CN102749269A - Determination method and determination apparatus for contact angle and interfacial tension - Google Patents

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 the contact angle in a kind of surface chemistry field and the determination techniques of interfacial tension, particularly relate to a kind of vertical rotation and lie and drip to measure the method and apparatus of contact angle and interfacial tension.

Background technology

In surface chemistry and widely in the related application field, the measurement of contact angle method is a lot, yet the overwhelming majority wherein is not suitable for the ultralow interfacial tension system.And improving in the oil recovery, particularly chemical flooding, the importance of wetting state (contact angle) is not less than the importance of interfacial tension at least.Current the instrument of various mensuration interfacial tensions is full of among the laboratory in improving the oil recovery research work, but does not have the suitable instrument that can measure low interfacial tension system contact angle.

For this reason, the inventor has proposed the method and the device that relatively are fit to the horizontal rotary drop method mensuration contact angle of above-mentioned system, and its patent No. is ZL02158756.6.Existing horizontal rotary drop is measured interfacial tension and is measured in the method for contact angle, describes in the second order differential equation of droplet profile, only considers interfacial tension and action of centrifugal force, and has ignored gravity.That is to say that normally used level revolves a computing formula that drip to measure interfacial tension and contact angle and be similar in theory, this gravity of ignoring brings a lot of problems sometimes, can cause the inaccurate of final measurement.Though the simple method of dripping of lying measures interfacial tension and contact angle only need be considered interfacial tension and action of gravity, be not suitable for higher but the system that liquid/liquid density difference is very little of ultralow liquid/liquid interface tension force system and interfacial tension.At list of references ⁽¹⁾In, Aronson and Princent are through having described the shape of vertical rotation meniscus to the numerical solution of the Laplace capillary equation under the vertical rotation status.Though can develop a kind of method of measuring interfacial tension in view of the above, only limit to the situation of the transparent and complete wetting glass round tube of dense fluids, more can not be used to measure contact angle.

Summary of the invention

Fundamental purpose of the present invention is; Overcome the defective that existing contact angle determination method exists; And a kind of new contact angle and the assay method and the determinator of interfacial tension are provided; Technical matters to be solved is to make it will contact the gravity factor that drips to take into account, thereby determines surface tension and contact angle more accurately, but has expanded the measurement range of contact angle greatly.

The object of the invention and solve its technical matters and adopt following technical scheme to realize.Measure the device of contact angle according to a kind of vertical rotary process of the present invention's proposition; (comprising data processor)?, DC servo motor, turning axle, sample hose, light source and image acquisition device; Described turning axle is vertical the setting; And be connected with DC servo motor, under the driving of DC servo motor, turning axle vertically rotates around its vertical axis.

Further, the device of contact angle is measured in aforesaid vertical rotary process, and described turning axle has the inner space that is used for the load sample pipe, and the cross sectional shape of this inner space is circle, ellipse or rectangle; Offer on the sidewall of this turning axle two relative can printing opacity window; Described sample hose has two logical light faces of opposing parallel; The sample hose upper end has blocking, and the lower surface of this blocking is provided with the solid-based surface layer; The material of described solid-based surface layer is glass, metal, paraffin or polymkeric substance or other required materials.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 lamp, when rotating speed is non-vanishing, uses stroboscopic lamp, uses normal bright lamp when rotating speed equals zero.Described image acquisition device is ccd video camera or CCD camera.

A kind of vertical rotation that proposes according to the present invention method of dripping of lying is measured the method for interfacial tension and contact angle, and first fluid is the higher fluid of density under a state is lain in rotation, and has certain transparency; Second fluid density is 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) constitute wetting (or claiming a contact angle) system; This method may further comprise the steps:

In sample hose, pack into the first fluid and second fluid; 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, and the bubble that drips that second fluid forms does not contact and contacts with the solid-based surface layer with the sample tube wall;

Sample hose is vertically rotated, and gather the contour images of second fluid behind the fluid stable in sample hose by image acquisition device;

Minimum point to above-mentioned contour images is that initial point is set up cylindrical-coordinate system; Being that gravity direction is the z axle; Horizontal direction is the x axle; And contour images carried out the outline line of osculatory on this coordinate system that digitized processing obtains the first fluid and the second fluid joint, and according to the symmetry of outline line the direction of z axle and the position of true origin are optimized, thus the enough coordinates accurately that make that each point on this outline line has all that this circular cylindrical coordinate fastens;

