CN109186500A - The contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column - Google Patents
The contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column Download PDFInfo
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Abstract
The contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column are fitted phase interface using cubic polynomial and calculate contact angle, which is adapted to asymmetric phase interface, is particularly suited for the measurement image obtained in actual experiment；Mode of the invention based on image local gray scale extreme value, realizes the phase interface of the low contrast images of liquid liquid displacement in microchannel, and then obtains contact angle.The present invention is based on the modes of image local gray scale extreme value, realize the phase interface, wall surface of the low contrast images of liquid liquid displacement and the identification of contact point in microchannel, serious forgiveness of the present invention is high, it is adapted to the image there are noise, can correct, efficient identification go out phase interface, wall surface and contact point, information above can be used for correct measurement contact angle.This method is suitable for the fitting of asymmetric phase interface, and algorithm robustness is strong, greatly improves the efficiency and measurement accuracy of data processing.
Description
Technical field
The present invention relates to a kind of contact angle acquisition methods of liquid-liquid diphase displacement image in micron capillary column, are suitable for micro- ruler
Spend the experiment of two-phase flow research field, petroleum enhanced recovery field.
Background technique
The driving mechanism of two kinds of immiscible liquid in the capillary of single micro-meter scale is in natural environment porous media
Two-phase displacement basis, the two-phase displacement in porous media occurs in numerous industry or natural process, such as fine and close oil
The characteristics of processes such as water drive oil, the polymer displacement of reservoir oil of hiding, above-mentioned industrial process is the faint (range 10 of capillary number of viscous force-10
<Ca<10-5), gravity is faint, and (Bond number Bo is less than 10-4).The definition of the two dimensionless numbers is Ca=μ V/ γ, μ viscous for liquid
Degree, V is phase boundary face velocity, and γ is interfacial tension；Bo=ρ gh2/ γ, ρ are fluid densities, and g is acceleration of gravity, and h is flow region
The characteristic size in domain.The key factor for influencing displacement process is capillary force, and the key parameter for calculating capillary force is two-phase interface
With the contact angle of pipeline wall surface.The calculating of capillary force is calculated according to Young-Laplace formula, as shown in formula (1).Contact angle θ
Actual range be 0~180 °, the P when θ < 90 °cFor positive value, when θ > 90 °, PcFor negative value, therefore capillary force is likely to be resistance
The resistance for hindering displacement is also likely to be the power for promoting displacement.Moreover, the mistake of contact angle assessment will be such that capillary force calculates
There are serious errors, make mistakes so as to cause the assessment of displacement process.Therefore, the dynamic contact angle under above-mentioned industrial condition is obtained
Information is most important for assessing liquid liquid displacement process in entire porous media.
The displacement test that the immiscible liquid of two-phase is carried out in minute yardstick capillary is the common side of research trends contact angle
Method.Existing experiment often carries out manual analysis, manual measurement contact angle to the micro-image of phase interface.And existing business is set
The standby image processing method used also only limits the droplet profile (sessile drop method measurement contact angle) with analysis in the surface of solids, drop shape
The image analysis algorithm of shape includes symmetric shape analysis method (ADSA-P), depth-width ratio method, ellipse fitting method etc..But with worthwhile
Method is to propose that the image high suitable for contrast is not suitable for liquid liquid in microchannel for the SHAPE DETECTION of drop in plane
The phase interface shape of low contrast when displacement.The contact angle for measuring liquid liquid displacement phase interface in microchannel, needs from image
In identify phase interface.
Summary of the invention
The object of the present invention is to provide a kind of contact angle acquisition methods of liquid-liquid diphase displacement image in micron capillary column, should
Method can identify wall surface, phase interface and contact point from image, while measure contact angle, contacting points position.
