of liquid do not have started diffusion, wick-containing column is saturating
Two parts are different to the refractive power of directional light up and down for mirror, directional light after the refraction of upper liquid in wick-containing cylindrical lens
The picture of a disperse can be formed on CMOS after the refraction of lower section liquid, such as Fig. 3 (b) on CMOS front with blur-free imaging
It is shown, wherein the refractive index of two kinds of liquid is respectively n1For n2, and n1< n2；Two kinds of liquid are once in the core of wick-containing cylindrical lens
When contacting in area, it is denoted as the t=0 moment, two kinds of solution contacts will be spread, and will form one along the Z axis of wick-containing cylindrical lens
Dynamic concentration gradient distribution also will form a dynamic refractive index gradient distribution accordingly, and each liquid lamella is to parallel
The refractive power of light is all different.If cmos image acquisition system is fixed on a specific position, directional light passes through
Wick-containing cylindrical lens can only be in the liquid lamella (n=n of a specific refractive indexc) could be presented clearly on CMOS after refraction
Picture, and will form different degrees of disperse after reflecting by other liquid lamellas on CMOS, imaging such as Fig. 3 (c) is shown,
In, n1<n2<n3=nc<n4, it can be seen that diffusion image at this time is " with a tight waist " image, and " waist " of diffusion image can be with two kinds of liquid
The progress of diffusion process between body and drift about.
In the present embodiment, in the transient state diffusion image of moment t selection, only the liquid lamella of specific refractive index is formed clearly
Imaging, remaining liquid lamella form different degrees of disperse.That is, the method for the present embodiment is when selecting diffusion image,
Preferential selection " with a tight waist " image.
In the present embodiment, according toCalculate liquid phase of the concentration at A point on C (Z)
The step of diffusion coefficient, specifically includes:
Matano plane is found on C (Z), and coordinate is carried out to C (Z) using Matano plane position as co-ordinate zero point
Transformation, wherein the closed figure that the area of the closed figure of the Matano plane left side and C (Z) composition is constituted with the right and C (Z)
Area equation；
Linear fit is re-started to the C (Z) after coordinate transform using least square method；According toCalculate Liquid Diffusion Coefficient of the concentration at A point on C (Z).
Wherein, which realized based on Bolzmann-Matano method,'s
Derivation process are as follows:
(1) diffusion coefficient D is not the solution under the conditions of constant
Diffusion coefficient D is usually relevant to concentration C.The concentration profile C that Matano is obtained according to experimental method
(x), it can solve the method with the diffusion coefficient D (C) under concentration change condition from obtained C (x), this method is
Boltzmann-Matano method.For the expression formula of Fick second lawD (C) in formula is not
One constant cannot propose to become from bracketThe form of formula cannot use common Analytic Method, still
It can be using the diffusion coefficient obtained after Boltzmann transformation by experimental method under concentration distribution and various concentration.It enablesForFick second law in formula exists:
(1)~(4) formula is substituted intoThe left and right ends derivation of the Fick second law of formula can obtain:
Abbreviation can obtain:
For two kinds of diffused liquids, there are following primary condition and boundary condition, wherein CLAnd CRIt is the upper and lower of concentration
Limit, when calculating various concentration Liquid Diffusion Coefficient in the present embodiment, CR=C1And CL=C2,
Primary condition:
Boundary condition:
Solute forms gradient distribution dC/d ξ, C=CRWhen without gradient distribution, can be obtained according to boundary condition abbreviation:
It can be obtained by transformation, the relational expression between diffusion coefficient D and concentration C are as follows:
In formula (12),It is the inverse that concentration is slope at C' on C-x curve,For from CRTo C'
Integral, XMIndicate the coordinate position of Matano plane.