According to vertical rotation Laplace capillary equation (formula 1), there are a lot of methods to optimize and interfacial tension γ and vertex curvature radius b; Wherein a kind of is that part or all of coordinate through this outline line carries out numerical solution-parameter fitting, draws interfacial tension γ and vertex curvature radius b; Perhaps the coordinate fitting according to outline line goes out a polynomial expression z=f (x) (for example the order of x is six times), returns out the γ and the b of optimum according to the approximate solution of multiple spot on the outline line;

Said vertical rotation Laplace capillary equation is:

$\mathrm{\γ}(\frac{1}{R_1}+\frac{1}{R_2})=\frac{2\mathrm{\γ}}{b}-\frac{1}{2}\mathrm{\Δ\ρ}{\mathrm{\ω}}^2{x}^2+\mathrm{\Δ\ρgz}---\left(1\right)$

The differential form of formula (1) does

$\frac{z^{\′\′}}{{(1+{z^{\′}}^2)}^{3/2}}+\frac{z^{\′}}{x{(1+{z^{\′}}^2)}^{1/2}}=\frac{\mathrm{\Δ\ρ}}{\mathrm{\γ}}(\mathrm{gz}-\frac{{\mathrm{\ω}}^2{x}^2}{2})+\frac{b}{\mathrm{\γ}}---\left(1a\right)$

γ is an interfacial tension in formula (1) and the formula (1a), 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 method of contact angle is measured in the vertical rotary process that the present invention proposes, and it is characterized in that may further comprise the steps:

Carry out the described method of claim 8 and obtain interfacial tension γ and vertex curvature radius b;

Calculate the join contact angle θ of contact C of first fluid, second fluid and solid basal plane three-phase according to formula (2) then,

$\sin \mathrm{\&theta;}=X_c-\frac{1}{4}\mathrm{\&alpha;}{\mathrm{<figure-callout\; id="3"\; label="X\; c"\; filenames="HDA00001853958200011.png,HDA00001853958200012.png"\; state="\{\{state\}\}">X</figure-callout>}}_c^{}+\frac{1}{2\mathrm{\&pi;}{X}_c}\mathrm{\&beta;}(\mathrm{\&pi;}{X}_c^2{Z}_c-V)---\left(2\right)$

In the formula (2), X _c=x _c/ b, x _cX axial coordinate value for a C; Z _c=z _c/ b, z _cBe the z axial coordinate value of a C, V=v/b ³, v is for dripping the volume of bubble, and this volume can record when adding drop, also can carry out volume integral and obtains dripping a bubble outline line according to formula (2a) or formula (2b);

$v=\mathrm{\&pi;}{\&Integral;}_0^{z_c}{x}^2\mathrm{dz}---\left(2a\right)$

Or

$V=\mathrm{\&pi;}{\&Integral;}_0^{Z_c}{X}^2\mathrm{dZ}---\left(2b\right)$

α is by formula $2c(\mathrm{\&alpha;}=\frac{1}{2}\mathrm{\&Delta;\; \&rho;}{\mathrm{\&omega;}}^2{\mathrm{<figure-callout\; id="3"\; label="b"\; filenames="HDA00001853958200011.png,HDA00001853958200012.png"\; state="\{\{state\}\}">b</figure-callout>}}^3/\mathrm{\&gamma;})$ Obtain;

β is by formula 2d (β=Δ ρ gb ²/ γ) obtain.

Wherein: γ is an 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 b is the radius-of-curvature at initial point place.

When rotational speed omega=0, employing formula (3) calculates contact angle:

$\sin \mathrm{\&theta;}=X_c+\frac{1}{2\mathrm{\&pi;}{X}_c}\mathrm{\&beta;}(\mathrm{\&pi;}{X}_c^2{Z}_c-V)---\left(3\right)$

After the present invention carries out the processing of digitizing rotary body coordinate through the bubble image that contacts with swivelling pipe mensuration basal plane to vertical rotation; Choose and drip bubble suitable part (or all); The Laplace capillary equation (formula 1) (considering interfacial tension, gravity and centrifugal force simultaneously) that drips bubble through the vertical rotation of numerical solution carries out parameter fitting; Obtain enough the numerical value of accurate interfacial tension value and the radius-of-curvature b that drips the bubble summit, the rotation of deriving according to us is again lain and is dripped a contact angle computing formula (2) and obtain contact angle θ.The method that the present invention provides can increase the span of interfacial tension and density difference between the tested systems fluid greatly, has more wide applications than existing method.