In order to achieve the above object, the present invention adopts the following technical scheme that:
The contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column, the micro-image of acquisition is carried out
Coordinate divides, if the Pixel Dimensions width of image is LxWith long Ly；Then it follows the steps below:
Step 1 searches for two point A and B of two wall surface left ends by multiple extremum search technique along the direction y first,
Obtaining coordinate is respectively (0, yA) and (0, yB)；
Step 2, along the E (0, y at A-B line midpointE) horizontal direction y=xESingle local minimum is searched for, is obtained
Certain point F on phase interface, coordinate points are (xF,yF)；
Step 3 searches for monopole value using sort algorithm along the direction y, and then searches for part wall, in order to avoid phase boundary
In face of the search of wall surface, a range is set to avoid phase interface, enables 0 < xD1=xC1<xF, in 0≤x≤xD1With 0≤y≤yEModel
It encloses interior search and obtains wall surface A-D1, wherein the coordinate of D1 is (xD1,yD1)；In 0 < xf<xC1And yE≤y≤LySearch obtains in range
Wall surface B-C1, wherein the coordinate of C1 is (xC1,yC1)；
Step 4 searches for monopole value, and then search section split-phase interface using sort algorithm along the direction x, in order to avoid two
Search of a wall surface to phase interface is arranged a range to avoid two wall surfaces, enables 0 < yD2<yF<yC2<Ly, in 0≤x≤LxWith
yD2≤y≤yC2Search obtains part phase interface C2-D2 in range, and the coordinate of two points is (x respectivelyD2,yD2)、(xC2,yC2)；
Step 5 is fitted coordinate points all in A-D1 and B-C1 line segment respectively using linear function and obtains linear function fAD
And fBC, using all the points in cubic function fitting C2-D2 curve, obtain cubic function fCD；Solve fADWith fCDIntersection point obtain
Coordinate (the x of contact point DD,yD), solve fADWith fCDIntersection point, obtain the coordinate (x of contact point CC,yC)；Line segment B-C and A-D are
Wall surface, curve C-D are phase interface；
Step 6, according to the fitting function x=f for the phase interface that step 5 obtainsCD(y), by the coordinate (x of CC,yC) and D
Coordinate (xD,yD) f is substituted into respectivelyCDFirst order derivative in, acquire phase interface in the contact angle θ of C point and D pointCAnd θD；fCDOne
Subderivative f 'CDFor
f′CD=3aCDy2+2bCDy+cCD (13)
By ordinate yCAnd yDIn substitution formula (13), slope is obtained, slope conversion is at an angle of and obtains contact angle θCAnd θD；
A further improvement of the present invention lies in that detailed process is as follows for step 1:
Point A and point B be on the straight line of x=0 gray scale minimum point and shade of gray along the direction y there are maximum
Two points, therefore find the coordinate of two points of shade of gray maximum and be distinguish, determine the coordinate of point A and point B；
The gray value for enabling arbitrary coordinate point (x, y) is I (x, y), then follows the steps below:
(1) forward difference is carried out to indicate variable gradient dI to the coordinate points gray value on the straight line of x=0, there are two by dI
A maximum point；
(2) y-coordinate for setting all the points on the straight line of x=0 carries out descending arrangement according to shade of gray value I (0, y), obtains one
A coordinate sequence (y1,y2,...yn), coordinate y1It is the position of one of maximum point, searching coordinates sequence, is searched in order
Meet the coordinate points y of formula (3) to firstk, wherein 1 < k≤n；α is the coefficient less than 1 in formula (3), and h is the perpendicular of point A to point B
Directly distance h=yB-yA；
|yk-y1|>αh (3)
(3) compare y1And ykSize, enabling in the two smaller value is ymin, the larger value ymax, then the ordinate of point A and point B
It is determined as yA=ymin, yB=ymax。
A further improvement of the present invention lies in that detailed process is as follows for step 2:
(1) the ordinate y of A-B line midpoint E is soughtE；
(2) by straight line y=yEGray value I (x, the y of upper all coordinate pointsE) gradient of gray scale is sought by formula (5), wherein x ∈
[0,LX]；Obtain straight line y=yEShade of gray dI (x, the y of upper all coordinate pointsE)；
(3) due to dI (x, yE) only one maximum, search for dI (x, yE) maximum point in sequence, determine phase interface
The abscissa x of upper FF, and the ordinate x of point FF=xE。
A further improvement of the present invention lies in that detailed process is as follows for step 3:
(1) in order to not influenced by phase interface when searching for wall surface along the direction y, the x range of limit search be 0≤x≤
xD1Or 0≤x≤xC1, wherein xD1=xC1=β xF, β is a coefficient less than 1；
(2) in order to search for wall surface A-D1, abscissa xiTraversal 0 to xD1, for each abscissa xi, seek straight line x=xiOn
Gray scale I (xi, y) and gradient in the direction y, as shown in formula (6)；Search for dI (xi, y) on maximum, obtain corresponding wall surface coordinate points
Ordinate yi, a series of coordinate points (xi,yi) constitute wall surface A-D1；
(3) in order to search for wall surface B-C1, abscissa xjTraversal 0 to xC1, for each abscissa xj, seek straight line x=xjOn
Gray scale I (xj, y) and gradient in the direction y, by x in formula (6)iIt is substituted for xjCalculate dI (xj, y), search for dI (xj, y) on it is very big
Value obtains the ordinate y of corresponding wall surface coordinate pointsj, a series of coordinate points (xj,yj) constitute wall surface B-C1.
