CN102749269B - Determination method and determination apparatus for contact angle and interfacial tension - Google Patents

Determination method and determination apparatus for contact angle and interfacial tension Download PDF

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CN102749269B
CN102749269B CN201210232079.1A CN201210232079A CN102749269B CN 102749269 B CN102749269 B CN 102749269B CN 201210232079 A CN201210232079 A CN 201210232079A CN 102749269 B CN102749269 B CN 102749269B
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fluid
contact angle
sample hose
interfacial tension
formula
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CN102749269A (en
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张禹负
邢义良
李春新
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Beijing forever Technology Co., Ltd.
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Beijing Yong Ruida Scientific & Trading Co Ltd
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Abstract

The invention relates to a determination method and a determination apparatus for a contact angle and interfacial tension. The apparatus for determining interfacial tension and a contact angle through a vertical rotary sessile drop process comprises (a data processor,) a direct current servo motor, a hollow rotating shaft capable of being used for positioning and installing a sample tube, the sample tube having parallel windows, a light source having the two work modes of frequent flashing and steady burning and an image collector, wherein the rotating shaft is vertically arranged and vertically rotates around its vertical axis under the driving of the direct current servo motor. According to the invention, parameter fitting is carried out after digital rotator coordinate processing is carried out on images of drop bubbles that vertically rotate and contact with a determination base surface of the rotating tube so as to obtain sufficiently accurate interfacial tension values and values of curvature radius of vertexes of the drop bubbles, and then contact angles are calculated according to a sessile drop contact angle calculation formula; spans of interfacial tension and density difference among fluids in a system to be determined can be substantially increased, and the determination method in the invention has a wider application scope compared to conventional methods.

Description

The assay method of contact angle and interfacial tension and determinator
Technical field
The present invention relates to a kind of contact angle in surface chemistry field and the determination techniques of interfacial tension, particularly relate to a kind of vertical rotary and to lie the method and apparatus dripping and measure contact angle and interfacial tension.
Background technology
In surface chemistry and widely in related application field, the assay method of contact angle is a lot, but the overwhelming majority wherein is not suitable for ultralow interfacial tension system.And in raising oil recovery, particularly chemical flooding, the importance of wetting state (contact angle) is at least not less than the importance of interfacial tension.Current in the research work of raising oil recovery, the instrument of various mensuration interfacial tension is full of among laboratory, but does not have a suitable instrument that can measure low interfacial tension system contact angle.
For this reason, inventor has proposed method and the device that is relatively applicable to the horizontal rotary drop method mensuration contact angle of above-mentioned system, and its patent No. is ZL02158756.6.Existing horizontal rotary drop measures interfacial tension and measures in the method for contact angle, describes in the second order differential equation of droplet profile, only considers the effect of interfacial tension and centrifugal force, and have ignored gravity.That is normally used horizontal rotary drips the computing formula measuring interfacial tension and contact angle is approximate in theory, and this gravity of ignoring brings a lot of problem sometimes, can cause the inaccurate of final measurement.Although the simple method of dripping of lying measures interfacial tension and contact angle only need consider interfacial tension and Action of Gravity Field, be not suitable for ultralow liquid/liquid interface tension force system and the higher but system that liquid/liquid density difference is very little of interfacial tension.At list of references (1)in, Aronson and Princent is by describing the shape of vertical rotary meniscus to the numerical solution of the Laplace capillary equation under vertical rotary state.Although a kind of method measuring interfacial tension can be developed accordingly, be only limitted to the transparent and situation of complete wetting glass round tube of dense fluids, more can not be used for measuring contact angle.
Summary of the invention
Fundamental purpose of the present invention is, overcome the defect that existing contact angle determination method exists, and assay method and the determinator of a kind of new contact angle and interfacial tension are provided, technical matters to be solved makes it be taken into account by gravity factor that contact is dripped, thus determine surface tension and contact angle more accurately, what greatly extend contact angle can measurement range.
The object of the invention to solve the technical problems realizes by the following technical solutions.A kind of vertical rotary method proposed according to the present invention measures the device of contact angle, (comprising data processor)?, DC servo motor, turning axle, sample hose, light source and image acquisition device, described turning axle is vertical setting, and be connected with DC servo motor, under the driving of DC servo motor, turning axle carries out vertical rotary around its vertical axis.