By technique scheme; The present invention has advantage at least: vertically rotate the method for dripping of lying has been considered gravity at the Laplace capillary equation that calculates interfacial tension and contact angle factor; The method of dripping is measured interfacial tension and contact angle is accurate in theory thereby the vertical rotation that has guaranteed the present invention's proposition is lain, rather than approximate.The contact angle computing formula that the present invention proposes makes to lie through vertical rotation drips (bubble) and measures contact angle and become possibility; It is more reliable to measure the result simultaneously; Particularly for the ultralow interfacial tension system, or interfacial tension is higher and system advantage that density difference is very little is more obvious.

Above-mentioned explanation only is the general introduction of technical scheme of the present invention, understands technological means of the present invention in order can more to know, and can implement according to the content of instructions, below with preferred embodiment of the present invention and conjunction with figs. specify as after.

Description of drawings

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 two embodiment of Fig. 4 sample hose.

Fig. 5 is the longitudinal profile synoptic diagram of sample hose.

Fig. 6 is the synoptic diagram of the image that drips bubble of steady state (SS) when vertically rotating.

Embodiment

Reach technological means and the effect that predetermined goal of the invention is taked for further setting forth the present invention; Below in conjunction with accompanying drawing and preferred embodiment; To the contact angle and assay method and its embodiment of determinator, structure, characteristic and the effect thereof of interfacial tension that proposes according to the present invention, specify as after.

See also shown in Figure 1, the structural representation of preferred embodiment contact angle determination device of the present invention, it mainly comprises this device: 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, is used for the driven in rotation axle and vertically rotates around its vertical axis.Sample hose 4 inserts in the turning axle with special angle, and along with turning axle vertically rotates, said special angle is that the light of guaranteeing light source 5 can see through sample hose and is standard by image acquisition device is received.Light source 5 is positioned at the both sides of turning axle with image acquisition device 6 and can slides so that obtain clear, complete image with the direction of rotating shaft parallel on the edge.Particularly when the high fluid of density is opaque, must use the static method of dripping of lying to accomplish mensuration work, opaque higher density fluid dripped and sank to the below of sample hose this moment.

As shown in Figures 2 and 3, described turning axle 3 is a hollow form, and its inner space is used for load sample pipe 4.The inner space of turning axle is shaped as circle, ellipse or rectangle, is used to hold circle, the oval perhaps sample hose of rectangle.Offer on the sidewall of this turning axle relative can printing opacity window 31, this is windowed can be uncovered shape, also can be by in the transparent material shutoff.Make light that light source 5 sends 31 shine on the image acquisition device 6 through described windowing.

Like Fig. 4, Fig. 5 and shown in Figure 6, the structure of described sample hose 4 can adopt No. 02158756.6 disclosed sample hose structure of Chinese patent.In the application's embodiment, as shown in Figure 6, be the longitudinal profile synoptic diagram of sample hose; This sample hose has two logical light faces 41 of opposing parallel; The sample hose upper end has blocking 42, and the lower surface of this blocking 42 is provided with solid-based surface layer 43, in the reality test, need carry out measurement of contact angle to the material of what material; Then selecting this material for use, for example is glass, metal, paraffin, polymkeric substance or the like.Outside the blocking 42 on sample hose top, also be provided with pipe and cover 44, be used to keep 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 good sealing property can also be pierced a back adding contact sample.Parallel logical light face 41 on the sidewall of sample hose 4, in the time of in sample hose 4 is packed turning axle into, windowing of described logical light face 41 and turning axle is 31 corresponding, thus the light that light source 5 is sent can pass through sample hose and turning axle shines on the image acquisition device 6.The cross sectional shape of sample hose 4 can be the circular and ellipse partly of rectangle, part.The effect of the logical light face on the sample hose sidewall is to make the directional light of incident not reflect, thereby can on image acquisition device, be met the image of liquid time of day in the sample hose more.Contact is dripped 10 and in test, is joined with solid-based surface layer and another liquid.

DC servo motor 2 is connected with turning axle 3, is used for the driven in rotation axle and rotates.This DC servo motor 2 can carry out controlled rotation under the control of data processor 1, can be rotated according to the instruction that data processor sends, for example the rotating speed of per minute.