A further improvement of the present invention lies in that detailed process is as follows for step 4:
(1) minimum for searching for gray scale in the x-direction determines phase interface, needs to avoid two wall surfaces, sets the search in the direction y
Range is yD2<y<yC2, wherein yD2And yC2Respectively
In formula (7), h is point A to the distance of point B, i.e. h=yB-yA, ε is a coefficient, and value range is 0 < ε < 0.5；
(2) in order to search for phase interface, yiCoordinate traverses yD2To yC2, for each ordinate yi, seek straight line y=yiUpper ash
Spend I (x, yi) gradient dI (x, y in the direction xi), as shown in formula (8)；Search for dI (x, yi) on maximum, obtain corresponding wall surface
The ordinate y of coordinate pointsi, a series of coordinate points (xi,yi) constitute wall surface C2-D2；
A further improvement of the present invention lies in that detailed process is as follows for step 5:
(1) using all the points in linear function fitting A-D1 line segment, using x coordinate as independent variable, y is dependent variable, is obtained
Linear function fADAs shown in formula (9), aADAnd bADFor the coefficient of linear function,
Y=fAD(x)=aADx+bAD (9)
Using all the points in linear function fitting B-C1 line segment, using x coordinate as independent variable, y is dependent variable, and what is obtained is primary
Function fBCAs shown in formula (10), aBCAnd bBCFor the coefficient of linear function
Y=fBC(x)=aBCx+bBC (10)
Phase interface C2-D2 is fitted using cubic function, using y-coordinate as independent variable, x is dependent variable, obtained cubic function
fCD, as shown in formula (11)；
X=fBC(y)=aCDy3+bCDy2+cCDy+dCD (11)
(2) contact point C and D is the intersection point of two wall surfaces and phase interface respectively, therefore by solving fCDWith fADIntersection point,
And fCDWith fBCIntersection point obtains the coordinate (x of contact point C and DC,yC) and (xD,yD), the above process is to solve for side shown in formula (12)
Journey group；
(3) phase interface, on wall surface all coordinate points determination: to seek all coordinate points on wall surface A-D, will each expire
Sufficient xA≤x≤xDAbscissa x bring into formula (9) and carry out that corresponding y-coordinate is calculated, to obtain all the points on wall surface A-D
Coordinate；All coordinate points on wall surface B-C are sought, meet x for eachB≤x≤xCAbscissa x bring into formula (10) and carry out
Corresponding y-coordinate is calculated, to obtain the coordinate of all the points on wall surface B-C；For all coordinate points on phase interface C-D,
Meet y for eachC≤y≤yDOrdinate y bring into formula (11) and carry out that corresponding x coordinate is calculated, to obtain phase interface C-
The coordinate of the upper all the points of D.
A further improvement of the present invention lies in that further including step 7: right when the wall surface actually acquired is not level
The contact angle that formula (14) obtains is modified, and detailed process is as follows: the tilt angle of wall surface is the inclination of wall surface A-D1 and B-C1
Angular average, i.e. (arctan aAD+arctan aBC)/2, the then end value of contact angle are as follows:
Compared with prior art, the invention has the benefit that
The present invention is using cubic polynomial fitting phase interface and calculates contact angle, and overcoming traditional algorithm ADSA-P can only intend
The limitation of symmetrical phase interface is closed, which is adapted to asymmetric phase interface, is particularly suited for the measurement obtained in actual experiment
Image；Mode of the invention based on image local gray scale extreme value realizes the phase of the low contrast images of liquid liquid displacement in microchannel
Interface, and then obtain contact angle.The present invention is based on the mode of image local gray scale extreme value, liquid liquid displacement in microchannel is realized
Phase interface, wall surface and the identification of contact point of low contrast images, algorithm serious forgiveness is high, is adapted to the image there are noise, can
Go out phase interface, wall surface and contact point with correct, efficient identification, information above can be used for correct measurement contact angle.The invention is realized
Liquid liquid displacement dynamic contact angular measurement under low capillary number, low Bond's number state.It is quasi- to phase interface using cubic polynomial
Merge measurement contact angle, this method is suitable for the fitting of asymmetric phase interface, and algorithm robustness is strong, greatly improves data processing
Efficiency and measurement accuracy.