Further, aforesaid vertical rotary method measures the device of contact angle, and described turning axle has the inner space for load sample pipe, and the cross sectional shape of this inner space is circular, oval or rectangle; The sidewall of this turning axle offers two relative can the windowing of printing opacity; Described sample hose has two opposing parallel logical light faces; Sample hose upper end has blocking, and the lower surface of this blocking is provided with solid-based surface layer; The material of described solid-based surface layer is glass, metal, paraffin or polymkeric substance or material needed for other.Described light source and image acquisition device are arranged at the both sides of turning axle, and described light source is stroboscopic lamp and/or long bright light, use stroboscopic lamp, use normal bright light when rotating speed equals zero when rotating speed is non-vanishing.Described image acquisition device is ccd video camera or CCD camera.
A kind of vertical rotary proposed according to the present invention method of dripping of lying measures the method for interfacial tension and contact angle, and under drop-wise state is lain in rotation, first fluid is the fluid that density is higher, and has certain transparency; Second fluid density, lower than first fluid, also can be referred to as environment liquid, and two kinds of immiscible fluids and a kind of solid (basal plane) form wetting (or claiming a contact angle) system; The method comprises the following steps:
First fluid and second fluid is loaded in sample hose, the density of first fluid is greater than the density of second fluid, the volume of second fluid controlled well makes second fluid when rotating along with sample hose, what second fluid was formed drip bubble do not contact with sample tube wall and with solid-based face layer contacts;
Sample hose is carried out vertical rotary, and is gathered the contour images of second fluid by image acquisition device after fluid stable in sample hose;
Be that initial point sets up cylindrical-coordinate system to the minimum point of above-mentioned contour images, with i.e. gravity direction for z-axis, horizontal direction is x-axis, and the outline line of osculatory on this coordinate system that digitized processing obtains first fluid and second fluid joint is carried out to contour images, symmetry according to outline line is optimized the direction of z-axis and the position of true origin, thus each point on this outline line is had enough coordinates accurately that this circular cylindrical coordinate fastens;
According to vertical rotary Laplace capillary equation (formula 1), there is a lot of method can optimization interfacial tension γ and vertex curvature radius b; Be wherein carry out numerical solution-parameter fitting by the part or all of coordinate of this outline line, draw interfacial tension γ and vertex curvature radius b; Or go out polynomial expression z=f (x) (order of such as x is six times) according to the coordinate fitting of outline line, return out optimum γ and b according to the approximate solution of multiple spot on outline line;
Described vertical rotary Laplace capillary equation is:
γ ( 1 R 1 + 1 R 2 ) = 2 γ b - 1 2 Δρ ω 2 x 2 + Δρgz - - - ( 1 )
The differential form of formula (1) is
z ′ ′ ( 1 + z ′ 2 ) 3 / 2 + z ′ x ( 1 + z ′ 2 ) 1 / 2 = Δρ γ ( gz - ω 2 x 2 2 ) + b γ - - - ( 1 a )
Formula (1) and the middle γ of formula (1a) are interfacial tension, and Δ ρ is the density of first fluid and the density difference of second fluid, and ω is the angular velocity of the rotation of sample hose, and g is the on-site acceleration of gravity of experiment, and b is the radius-of-curvature at initial point place.
The vertical rotary method that the present invention proposes measures the method for contact angle, it is characterized in that comprising the following steps:
Carry out method according to claim 8 and obtain interfacial tension γ and vertex curvature radius b;
Then calculate first fluid, second fluid according to formula (2) to connect with solid basal plane three-phase the contact angle θ of contact C,
sin θ = X c - 1 4 α X c 3 + 1 2 π X c β ( π X c 2 Z c - V ) - - - ( 2 )
In formula (2), X c=x c/ b, x cfor the X-axis coordinate figure of a C; Z c=z c/ b, z cfor the z-axis coordinate figure of a C, V=v/b 3, v is the volume dripping bubble, and this volume can record by when adding drop, also can carry out volume integral according to formula (2a) or formula (2b) to a bubble outline line and obtain;
v = π ∫ 0 z c x 2 dz - - - ( 2 a )
Or
V = π ∫ 0 Z c X 2 dZ - - - ( 2 b )
α is by formula 2 c ( α = 1 2 Δρ ω 2 b 3 / γ ) Obtain;
β is by formula 2d(β=Δ ρ gb 2/ γ) obtain.
Wherein: γ is interfacial tension, Δ ρ is the density of first fluid and the density difference of second fluid, and ω is the angular velocity of the rotation of sample hose, and b is the radius-of-curvature at initial point place.