(2) Boltzmann-Matano method calculates Liquid Diffusion Coefficient
As shown in figure 4, be the geometry schematic diagram that concentration profile is obtained using Boltzmann-Matano method,
XMIndicate Matano plane, CLAnd CRIt is concentration limits.It is dense in diffusion process since diffusion coefficient D (C) is related with concentration C
Degree distribution curve will not generally keep central symmetry relationship, therefore need to be coordinately transformed concentration function for convenience of calculating,
Find Matano plane.The physical significance of Matano plane is that this plane of substance therethrough is spread at plane both ends,
It spreads the amount flowed into and the amount of diffusion outflow is just equal, therefore can have by conservation of mass conditional decision " face Matano ":
Formula (13) is deformed and can be obtained:
It can be obtained by the integral that boundary condition calculates:
Abbreviation can obtain:
It is coordinately transformed, co-ordinate zero point is moved to XMPlace, i.e. XM=0, after coordinate transform, formula (16) can abbreviation are as follows:
There are following relationships by the diffusion time t fixed for one:
After determining Matano plane, the liquid phase that can solve various concentration after being coordinately transformed according to formula (12) spreads system
Number, with away from the Z replacement formula derivation process of diffusion image boundary when calculating various concentration Liquid Diffusion Coefficient in the present embodiment
X.
On the other hand, according toConcentration is in A in calculating C (Z)
Point at Liquid Diffusion Coefficient the step of be to be realized based on Sauer-Freise method,Derivation process are as follows:
In the present embodiment, according to
Calculate C
(Z) the step of Liquid Diffusion Coefficient of the concentration at A point, specifically includes on:
It introduces mathematics and changes Y (CA)=(CA-C1)/(C2-C1), C1And C2Indicate two asymptotes of C (Z), and C1< C2,
Substituting into calculation formula can be obtained the Liquid Diffusion Coefficient at A point.
When calculating the Liquid Diffusion Coefficient of various concentration using Boltzmann-Matano method, need to find Matano
Plane, but be sometimes difficult accurately to search out Matano plane, therefore Sauer-Freise etc. is mathematically right
Boltzmann-Matano method is improved, by improve after can to avoid find Matano plane.As shown in figure 5, being to adopt
The geometry schematic diagram of concentration profile is obtained with Sauer-Freise method.Sauer-Freise method is mathematically right
Boltzmann-Matano method is improved, by improve after can to avoid find Matano plane.With Boltzmann-
Matano method is identical, the C in formulation processLAnd CRIt is the bound of concentration, x indicates position, calculates in the present embodiment
When various concentration Liquid Diffusion Coefficient, CR=C1And CL=C2, with away from the x in the Z replacement formula derivation process of diffusion image boundary.
When calculating diffusion coefficient by Sauer-Freise method, to avoid finding Matano plane, enable
According to relationship shown in the definition of Y (x) in formula (19) and Fig. 5 there are following relational expression,
A2=Y (A2+A3+A4)(20)
A1=YA1+(1-Y)A1(21)
(20) and (21) two formula left and right ends are separately summed and can be obtained:
A1+A2=(1-Y) A1+Y(A1+A2+A3+A4)(22)
For using Matano plane as separation, there are following relationships:
A1+A2+A3=A5(23)
It can be obtained in conjunction with (22) and (23) two formulas:
A1+A2=(1-Y) A1+Y(A4+A5)(24)
Integral expression is obtained to the reversed solution of (24) formula that obtains of Sauer-Freise:
When calculating the diffusion coefficient of various concentration using formula (25), it can be more convenient to avoid Matano plane is found
Calculating various concentration diffusion coefficient.
Below to calculate various concentration KCl solution, BaCl2For the Liquid Diffusion Coefficient of solution to method of the invention into
Row is described in detail.
Embodiment 1
The Liquid Diffusion Coefficient of various concentration KCl aqueous solution is calculated using Boltzmann-Matano method.
Since 10min, with nc=1.3364 liquid lamella is observation thin layer, shoots a width diffusion image every 60s,
Part diffusion image is listed, as shown in Figure 7.When the image on two kinds of diffused liquid both sides merges completely, observation thin layer is become
More nc=1.3459 liquid lamella, the position start recording diffusion image of Orientation observation plane.
A width transient state diffusion image is selected in moment t=4800s, transient state diffusion image is as shown in figure 8, Fig. 8 is t=
Transient state diffusion image of the 3.00Mol/L KCl of 4800s shooting in pure water is calculated different dense with Boltzmann-Matano method
The Liquid Diffusion Coefficient of degree.Width and the position that diffusion image shown in Fig. 8 is measured by Matlab software program, obtain (Zi,
Σi), picture traverse is read using the program write.Go out picture traverse according to obtained feature modeling, then utilizes width and folding
The relationship between rate is penetrated to (Zi, Σi) converted to obtain (Zi,ni), (Zi,ni) relationship it is as shown in Figure 10.Then according to KCl
Relationship C=111.7708*n-149.0175 (Mol/L) between the refractive index and concentration of aqueous solution, acquisition concentration and position
Distribution relation (Zi,Ci), (Zi,Ci) relationship it is as shown in figure 11.Using least square method to (Zi, Ci) linear fit is carried out, it obtains
To concentration profile C (Z), concentration profile is as shown in Figure 9.