Detailed description of the invention
Fig. 1 is the micro-image of liquid liquid displacement.
Fig. 2 is the intensity profile figure in the gray level image of liquid liquid displacement.
Fig. 3 is the setting coordinate of liquid liquid displacement image.
Fig. 4 is the position of key point in image procossing.
Fig. 5 is that gray scale and shade of gray are distributed on the straight line of x=0 that there are two minimum points.
Fig. 6 is that gray scale and shade of gray are distributed on the straight line of x=0 that there are two maximum points.
Fig. 7 is that two contact angles are the angle that phase interface and wall surface are formed on two contact points.
Relationship of the Fig. 8 between cubic polynomial derivative and contact angle.
Specific embodiment
The present invention is described in detail with reference to the accompanying drawing.
The present invention provides the methods for finding local extremum in the picture, determine boundary point, then from boundary point identification wall surface,
Phase interface and contact point.
Liquid liquid displacement characteristics of image is specific as follows:
The micro-image of liquid liquid displacement process is using incident light (microscopical back light source is irradiated) view mode, therefore
Wall surface can be obtained, the image that phase interface is obviously distinguished with body phase liquid.The micro-image of liquid liquid displacement belongs to low contrast figure
Picture, as depicted in figs. 1 and 2.The histogram distribution feature of the low image of contrast is exactly that intensity profile is concentrated within a certain area,
The pixel quantity of high gray scale and low gray level areas is less.Two straight lines are the wall surface of microchannel in Fig. 2, and curve is phase interface.Benefit
With this feature, by calculating, identified from a series of micro-images phase interface, measurement contact angle, phase interface displacement etc. its
His parameter.This method can accurately and accurately handle the image data of substantial amounts, greatly improve dynamic Contact in microcapillary
The efficiency of angle research.
The histogram distribution feature of the low image of contrast is exactly that intensity profile is concentrated within a certain area.Liquid liquid displacement figure
As in, two straight lines are the wall surface of microchannel, and curve is phase interface.
The identification of microchannel wall surface and phase interface
The meaning on boundary is the microchannel wall surface in micro-image and the phase interface between immiscible liquid phase herein.It will obtain
The image obtained carries out coordinate division according to method shown in Fig. 3.If the Pixel Dimensions width of image is LxWith long Ly。
On image, two near linears that wall surface is made of a series of lower pixels of gray value.This two straight line bases
It originally is to prolong Shen in horizontal (direction x), it is therefore desirable to which (direction y) searches for the local minimum of gray scale to determine along vertical direction
Wall surface.Searching for single extreme value and its position in an array sequence has had mature algorithm, but simultaneously scans for multiple poles
Value and multiple positions, do not there is ripe algorithm also.The identification to wall surface and phase interface is illustrated respectively below.
The identification of part wall
Step 1, two for searching for two wall surface left ends (x=0) along the direction y by multiple extremum search technique first
Point A and B, obtaining coordinate is respectively (0, yA) and (0, yB), also just obtain the approximate location of two wall surfaces；
Detailed process is as follows for step 1:
Point A and point B is gray scale minimum point on the straight line of x=0, that is, there are maximum along the direction y for shade of gray
Two points, therefore find the coordinate of two points of shade of gray maximum and be distinguish, so that it may determine point A's and point B
Coordinate.As shown in Figure 5 and Figure 6；
The gray value for enabling arbitrary coordinate point (x, y) is I (x, y), then follows the steps below:
(1) forward difference is carried out to indicate variable gradient dI to the coordinate points gray value on the straight line of x=0, there are two by dI
A maximum point, as shown in Figure 6.