When rotational speed omega=0, formula (3) is adopted to calculate contact angle:
sin θ = X c + 1 2 π X c β ( π X c 2 Z c - V ) - - - ( 3 )
The present invention is by steeping after image carries out the process of digitizing rotary body coordinate to vertical rotary with swivelling pipe dripping of measuring that basal plane contacts, choose and drip bubble suitably part (or whole), Laplace capillary equation (formula 1) (the considering interfacial tension, gravity and centrifugal force) that dripped bubble by numerical solution vertical rotary carries out parameter fitting simultaneously, obtain enough accurate interfacial tension value and drip the numerical value of radius-of-curvature b on bubble summit, then lie according to the rotation that we derive and drip a contact angle computing formula (2) and obtain contact angle θ.The method that the present invention provides, greatly can increase the span of interfacial tension and density difference between tested systems fluid, have more wide range of application than existing method.
By technique scheme, the present invention at least has following advantages: the vertical rotary method of dripping of lying take into account the factor of gravity at the Laplace capillary equation calculating interfacial tension and contact angle, thus ensure that vertical rotary that the present invention the proposes method of dripping of lying measures interfacial tension and contact angle is accurate in theory, instead of approximate.The contact angle computing formula that the present invention proposes makes to be lain by vertical rotary to drip (bubble) and measure contact angle and become possibility, Simultaneously test result is more reliable, particularly for ultralow interfacial tension system, or interfacial tension is higher and the system advantage that density difference is very little is more obvious.
Above-mentioned explanation is only the general introduction of technical solution of the present invention, in order to better understand technological means of the present invention, and can be implemented according to the content of instructions, coordinates accompanying drawing to be described in detail as follows below with preferred embodiment of the present invention.
Accompanying drawing explanation
Fig. 1 is the structural representation of contact angle determination device.
Fig. 2 is the structural representation of the embodiment of turning axle.
The cross sectional representation of Fig. 3 and Fig. 4 sample hose two embodiments.
Fig. 5 is the longitudinal profile schematic diagram of sample hose.
The schematic diagram dripping the image of bubble of steady state (SS) when Fig. 6 is vertical rotary.
Embodiment
For further setting forth the present invention for the technological means reaching predetermined goal of the invention and take and effect, below in conjunction with accompanying drawing and preferred embodiment, to the contact angle proposed according to the present invention and the assay method of interfacial tension and its embodiment of determinator, structure, feature and effect thereof, be described in detail as follows.
Refer to shown in Fig. 1, the structural representation of present pre-ferred embodiments contact angle determination device, this device its mainly comprise: data processor 1, DC servo motor 2, turning axle 3, sample hose 4, light source 5 and image acquisition device 6.Described data processor 1 is connected to DC servo motor 2, light source 5 and image acquisition device 6.DC servo motor 2 is connected with turning axle 3, carries out vertical rotary for driving turning axle around its vertical axis.Sample hose 4 inserts in turning axle with special angle, and along with turning axle carries out vertical rotary, described special angle is for guaranteeing that the light of light source 5 can through sample hose and be standard received by image acquisition device.Light source 5 and image acquisition device 6 are positioned at the both sides of turning axle and can slide to obtain clear, complete image along the direction parallel with turning axle.Particularly when the fluid that density is high is opaque, the static method of dripping of lying must be used to complete mensuration work, and now opaque higher density fluid drips and sinks to the below of sample hose.
As shown in Figures 2 and 3, described turning axle 3 is hollow form, and its inner space is used for load sample pipe 4.The interior space shape of turning axle is circular, oval or rectangle, for holding the sample hose of circle, ellipse or rectangle.The sidewall of this turning axle offers relative can printing opacity window 31, this is windowed can be uncovered shape, also can by transparent material shutoff.The light that light source 5 is sent 31 to be irradiated on image acquisition device 6 by described windowing.