Described light source 5 can be stroboscopic lamp, and it provides the flash of light of certain frequency according to the frequency of setting or according to the triggering frequency signal that data processor 1 sends.The image acquisition device 6 of this moment can be ccd video camera, when this stroboscopic lamp flash of light, can obtain distinct image.Light source 5 can also be normal bright lamp; Be that it can be lasting luminous at test period, the image acquisition device 6 of this moment then is the CCD camera, the speed of controller shutter and the opportunity of exposure; Make its turning axle window with its over against the time; Start shutter and make public, then can photograph the transmitted light that light source 5 sends, thereby can obtain the image of sample profile through sample.

This data processor 1 can be controlled the image acquisition process of image acquisition device 6, and the image of being gathered is handled.The function that it has the action of control image acquisition device, DC servo motor and light source makes image acquisition device set the profile photo that the acquisition contact is dripped under the rotating speed.This data processor is handled the image of gathering, and the image that contact is dripped carries out digitizing, carries out mathematical computations then, surface tension and contact angle that final acquisition contact is dripped.

The present invention also proposes a kind of surface tension of liquid and measurement of contact angle method, and it adopts above-mentioned determinator.This assay method specifically may further comprise the steps:

1, in sample hose, add the two mutual immiscible first fluid and second fluids, for example first fluid is that (density is ρ to water ₂) second fluid is air or crude oil isodensity (ρ ₁) than the little material of water, two phase density difference Δ ρ=ρ ₂-ρ ₁>0.The upper end of sample hose is the solid basal plane of a level (vertical with turning axle).Making sample hose is that axle is rotated (promptly vertical rotation) with the gravity direction; And the rotating speed of the size of the little drop of adjustment density or bubble (below be referred to as drip bubble) and sample hose make in the bubble that drips of phase contact and contacts with basal plane with tube wall, and a lower end of steeping is a free end.

2, start light source and image acquisition device, the image that drips bubble of picked-up steady state (SS) obtains the outline line under the rotation status of bubble, and is as shown in Figure 6.

3, the minimum point to above-mentioned contour images is initial point O (0; 0) sets up cylindrical-coordinate system; To be that gravity direction is the z axle, horizontal direction is the x axle, and contour images is carried out the outline line of osculatory on this coordinate system that digitized processing obtains the first fluid and the second fluid joint; Symmetry according to outline line is optimized the direction of z axle and the position of true origin, thus the enough coordinates accurately that make that each point on this outline line has all that this circular cylindrical coordinate fastens;

According to vertical rotation Laplace capillary equation (formula 1), there are a lot of methods can calculate interfacial tension γ and vertex curvature radius b.Wherein the most accurate method is that the part or all of coordinate through this outline line carries out numerical solution-parameter fitting, draws interfacial tension and vertex curvature radius b.Also can go out a polynomial expression z=f (x) (for example the order of x is six times) according to the coordinate fitting of outline line, return out the γ and the b of optimum according to the approximate solution of multiple spot on the outline line.

Vertical rotation Laplace capillary equation does

$\mathrm{\&gamma;}(\frac{1}{R_1}+\frac{1}{R_2})=\frac{2\mathrm{\&gamma;}}{b}-\frac{1}{2}\mathrm{\&Delta;\&rho;}{\mathrm{\&omega;}}^2{x}^2+\mathrm{\&Delta;\&rho;gz}---\left(1\right)$

The differential form of equation 1 does

$\frac{z^{\&prime;\&prime;}}{{(1+{z^{\&prime;}}^2)}^{3/2}}+\frac{z^{\&prime;}}{x{(1+{z^{\&prime;}}^2)}^{1/2}}=\frac{\mathrm{\&Delta;\&rho;}}{\mathrm{\&gamma;}}(\mathrm{gz}-\frac{{\mathrm{\&omega;}}^2{x}^2}{2})+\frac{b}{\mathrm{\&gamma;}}---\left(1a\right)$

γ is an interfacial tension in the formula (1); 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, and g is the on-site acceleration of gravity of behavioral test, and b is the radius-of-curvature at initial point place; Z ' is the first order differential of z in the formula (1), z " is the second-order differential of z in the formula (1).