(2) y-coordinate for setting all the points on the straight line of x=0 carries out descending arrangement according to shade of gray value I (0, y), obtains one
A coordinate sequence (y1,y2,...yn), coordinate y1It is the position of one of maximum point, searching coordinates sequence, is searched in order
Meet the coordinate points y of formula (3) to firstk, wherein 1 < k≤n；α is the coefficient less than 1 in formula (3), and h is the perpendicular of point A to point B
Directly distance h=yB-yA。
|yk-y1|>αh (3)
(3) compare y1And ykSize, enabling in the two smaller value is ymin, the larger value ymax, then the ordinate of point A and point B
It can be identified as yA=ymin, yB=ymax。
Step 2, along the E (0, y at A-B line midpointE) horizontal direction y=xESingle local minimum is searched for, is obtained
Certain point F on phase interface, coordinate points are (xF,yF)；
Detailed process is as follows for step 2:
(1) the ordinate y of A-B line midpoint E is soughtE(x known to abscissaE=0),
(2) by straight line y=yEGray value I (x, the y of upper all coordinate pointsE) gradient of gray scale is sought by formula (5), wherein x ∈
[0,LX].Obtain straight line y=yEShade of gray dI (x, the y of upper all coordinate pointsE)；
(3) due to dI (x, yE) only one maximum, search for dI (x, yE) maximum point in sequence, so that it may it determines
The abscissa x of point F on phase interfaceF, and the ordinate x of point FF=xE。
Step 3 searches for monopole value using existing sort algorithm along the direction y, and then searches for part wall, in order to keep away
Exempt from search of the phase interface to wall surface, a range is set to avoid phase interface, enables 0 < xD1=xC1<xF.In 0≤x≤xD1With 0≤y
≤yESearch obtains wall surface A-D1 in range, and wherein the coordinate of D1 is (xD1,yD1)；In 0 < xf<xC1And yE≤y≤LyIt is searched in range
Rope obtains wall surface B-C1, and wherein the coordinate of C1 is (xC1,yC1), referring to fig. 4；
Detailed process is as follows for step 3:
(1) in order to not influenced by phase interface when searching for wall surface along the direction y, the x range of limit search be 0≤x≤
xD1Or 0≤x≤xC1, wherein xD1=xC1=β xF, β is a coefficient less than 1；
(2) in order to search for wall surface A-D1, abscissa xiTraversal 0 to xD1, for each abscissa xi, seek straight line x=xiOn
Gray scale I (xi, y) and gradient in the direction y, as shown in formula (6)；Search for dI (xi, y) on maximum, corresponding wall surface can be obtained and sat
The ordinate y of punctuatei, and a series of coordinate points (xi,yi) just constitute wall surface A-D1；
(3) in order to search for wall surface B-C1, abscissa xjTraversal 0 to xC1, for each abscissa xj, seek straight line x=xjOn
Gray scale I (xj, y) and gradient in the direction y, by x in formula (6)iIt is substituted for xjCalculate dI (xj, y), search for dI (xj, y) on it is very big
Value, can obtain the ordinate y of corresponding wall surface coordinate pointsj, and a series of coordinate points (xj,yj) just constitute wall surface B-C1.
The determination of phase interface and contact point:
According to above step obtain as a result, may further determine that phase interface and contact point.And then above-mentioned step
Three:
Step 4 searches for monopole value, and then search section split-phase interface using existing sort algorithm along the direction x, in order to
Search of two wall surfaces to phase interface is avoided, a range is set to avoid two wall surfaces, enables 0 < yD2<yF<yC2<Ly.In 0≤x
≤LxAnd yD2≤y≤yC2Search obtains part phase interface C2-D2 in range, and the coordinate of two points is (x respectivelyD2,yD2)、(xC2,
yC2)。
Detailed process is as follows for step 4:
(1) minimum for searching for gray scale in the x-direction determines phase interface, needs to avoid two wall surfaces, sets the search in the direction y
Range is yD2<y<yC2, wherein yD2And yC2Respectively
In formula (7), h is point A to the distance of point B, i.e. h=yB-yA, ε is a coefficient, and value range is 0 < ε < 0.5.
(2) in order to search for phase interface, yiCoordinate traverses yD2To yC2, for each ordinate yi, seek straight line y=yiUpper ash
Spend I (x, yi) gradient dI (x, y in the direction xi), as shown in formula (8)；Search for dI (x, yi) on maximum, correspondence can be obtained
The ordinate y of wall surface coordinate pointsi, and a series of coordinate points (xi,yi) just constitute wall surface C2-D2.