As shown in Figure 4, Figure 5 and Figure 6, the structure of described sample hose 4 can adopt the sample hose structure disclosed in No. 02158756.6, Chinese patent.In the embodiment of the application, as shown in Figure 6, it is the longitudinal profile schematic diagram of sample hose, this sample hose has two opposing parallel logical light faces 41, sample hose upper end has blocking 42, and the lower surface of this blocking 42 is provided with solid-based surface layer 43, in reality test, need the mensuration of the material of what material being carried out to contact angle, then selecting this material, such as, is glass, metal, paraffin, polymkeric substance etc.Blocking 42 on sample hose top is outer is also provided with pipe lid 44, for keeping the stable of blocking.Be provided with sample plug 45 in the bottom of sample hose, this sample plug is generally silicon rubber, and it had both had and to add contact after good sealing can also be pierced and drip a sample.Parallel logical light face 41 on the sidewall of sample hose 4, when sample hose 4 loads in turning axle, windowing of described logical light face 41 and turning axle is 31 corresponding, thus the light that light source 5 can be made to send can be irradiated on image acquisition device 6 through sample hose and turning axle.The cross sectional shape of sample hose 4 can be rectangle, the circle of part and the ellipse of part.The effect in the logical light face on sample hose sidewall is incident directional light is not reflected, thus on image acquisition device, more can be met the image of liquid time of day in sample hose.Contact is dripped 10 and is connected with solid-based surface layer and another liquid in testing.
DC servo motor 2 is connected with turning axle 3, rotates for driving turning axle.This DC servo motor 2 can carry out controlled rotation under the control of data processor 1, and the instruction that can send according to data processor rotates, rotating speed such as per minute.
Described light source 5 can be stroboscopic lamp, and it is according to the frequency of setting or the flash of light providing certain frequency according to the trigger rate signal that data processor 1 sends.Image acquisition device 6 now can be ccd video camera, can obtain image clearly when this stroboscopic lamp glistens.Light source 5 can also be normal bright lamp, namely it can at test period continuous illumination, image acquisition device 6 is now then CCD camera, the speed of controller shutter and the opportunity of exposure, make its turning axle to window with it just pair time, start shutter to expose, then can photograph the transmitted light through sample that light source 5 sends, thus the image of sample profile can be obtained.
This data processor 1 can control the image acquisition process of image acquisition device 6, and processes gathered image.It has the function of the action controlling image acquisition device, DC servo motor and light source, makes image acquisition device can obtain the profile photograph contacting and drip under setting speed.This data processor processes the image gathered, and carries out digitizing, then carry out mathematical computations to the image that contact is dripped, the surface tension that final acquisition contact is dripped and contact angle.
The present invention also proposes the assay method of a kind of surface tension of liquid and contact angle, and it adopts above-mentioned determinator.This assay method specifically comprises the following steps:
1, in sample hose, add the immiscible first fluid of two-phase and second fluid, such as first fluid is that (density is ρ to water 2) second fluid is air or crude oil isodensity (ρ 1) material less than water, two-phase density difference Δ ρ=ρ 21>0.The upper end of sample hose is the solid basal plane of a level (with rotational axis vertical).Sample hose is made to be that axle carries out rotating (i.e. vertical rotary) with gravity direction, and the size adjusting the little drop of density or bubble (be referred to as below and drip bubble) makes a bubble for interior phase not contact with tube wall with the rotating speed of sample hose and contacts with basal plane, and the lower end of dripping bubble is free end.
2, start light source and image acquisition device, the image dripping bubble of picked-up steady state (SS) obtains the outline line dripped under the rotation status of bubble, as shown in Figure 6.
3, be initial point O(0 to the minimum point of above-mentioned contour images, 0) cylindrical-coordinate system is set up, with i.e. gravity direction for z-axis, horizontal direction is x-axis, and the outline line of osculatory on this coordinate system that digitized processing obtains first fluid and second fluid joint is carried out to contour images, symmetry according to outline line is optimized the direction of z-axis and the position of true origin, thus each point on this outline line is had enough coordinates accurately that this circular cylindrical coordinate fastens;
According to vertical rotary Laplace capillary equation (formula 1), there is a lot of method can calculate interfacial tension γ and vertex curvature radius b.Wherein the most accurate method carries out numerical solution-parameter fitting by the part or all of coordinate of this outline line, draws interfacial tension and vertex curvature radius b.Also can go out polynomial expression z=f (x) (order of such as x is six times) according to the coordinate fitting of outline line, return out optimum γ and b according to the approximate solution of multiple spot on outline line.