Calculate first fluid, second fluid and the solid basal plane three-phase contact C (x that joins according to formula (2) then _c, z _c) contact angle θ,

$\sin \mathrm{\&theta;}=X_c-\frac{1}{4}\mathrm{\&alpha;}{\mathrm{<figure-callout\; id="3"\; label="X\; c"\; filenames="HDA00001853958200011.png,HDA00001853958200012.png"\; state="\{\{state\}\}">X</figure-callout>}}_c^{}+\frac{1}{2\mathrm{\&pi;}{X}_c}\mathrm{\&beta;}(\mathrm{\&pi;}{X}_c^2{Z}_c-V)---\left(2\right)$

In the formula (2), X _c=x _c/ b, x _cBe a C abscissa value; Z _c=z _c/ b, z _cBe a C ordinate value, V=v/b ³, v is for dripping the volume of bubble, and this volume v can record (if drip in the mensuration process foam long-pending constant) when adding drop, also can be through carrying out volume integral and obtain dripping a bubble outline line;

$v=\mathrm{\&pi;}{\&Integral;}_0^{z_c}{x}^2\mathrm{dz}---\left(2a\right)$

Or

$V=\mathrm{\&pi;}{\&Integral;}_0^{Z_c}{X}^2\mathrm{dZ}---\left(2b\right)$

α is by formula $(\mathrm{\&alpha;}=\frac{1}{2}\mathrm{\&Delta;\; \&rho;}{\mathrm{\&omega;}}^2{\mathrm{<figure-callout\; id="3"\; label="b"\; filenames="HDA00001853958200011.png,HDA00001853958200012.png"\; state="\{\{state\}\}">b</figure-callout>}}^3/\mathrm{\&gamma;})---\left(2c\right)$ Obtain,

β is by formula (β=Δ ρ gb ²/ γ) (2d) obtain.

Wherein: γ is an 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 b is the radius-of-curvature at initial point place.

When rotational speed omega=0, obtain lying and drip a contact angle determination formula:

$\sin \mathrm{\&theta;}=X_c+\frac{1}{2\mathrm{\&pi;}{X}_c}\mathrm{\&beta;}(\mathrm{\&pi;}{X}_c^2{Z}_c-V)---\left(3\right)$

Because consider the influence of the gravity that drips bubble of vertical rotation, the three-phase contact angle that the method that the present invention proposes is measured is more accurate.

Actual measurement through to air-water-paraffin, air-water-argent, air-water-polymethylmethacrylate three-phase contact angle has obtained good mensuration result, like table 1.

Table 1

Among the application in all formula the unit of physical quantity all adopt International System of Units.

The above; It only is preferred embodiment of the present invention; Be not in order to limiting the present invention, anyly be familiar with the professional and technical personnel, in not breaking away from technical scheme scope of the present invention; When the technology contents of above-mentioned announcement capable of using is made a little change or is modified to the equivalent embodiment of equivalent variations; In every case be the content that does not break away from technical scheme of the present invention, to any simple modification, equivalent variations and modification that above embodiment did, all still belong in the scope of technical scheme of the present invention according to technical spirit of the present invention.

Claims (10)

1. the device of contact angle is measured in a vertical rotary process; 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 vertical the setting, and under the driving of DC servo motor, turning axle vertically rotates around its vertical axis.

2. the device of contact angle is measured in vertical rotary process according to claim 1; It is characterized in that; Described turning axle has the inner space that is used for the load sample pipe; The cross sectional shape of this inner space is circular, ellipse or rectangle, and has positioning function, and parallel windows and the opening direction of turning axle of the sample hose of insertion are consistent.

3. the device of contact angle is measured in vertical rotary process according to claim 2, it is characterized in that, offer on the sidewall of this turning axle two parallel relative can printing opacity window.

4. according to the device of each described vertical rotary process mensuration contact angle of claim 1-3, it is characterized in that described sample hose has two logical light faces of opposing parallel.

5. the device of contact angle is measured in vertical rotary process according to claim 4, it is characterized in that, described sample hose upper end has blocking, and the lower surface of this blocking is provided with the solid-based surface layer.

6. the device of contact angle is measured in vertical rotary process according to claim 5, it is characterized in that the material of described solid-based surface layer is the material of glass, metal, paraffin, polymkeric substance or actual needs.

7. the device of contact angle is measured in vertical rotary process according to claim 1; 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.