Step 5 is fitted coordinate points all in A-D1 and B-C1 line segment respectively using linear function and obtains linear function fAD
And fBC, using all the points in cubic function fitting C2-D2 curve, obtain cubic function fCD.Solve fADWith fCDIntersection point can obtain
Coordinate (the x of contact point DD,yD), solve fADWith fCDIntersection point can obtain the coordinate (x of contact point CC,yC).Line segment B-C and A-D are then
Wall surface, curve C-D are phase interface.
Detailed process is as follows for step 5:
(1) using all the points in linear function fitting A-D1 line segment, using x coordinate as independent variable, y is dependent variable, is obtained
Linear function fADAs shown in formula (9), aADAnd bADFor the coefficient of linear function,
Y=fAD(x)=aADx+bAD (9)
Using all the points in linear function fitting B-C1 line segment, using x coordinate as independent variable, y is dependent variable, and what is obtained is primary
Function fBCAs shown in formula (10), aBCAnd bBCFor the coefficient of linear function
Y=fBC(x)=aBCx+bBC (10)
Phase interface C2-D2 is fitted using cubic function, using y-coordinate as independent variable, x is dependent variable, obtained cubic function
fCD, as shown in formula (11).
X=fBC(y)=aCDy3+bCDy2+cCDy+dCD (11)
(2) contact point C and D is the intersection point of two wall surfaces and phase interface respectively, therefore by solving fCDWith fADIntersection point,
And fCDWith fBCIntersection point, so that it may obtain the coordinate (x of contact point C and DC,yC) and (xD,yD), the above process is just to solve for formula (12)
Shown in equation group.
(3) phase interface, on wall surface all coordinate points determination.All coordinate points on wall surface A-D are sought, will each be expired
Sufficient xA≤x≤xDAbscissa x bring into formula (9) carry out calculate can be obtained by corresponding y-coordinate, it is hereby achieved that wall surface A-D
The coordinate of upper all the points；All coordinate points on wall surface B-C are sought, meet x for eachB≤x≤xCAbscissa x bring formula into
(10) carried out in calculate can be obtained by corresponding y-coordinate, it is hereby achieved that on wall surface B-C all the points coordinate；For phase boundary
All coordinate points on the C-D of face meet y for eachC≤y≤yDOrdinate y bring into formula (11) carry out calculate can be obtained by
Corresponding x coordinate, it is hereby achieved that on phase interface C-D all the points coordinate.
The measurement of contact angle:
The definition of contact angle is the angle that with wall surface is formed of the phase interface in contacting points position.Phase interface is solved below to connect
The contact angle of contact position, according to the fitting function x=f of phase interface obtained in the previous stepCD(y), by the coordinate (x of CC,yC) with
And coordinate (the x of DD,yD) f is substituted into respectivelyCDFirst order derivative in, can in the hope of phase interface C point and D point contact angle θCAnd θD。
fCDFirst order derivative f 'CDFor,
f′CD=3aCDy2+2bCDy+cCD (13)
By ordinate yCAnd yDIn substitution formula (13), available slope, slope conversion, which is at an angle of, be can be obtained by such as figure
Contact angle θ shown in 6CAnd θD。
Additionally, it is contemplated that the wall surface actually acquired is not necessarily horizontal, certain tilt angle may be had, therefore is wanted
The contact angle obtained to formula (14) is modified.The tilt angle of wall surface is the tilt angle average value of wall surface A-D1 and B-C1,
That is (arctan aAD+arctan aBC)/2.Then the end value of contact angle is,
Method proposed by the present invention and the test result of existing business equipment Kr ü ss DSA100 contact angle instrument compare,
As shown in table 1 below.
The method of the invention of table 1 and the test result of existing business equipment Kr ü ss DSA100 contact angle instrument compare
As it can be seen from table 1 contact angle is in the measured deviation within the scope of 40 ° to 120 ° less than 0.5 °, illustrate the present invention
Method measurement it is accurate.