Vertical rotary Laplace capillary equation is
γ ( 1 R 1 + 1 R 2 ) = 2 γ b - 1 2 Δρ ω 2 x 2 + Δρgz - - - ( 1 )
The differential form of equation 1 is
z ′ ′ ( 1 + z ′ 2 ) 3 / 2 + z ′ x ( 1 + z ′ 2 ) 1 / 2 = Δρ γ ( gz - ω 2 x 2 2 ) + b γ - - - ( 1 a )
In formula (1), γ is interfacial tension, Δ ρ is the density of first fluid and the density difference of second fluid, ω is the angular velocity of the rotation of sample hose, g is the on-site acceleration of gravity of behavioral test, b is the radius-of-curvature at initial point place, z ' is the first differential of z in formula (1), z " is the second-order differential of z in formula (1).
Then calculate first fluid, second fluid according to formula (2) to connect with solid basal plane three-phase contact C (x c, z c) contact angle θ,
sin θ = X c - 1 4 α X c 3 + 1 2 π X c β ( π X c 2 Z c - V ) - - - ( 2 )
In formula (2), X c=x c/ b, x cfor a C abscissa value; Z c=z c/ b, z cfor a C ordinate value, V=v/b 3, v is the volume dripping bubble, and this volume v by recording when adding drop (if dripping bubble constancy of volume in mensuration process), also can obtain by carrying out volume integral to a bubble outline line;
v = π ∫ 0 z c x 2 dz - - - ( 2 a )
Or
V = π ∫ 0 Z c X 2 dZ - - - ( 2 b )
α is by formula ( α = 1 2 Δρ ω 2 b 3 / γ ) - - - ( 2 c ) Obtain,
β is by formula (β=Δ ρ gb 2/ γ) (2d) obtain.
Wherein: γ is interfacial tension, Δ ρ is the density of first fluid and the density difference of second fluid, and ω is the angular velocity of the rotation of sample hose, and b is the radius-of-curvature at initial point place.
When rotational speed omega=0, obtain lying and drip contact angle determination formula:
sin θ = X c + 1 2 π X c β ( π X c 2 Z c - V ) - - - ( 3 )
Owing to considering the impact of dripping the gravity of bubble of vertical rotary, the three-phase contact angle that the method that the present invention proposes measures is more accurate.
By the actual measurement to Air-Water-paraffin, Air-Water-argent, Air-Water-polymethylmethacrylate three-phase contact angle, achieve good measurement result, as table 1.
Table 1
In the application, in all formula, the unit of physical quantity all adopts International System of Units.
The above, it is only preferred embodiment of the present invention, and be not used to limit the present invention, any those skilled in the art, do not departing within the scope of technical solution of the present invention, make a little change when the technology contents of above-mentioned announcement can be utilized or be modified to the Equivalent embodiments of equivalent variations, in every case be the content not departing from technical solution of the present invention, the any simple modification done above embodiment according to technical spirit of the present invention, equivalent variations and modification, all still belong in the scope of technical solution of the present invention.

Claims (9)

1. the device of a vertical rotary method mensuration contact angle, comprise data processor, DC servo motor, turning axle, sample hose, light source and image acquisition device, it is characterized in that, described turning axle is vertically arrange, under the driving of DC servo motor, turning axle vertically rotates around its vertical axis;
Described turning axle is connected with described sample hose, vertically rotates for driving described sample hose;
The sample hose upper end of described vertical rotation has blocking, and the lower surface of this blocking is provided with solid-based surface layer; Described sample hose is for loading first fluid and second fluid, and the volume of second fluid controlled well makes second fluid when rotating along with sample hose, what second fluid was formed drip bubble do not contact with sample tube wall and with solid-based face layer contacts;
Described data processor is connected to DC servo motor, light source and image acquisition device, for controlling the action of image acquisition device, DC servo motor and light source, to realize controlling the profile photograph that described image acquisition device obtains second fluid under setting speed, described data processor processes the image gathered, digitizing is carried out to the image of second fluid, then carry out mathematical computations, surface tension and the contact angle of bubble are dripped in final acquisition.
2. vertical rotary method according to claim 1 measures the device of contact angle, it is characterized in that, described turning axle has the inner space for load sample pipe, the cross sectional shape of this inner space is circular, oval or rectangle, and there is positioning function, the direction of windowing of the parallel windows of the sample hose of insertion and turning axle is consistent.
3. vertical rotary method according to claim 2 measures the device of contact angle, it is characterized in that, the sidewall of this turning axle offers two parallel relatively can the windowing of printing opacity.
4. the vertical rotary method according to any one of claim 1-3 measures the device of contact angle, and it is characterized in that, described sample hose has two opposing parallel logical light faces.
5. vertical rotary method according to claim 4 measures the device of contact angle, and it is characterized in that, the material of described solid-based surface layer is glass, metal, paraffin, polymkeric substance or other desired material.