It needs to find Matano plane when calculating Liquid Diffusion Coefficient using Boltzmann-Matano method, is closed according to C (Z)
It is with the definition of Matano plane so that two kinds of shaded areas are equal in Figure 11, and then it is (empty in such as Figure 11 to obtain Matano plane
Shown in line), two asymptotes of concentration profile C (Z) are C1And C2.Concentration profile C (Z) is coordinately transformed, is become
Concentration profile after changing is as shown in figure 12.
To after coordinate transform concentration C and position Z re-start fitting of a polynomial, according toLiquid Diffusion Coefficient of the concentration at A point on C (Z) can be calculated by integrating meter.Meter
When calculating the diffusion coefficient of other concentration, it is only necessary to changeMiddle upper limit of integral can be according to one
Width transient state diffusion image quickly acquires the diffusion coefficient of various concentration.Different moments are calculated with Boltzmann-Matano method, no
Diffusion coefficient with concentration KCl is as shown in table 1.
The Liquid Diffusion Coefficient measurement result of 1 various concentration KCl aqueous solution of table
In table 1, the 2 to 11st is classified as the measured value of different moments Liquid Diffusion Coefficient, the 12nd be classified as 3000s -4800s it
Between six different moments measured value average value, the 13rd is classified as standard deviation, Liquid Diffusion Coefficient under the 14th column respective concentration
Literature value.It can be seen that by the data in table 1 and measure what Liquid Diffusion Coefficient obtained using Boltzmann-Matano method
As a result the data between 0.2Mol/L -2.3Mol/L are relatively stable, and at both ends, the main of large error occurs in concentration
The reason is that according toWhen formula calculates Liquid Diffusion Coefficient, need to ask concentration profile C (Z)
The inverse of slope at required concentration position, and the slope of concentration curve is smaller at end positions, inverse can become very
Greatly, the Liquid Diffusion Coefficient that error so slightly will lead to calculate has biggish error.2400s -3000s it
Between measured value it is larger, mainly since Boltzmann-Matano method needs to know that the concentration distribution in entire space could calculate
Liquid Diffusion Coefficient, the diffusion pattern obtained from Fig. 7 can be seen that in 1800s or so two kinds of dispersion solutions interface
Preferable transition bonding image is formed, obtaining concentration distribution by the width of measurement image at this time, there is also larger fluctuations, cause
Measurement data deviation is larger.And measurement data measured value and the larger reason of document deviation in 5100s, it is in cmos detector
In the case that size is certain, due to the progress of diffusion, the pure dispersion solutions part (i.e. the parallel part of image) at high concentration end
Not in cmos detector, it will lead to integral when measuring Liquid Diffusion Coefficient according to a width diffusion image in this way and find
The Matano plane inaccuracy arrived, and then lead to the diffusion coefficient calculated there are biggish deviations.
Embodiment 2
High concentration (1.4Mol/L) BaCl is calculated using method same as Example 12The Liquid Diffusion Coefficient of aqueous solution,
The measurement result of different moments is as shown in table 2.
2 various concentration BaCl of table2The Liquid Diffusion Coefficient measurement result of aqueous solution
In table 2, the 2 to 9th is classified as the measured value of different moments Liquid Diffusion Coefficient, and the 10th is classified as between 4800s -6300s
The average value of the measured value of six different moments, the 11st is classified as standard deviation, Liquid Diffusion Coefficient under the 12nd column respective concentration
Literature value.Due to BaCl2Diffusion ratio KCl diffusion it is slow, the diffusion image that obtain can be used for calculating Liquid Diffusion Coefficient needs
The longer time is wanted, as shown in table 2.It is identical as the Liquid Diffusion Coefficient of various concentration KCl is calculated, it is calculated at the concentration of both ends
The Liquid Diffusion Coefficient come has biggish error.The calculated Liquid Diffusion Coefficient deviation of 6900s and 7500s is larger, main former
Because being the progress due to diffusion, the pure dispersion solutions part (i.e. the parallel part of image) at high concentration end is not visited in CMOS
It surveys in device, eventually leading to the Liquid Diffusion Coefficient calculated, there are biggish deviations.