Claims (7)
1. the contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column, which is characterized in that by the aobvious of acquisition
Micro- image carries out coordinate division, if the Pixel Dimensions width of image is LxWith long Ly；Then it follows the steps below:
Step 1 is searched for two point A and B of two wall surface left ends along the direction y by multiple extremum search technique first, obtained
Coordinate is respectively (0, yA) and (0, yB)；
Step 2, along the E (0, y at A-B line midpointE) horizontal direction y=xESingle local minimum is searched for, phase boundary is obtained
Certain point F on face, coordinate points are (xF,yF)；
Step 3 searches for monopole value using sort algorithm along the direction y, and then searches for part wall, in order to avoid phase interface pair
The search of wall surface is arranged a range to avoid phase interface, enables 0 < xD1=xC1<xF, in 0≤x≤xD1With 0≤y≤yEIn range
Search obtains wall surface A-D1, and wherein the coordinate of D1 is (xD1,yD1)；In 0 < xf<xC1And yE≤y≤LySearch obtains wall surface in range
B-C1, wherein the coordinate of C1 is (xC1,yC1)；
Step 4 searches for monopole value, and then search section split-phase interface using sort algorithm along the direction x, in order to avoid two walls
In face of the search of phase interface, a range is set to avoid two wall surfaces, enables 0 < yD2<yF<yC2<Ly, in 0≤x≤LxAnd yD2≤y
≤yC2Search obtains part phase interface C2-D2 in range, and the coordinate of two points is (x respectivelyD2,yD2)、(xC2,yC2)；
Step 5 is fitted coordinate points all in A-D1 and B-C1 line segment respectively using linear function and obtains linear function fADWith
fBC, using all the points in cubic function fitting C2-D2 curve, obtain cubic function fCD；Solve fADWith fCDIntersection point connect
Coordinate (the x of contact DD,yD), solve fADWith fCDIntersection point, obtain the coordinate (x of contact point CC,yC)；Line segment B-C and A-D are wall
Face, curve C-D are phase interface；
Step 6, according to the fitting function x=f for the phase interface that step 5 obtainsCD(y), by the coordinate (x of CC,yC) and D seat
Mark (xD,yD) f is substituted into respectivelyCDFirst order derivative in, acquire phase interface in the contact angle θ of C point and D pointCAnd θD；fCDOnce lead
Number f 'CDFor
f′CD=3aCDy2+2bCDy+cCD (13)
By ordinate yCAnd yDIn substitution formula (13), slope is obtained, slope conversion is at an angle of and obtains contact angle θCAnd θD；
2. the contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column according to claim 1,
It is characterized in that, detailed process is as follows for step 1:
Point A and point B are two along the direction y there are maximum of gray scale minimum point and shade of gray on the straight line of x=0
Point, therefore find the coordinate of two points of shade of gray maximum and be distinguish, determine the coordinate of point A and point B；
The gray value for enabling arbitrary coordinate point (x, y) is I (x, y), then follows the steps below:
(1) forward difference is carried out to indicate variable gradient dI to the coordinate points gray value on the straight line of x=0, there are two poles by dI
Big value point；
(2) y-coordinate for setting all the points on the straight line of x=0 carries out descending arrangement according to shade of gray value I (0, y), obtains a seat
Mark sequence (y1,y2,...yn), coordinate y1It is the position of one of maximum point, searching coordinates sequence, searches in order
One meets the coordinate points y of formula (3)k, wherein 1 < k≤n；α is coefficient less than 1 in formula (3), h be point A to point B it is vertical away from
From h=yB-yA；
|yk-y1|>αh (3)
(3) compare y1And ykSize, enabling in the two smaller value is ymin, the larger value ymax, then the ordinate of point A and point B determines
For yA=ymin, yB=ymax。
3. the contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column according to claim 1,
It is characterized in that, detailed process is as follows for step 2:
(1) the ordinate y of A-B line midpoint E is soughtE；
(2) by straight line y=yEGray value I (x, the y of upper all coordinate pointsE) gradient of gray scale is sought by formula (5), wherein x ∈ [0,
LX]；Obtain straight line y=yEShade of gray dI (x, the y of upper all coordinate pointsE)；
(3) due to dI (x, yE) only one maximum, search for dI (x, yE) maximum point in sequence, determine point F on phase interface
Abscissa xF, and the ordinate x of point FF=xE。
4. the contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column according to claim 1,
It is characterized in that, detailed process is as follows for step 3:
(1) in order to not influenced by phase interface when searching for wall surface along the direction y, the x range of limit search is 0≤x≤xD1Or 0
≤x≤xC1, wherein xD1=xC1=β xF, β is a coefficient less than 1；
(2) in order to search for wall surface A-D1, abscissa xiTraversal 0 to xD1, for each abscissa xi, seek straight line x=xiUpper gray scale
I(xi, y) and gradient in the direction y, as shown in formula (6)；Search for dI (xi, y) on maximum, obtain the vertical of corresponding wall surface coordinate points
Coordinate yi, a series of coordinate points (xi,yi) constitute wall surface A-D1；
(3) in order to search for wall surface B-C1, abscissa xjTraversal 0 to xC1, for each abscissa xj, seek straight line x=xjUpper gray scale
I(xj, y) and gradient in the direction y, by x in formula (6)iIt is substituted for xjCalculate dI (xj, y), search for dI (xj, y) on maximum, obtain
The ordinate y of wall surface coordinate points must be corresponded toj, a series of coordinate points (xj,yj) constitute wall surface B-C1.