8. capillary method is measured in a vertical rotary process, and this method may further comprise the steps:

In sample hose, pack into the first fluid and second fluid, the volume of second fluid controlled well makes second fluid when rotating along with sample hose, and the bubble that drips that second fluid forms does not contact and contacts with the solid-based surface layer with the sample tube wall;

Sample hose is vertically rotated, and gather the contour images of second fluid behind the fluid stable in sample hose by image acquisition device;

Minimum point to above-mentioned contour images is that initial point is set up cylindrical-coordinate system; Being that gravity direction is the z axle; Horizontal direction is the x axle; And contour images carried out the outline line of osculatory on this coordinate system that digitized processing obtains the first fluid and the second fluid joint, and according to the symmetry of outline line the direction of z axle and the position of true origin are optimized, thus the enough coordinates accurately that make that each point on this outline line has all that this circular cylindrical coordinate fastens;

According to vertical rotation Laplace capillary equation (formula 1), there are a lot of methods to optimize and interfacial tension γ and vertex curvature radius b; Wherein a kind of is that part or all of coordinate through this outline line carries out numerical solution-parameter fitting, draws interfacial tension γ and vertex curvature radius b; Perhaps the coordinate fitting according to outline line goes out a polynomial expression z=f (x) (for example the order of x is six times), returns out the γ and the b of optimum according to the approximate solution of multiple spot on the outline line;

Said vertical rotation Laplace capillary equation is:

$\mathrm{\&gamma;}(\frac{1}{R_1}+\frac{1}{R_2})=\frac{2\mathrm{\&gamma;}}{b}-\frac{1}{2}\mathrm{\&Delta;\&rho;}{\mathrm{\&omega;}}^2{x}^2+\mathrm{\&Delta;\&rho;gz}---\left(1\right)$

The differential form of formula (1) does

$\frac{z^{\&prime;\&prime;}}{{(1+{z^{\&prime;}}^2)}^{3/2}}+\frac{z^{\&prime;}}{x{(1+{z^{\&prime;}}^2)}^{1/2}}=\frac{\mathrm{\&Delta;\&rho;}}{\mathrm{\&gamma;}}(\mathrm{gz}-\frac{{\mathrm{\&omega;}}^2{x}^2}{2})+\frac{b}{\mathrm{\&gamma;}}---\left(1a\right)$

γ is an interfacial tension in formula (1) and the formula (1a), 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.

9. the method for contact angle is measured in a vertical rotary process, it is characterized in that may further comprise the steps:

Carry out the described method of claim 8 and obtain interfacial tension γ and vertex curvature radius b;

Calculate the join contact angle θ of contact C of first fluid, second fluid and solid basal plane three-phase according to formula (2) then,

$\sin \mathrm{\&theta;}=X_c-\frac{1}{4}\mathrm{\&alpha;}{X}_c^3+\frac{1}{2\mathrm{\&pi;}{X}_c}\mathrm{\&beta;}(\mathrm{\&pi;}{X}_c^2{Z}_c-V)---\left(2\right)$

In the formula (2), X _c=x _c/ b, x _cX axial coordinate value for a C; Z _c=z _c/ b, z _cBe the z axial coordinate value of a C, V=v/b ³, v is for dripping the volume of bubble, and this volume can record when adding drop, also can carry out volume integral and obtains dripping a bubble outline line according to formula (2a) or formula (2b);

$v=\mathrm{\&pi;}{\&Integral;}_0^{z_c}{x}^2\mathrm{dz}---\left(2a\right)$

Or

$V=\mathrm{\&pi;}{\&Integral;}_0^{Z_c}{X}^2\mathrm{dZ}---\left(2b\right)$

α is by formula $2c(\mathrm{\&alpha;}=\frac{1}{2}\mathrm{\&Delta;\; \&rho;}{\mathrm{\&omega;}}^2{b}^3/\mathrm{\&gamma;})$ Obtain;

β is by formula 2d (β=Δ ρ gb ²/ γ) obtain.

Wherein: γ is an 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 b is the radius-of-curvature at initial point place.

10. the method for contact angle is measured in vertical rotary process according to claim 9, it is characterized in that, when rotational speed omega=0, employing formula (3) calculates contact angle:

$\sin \mathrm{\&theta;}=X_c+\frac{1}{2\mathrm{\&pi;}{X}_c}\mathrm{\&beta;}(\mathrm{\&pi;}{X}_c^2{Z}_c-V)---\left(3\right).$

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