Embodiment 3
Various concentration KCl aqueous solution, BaCl are calculated using Sauer-Freise method2The Liquid Diffusion Coefficient of aqueous solution, i.e.,
According toCalculate concentration on C (Z)
Liquid Diffusion Coefficient at A point.
The measurement result of the KCl aqueous solution of different moments such as table 3, the BaCl of different moments2The measurement result of aqueous solution is such as
Shown in table 4.
The Liquid Diffusion Coefficient measurement result of 3 various concentration KCl aqueous solution of table
4 various concentration BaCl of table2The Liquid Diffusion Coefficient measurement result of aqueous solution
The difference being calculated it can be seen from 1~table of table 4 with Boltzmann-Matano method and Sauer-Freise method
Concentration KCl and BaCl2Liquid Diffusion Coefficient it is very close, rule is also completely the same, but is avoided with Sauer-Freise
Find Matano plane, calculating process relative ease.
The above description is only an embodiment of the present invention, is not intended to limit the scope of the invention, all to utilize this hair
Equivalent structure or equivalent flow shift made by bright specification and accompanying drawing content is applied directly or indirectly in other relevant skills
Art field, is included within the scope of the present invention.
Claims (4)
1. a kind of method using transient images rapid survey various concentration Liquid Diffusion Coefficient characterized by comprising
Two kinds of liquid are injected in the preceding wick-containing of biliquid stem lens, are incident on biliquid stem lens using monochromatic collimated light,
And the liquid lamella formed after spreading to two kinds of liquid carries out Image Acquisition and obtains diffusion image, wherein biliquid stem lens
Wick-containing is injected with the liquid of predetermined refraction afterwards, to eliminate system spherical aberration；
The width transient state diffusion image for selecting t moment shooting, measures width and the position of the transient state diffusion image, obtains width
With the distribution relation of position, it is expressed as (Zi, Σi), wherein ΣiIt indicates away from image boundary ZiThe width of distance, i are positive integer；
According to the relationship between the width and refractive index of known liquid to (Zi, Σi) converted, obtain refractive index and position
Distribution relation, be expressed as (Zi, ni), wherein niIt indicates away from image boundary ZiThe refractive index of distance；
According to the relationship between the refractive index and concentration of known liquid to (Zi, ni) converted, obtain point of concentration and position
Cloth relationship, is expressed as (Zi, Ci), wherein CiIt indicates away from image boundary ZiThe concentration of distance；
Using least square method to (Zi, Ci) linear fit is carried out, concentration is obtained with the concentration profile of change in location, is indicated
For C (Z)；
According toOrIt calculates dense on C (Z)
Spend the Liquid Diffusion Coefficient at A point, whereinIndicate the inverse of concentration slope at A point on C (Z),Table
Show from C1To CAIntegral, Y (CA)=(CA-C1)/(C2-C1), C1And C2Indicate two asymptotes of C (Z), and C1< C2。
2. the method according to claim 1, wherein the basisIt calculates
The step of Liquid Diffusion Coefficient of the concentration at A point, specifically includes on C (Z):
Matano plane is found on C (Z), and coordinate change is carried out to C (Z) using Matano plane position as co-ordinate zero point
It changes, wherein closed figure of the area of the closed figure of the Matano plane left side and C (Z) composition and the right and C (Z) composition
Area equation；
Linear fit is re-started to the C (Z) after coordinate transform using least square method；
According toCalculate Liquid Diffusion Coefficient of the concentration at A point on C (Z).
3. method according to claim 1 or 2, which is characterized in that in the transient state diffusion image of the moment t selection, only
The liquid lamella of specific refractive index forms blur-free imaging, remaining liquid lamella forms different degrees of disperse.
4. the method according to claim 1, wherein preferred, the basisIt calculates dense on C (Z)
The step of Liquid Diffusion Coefficient spent at A point, specifically includes:
It introduces mathematics and changes Y (CA)=(CA-C1)/(C2-C1), C1And C2Indicate two asymptotes of C (Z), and C1< C2, substitute into
The Liquid Diffusion Coefficient at A point can be obtained in calculation formula.
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