5. the contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column according to claim 1,
It is characterized in that, detailed process is as follows for step 4:
(1) minimum for searching for gray scale in the x-direction determines phase interface, needs to avoid two wall surfaces, sets the search range in the direction y
For yD2<y<yC2, wherein yD2And yC2Respectively
In formula (7), h is point A to the distance of point B, i.e. h=yB-yA, ε is a coefficient, and value range is 0 < ε < 0.5；
(2) in order to search for phase interface, yiCoordinate traverses yD2To yC2, for each ordinate yi, seek straight line y=yiUpper gray scale I
(x,yi) gradient dI (x, y in the direction xi), as shown in formula (8)；Search for dI (x, yi) on maximum, obtain corresponding wall surface and sit
The ordinate y of punctuatei, a series of coordinate points (xi,yi) constitute wall surface C2-D2；
6. the contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column according to claim 1,
It is characterized in that, detailed process is as follows for step 5:
(1) using all the points in linear function fitting A-D1 line segment, using x coordinate as independent variable, y is dependent variable, and what is obtained is primary
Function fADAs shown in formula (9), aADAnd bADFor the coefficient of linear function,
Y=fAD(x)=aADx+bAD (9)
Using all the points in linear function fitting B-C1 line segment, using x coordinate as independent variable, y is dependent variable, obtained linear function
fBCAs shown in formula (10), aBCAnd bBCFor the coefficient of linear function
Y=fBC(x)=aBCx+bBC (10)
Phase interface C2-D2 is fitted using cubic function, using y-coordinate as independent variable, x is dependent variable, obtained cubic function fCD, such as
Shown in formula (11)；
X=fBC(y)=aCDy3+bCDy2+cCDy+dCD (11)
(2) contact point C and D is the intersection point of two wall surfaces and phase interface respectively, therefore by solving fCDWith fADIntersection point and fCD
With fBCIntersection point obtains the coordinate (x of contact point C and DC,yC) and (xD,yD), the above process is to solve for equation shown in formula (12)
Group；
(3) phase interface, on wall surface all coordinate points determination: to seek all coordinate points on wall surface A-D, meet x for eachA
≤x≤xDAbscissa x bring into formula (9) and carry out that corresponding y-coordinate is calculated, to obtain the seat of all the points on wall surface A-D
Mark；All coordinate points on wall surface B-C are sought, meet x for eachB≤x≤xCAbscissa x bring into formula (10) and counted
Calculation obtains corresponding y-coordinate, to obtain the coordinate of all the points on wall surface B-C；It, will for all coordinate points on phase interface C-D
It is each to meet yC≤y≤yDOrdinate y bring into formula (11) and carry out that corresponding x coordinate is calculated, to obtain phase interface C-D
The coordinate of upper all the points.
7. the contact angle acquisition methods of liquid-liquid diphase displacement image in a kind of micron capillary column according to claim 1,
It is characterized in that, further includes step 7: when the wall surface actually acquired is not level, the contact angle that formula (14) obtain being carried out
Amendment, detailed process is as follows: the tilt angle of wall surface is the tilt angle average value of wall surface A-D1 and B-C1, i.e. (arctanaAD+
arctanaBC)/2, the then end value of contact angle are as follows:
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