6. vertical rotary method according to claim 1 measures the device of contact angle, it is characterized in that, described light source and image acquisition device are arranged at the both sides of turning axle, and described light source is stroboscopic lamp and/or normal bright lamp, and described image acquisition device is ccd video camera or CCD camera.
7. use the device described in any one of claim 1-6 to carry out vertical rotary method and measure a capillary method, the method comprises the following steps:
First fluid and second fluid is loaded in sample hose, the volume of second fluid controlled well makes second fluid when rotating along with sample hose, second fluid formed drip bubble do not contact with sample tube wall and with solid-based face layer contacts, wherein solid-based surface layer is arranged on the lower surface of described sample hose upper end blocking;
Sample hose is vertically rotated, and is gathered the contour images of second fluid by image acquisition device after fluid stable in sample hose;
Be that initial point sets up cylindrical-coordinate system to the minimum point of above-mentioned contour images, with i.e. gravity direction for z-axis, horizontal direction is x-axis, and the outline line of osculatory on this coordinate system that digitized processing obtains first fluid and second fluid joint is carried out to contour images, symmetry according to outline line is optimized the direction of z-axis and the position of true origin, thus each point on this outline line is had enough coordinates accurately that this circular cylindrical coordinate fastens;
According to vertically rotating Laplace capillary equation, carrying out numerical solution-parameter fitting by the part or all of coordinate of this outline line, drawing interfacial tension γ and vertex curvature radius b; Or go out polynomial expression z=f (x) according to the coordinate fitting of outline line, return out optimum γ and b according to the approximate solution of multiple spot on outline line;
Described vertical rotation Laplace capillary equation is:
γ ( 1 R 1 + 1 R 2 ) = 2 γ b - 1 2 Δ ρω 2 x 2 + Δρgz - - - ( 1 )
The differential form of formula (1) is
z ′ ′ ( 1 + z ′ 2 ) 3 / 2 + z ′ x ( 1 + z ′ 2 ) 1 / 2 = Δρ γ ( gz - ω 2 x 2 2 ) + b γ - - - ( 1 a )
Formula (1) and the middle γ of formula (1a) are interfacial tension, and Δ ρ is the density of first fluid and the density difference of second fluid, and ω is the angular velocity of the rotation of sample hose, and g is the on-site acceleration of gravity of experiment, and b is the radius-of-curvature at initial point place, R 1and R 2for the principal radius of curvature at interface, point (x, z) place.
8. vertical rotary method measures a method for contact angle, it is characterized in that comprising the following steps:
Carry out method according to claim 7 and obtain interfacial tension γ and vertex curvature radius b;
Then calculate first fluid, second fluid according to formula (2) to connect with solid basal plane three-phase the contact angle θ of contact C,
sin θ = X c - 1 4 αX c 3 + 1 2 π X c β ( π X c 2 Z c - V ) - - - ( 2 )
In formula (2), X c=x c/ b, x cfor the X-axis coordinate figure of a C; Z c=z c/ b, z cfor the z-axis coordinate figure of a C, V=v/b 3, v is the volume dripping bubble, and this volume records by when adding drop, or carries out volume integral according to formula (2a) or formula (2b) obtain dripping a bubble outline line;
v = π ∫ 0 z c x 2 dz - - - ( 2 a )
Or
V = π ∫ 0 Z c X 2 dZ - - - ( 2 b )
α is obtained by formula (2c);
β is obtained by formula (2d);
α = 1 2 Δ ρω 2 b 3 / γ - - - ( 2 c )
β=Δρgb 2/γ (2d)
Wherein: γ is interfacial tension, Δ ρ is the density of first fluid and the density difference of second fluid, and ω is the angular velocity of the rotation of sample hose, and b is the radius-of-curvature at initial point place.
9. vertical rotary method according to claim 8 measures the method for contact angle, it is characterized in that, when rotational speed omega=0, adopts formula (3) to calculate contact angle:
sin θ = X c + 1 2 πX c β ( πX c 2 Z c - V ) - - - ( 3 ) .
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CN105675452A (en) * 2016-03-14 2016-06-15 西安近代化学研究所 Coating layer material anti-migration performance representation method based on contact angle measurement
CN105675452B (en) * 2016-03-14 2018-07-31 西安近代化学研究所 A kind of coating layer material ability of resisting to migration characterizing method based on Contact-angle measurement

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