JPH06341941A - Surface tension measuring method of pendant type droplet - Google Patents

Abstract

PURPOSE:To enable the simple, accurate, and speedy measurement of surface tension by minimizing a difference between the measured value of coordinate on a surface of a droplet which hangs at a tip of a capillary vertically and coordinate value which is calculated theoretically. CONSTITUTION:A pendant type droplet hangs at a tip of a capillary vertically, light from a light source is cast on the droplet, and a picture of its shape is taken by a CCD camera. Concerning 50 to 100 measurement points i (1, 2...n) on the surface of the droplet, its coordinate positions (x, z) are observed and determined. In coordinate (x, y), the shape of the droplet (droplet curve) (xi, zi) is obtained as a function. The droplet curve (xi, zi) obtained by the actual measurement is compared with the theoretical curve Xi, Zi obtained by using capillary constant q, droplet radius R, coordinate positions at the time of measurement DELTAx, DELTAz and an angle omega at the time of coordinate conversion as parameters, and surface tension r is obtained from each parameter (q, R, DELTAx, DELTAz, omega) when a difference phi between the actually measured value and theoretical value becomes minimum.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a pendant droplet type surface tension measuring method. More specifically, the present invention is directed to the measurement of liquid surface tension, liquid purity, liquid surface charge or surface charge capacity in the chemical and pharmaceutical fields, surfactant performance tests, and color liquids for printing copiers and jet printers. Surface properties measurement, wetting property of liquid for solid surface coating, foaming test for flotation in metal mining industry, property test of metal lubricating oil in machinery industry, gas-liquid or liquid-liquid interface in biochemistry and food The present invention relates to a pendant droplet type surface tension measuring method, which is useful for detecting the tension of water.

[0002]

2. Description of the Related Art Conventionally, measurement of liquid surface tension, liquid purity, liquid surface charge or surface charge capacity in the fields of chemistry and chemicals, surface activity in various fields,
The surface tensions of liquid-liquid and gas-liquid interfaces have been measured in order to detect the wetting properties, foaming properties, and tensions of gas-liquid and liquid-liquid interfaces. For that purpose, it is also possible to devise a more accurate and simple method. It has been studied in various ways.

As a method for measuring such surface tension, for example, a capillary rising method, a bubble utilization method, a droplet weight method, a Wilhelmy method and the like are widely used. The capillary rising method, which is one of the conventional methods, is to immerse the capillary tube in the liquid, and when the adhesive force between the liquid and the inner wall of the capillary is larger than the cohesive force of the liquid, the liquid rises in the capillary tube.
The surface tension is obtained from the height of the liquid surface when the equilibrium is reached, the density of the liquid, the gravitational acceleration, and the helix angle of the liquid. However, in reality, it is very difficult to accurately measure the wetting angle of the liquid on the inner wall of the capillary by this capillary rising method. Therefore, it is impossible to accurately determine the surface tension.

In the bubble utilization method, a bubble of gas is pushed into a liquid by using a tube or the like, the bubble is gradually expanded, and the surface tension is estimated from the difference between the internal pressure and the external pressure of the bubble. However, the surface tension obtained by this method is not a surface tension at the time of equilibrium but a dynamic characteristic, so that there is a drawback that the error becomes very large. The droplet weight method is a method of slowly growing a droplet at the tip of a thin tube and calculating the surface tension from the phenomenon that the weight of the droplet becomes larger than the surface tension of the liquid and drops. Also in this method, the surface tension is obtained from the dynamic characteristics, and therefore the error is very large compared to the actual surface tension. Further, in this method, not all of the droplets drop, but some droplets remain in the capillary, so it is necessary to correct this amount, and the measurement becomes very complicated.

The Wilhelmi method is a method in which a measuring plate such as glass or platinum is brought into contact with the surface of a liquid, and the weight increase due to the surface tension of the measuring plate is measured using a balance. However, this method requires the data of the wetting angle, and has the drawback that the surface tension cannot be measured easily and accurately. The present invention has been made in view of the above circumstances, and a new surface tension that solves the drawbacks of the conventional surface tension measuring method and enables simple and accurate surface tension measurement. It is intended to provide a measurement method.

[0006]

In order to solve the above-mentioned problems, the present invention hangs a droplet on the tip of a thin tube and observes and determines the coordinate value of the surface of the droplet. The coordinate value and the capillary constant are determined. , Radius of curvature of pendant droplet, coordinate position at measurement,
Provided is a pendant droplet type surface tension measuring method characterized by minimizing a difference from a calculated coordinate value of a droplet surface having an angle at the time of coordinate conversion as a parameter and obtaining the surface tension from the parameter at this time.

That is, according to the present invention, a droplet is made to hang down from the tip of a thin tube, the surface shape of the pendant type droplet is actually measured, and a complex pendant type surface shape is theoretically obtained, and the difference between them is minimized. Then, the surface tension is obtained. Therefore, in the surface tension measuring method of the present invention, it is not necessary to consider weight, water pressure, wetting angle and the like. Further, in the present invention, the surface tension can be quickly obtained, and not only the surface tension at a specific time but also the change with time of the surface tension can be measured. Then, since only the shape of the droplet is used as the actual measurement value, and it is not necessary to measure other amounts, even when the droplet is submerged in a liquid such as water, an electric potential is applied from the outside and the electrocapillary force is applied. (Potential dependent surface tension)
Can also be asked.

It is also possible to measure the gas adsorption amount by obtaining the surface tension of the droplet in the gas. The rheology of the droplet adsorption molecular layer can also be measured. Of course, in this invention,
The automation of the measurement system makes it possible to measure the surface tension more quickly and accurately. For example, the shape of the droplet is optically read and analyzed by a CCD camera or the like. This reading and analysis is automated.

[0009]

(I) General Principle First, first, a droplet (1) is made to hang down from a thin tube (2) as shown in FIG. 1, and is formed in air or in a different insoluble solution. At this time, the droplet has a pendant shape as shown in FIG. Therefore, for example, considering the reference coordinates with the origin at the center of the lowermost portion of the droplet, the coordinate position of a certain point of the droplet is determined by actual measurement.

Next, the shape of this pendant type droplet is determined. At the coordinates (x, z) shown in Fig. 1, the droplet shape is x =
Given as a functional form of x (z), its theoretical formula (Laplace equation) is

[0011]

[Equation 1]

[0012] The relationship between the parametric variables θ and x and z in Equation 1 is

[0013]

[Equation 2]

[0014] Here, the physicochemical parameters required for Equation 1 are the surface tension γ, the density difference Δρ between the two phases inside and outside the droplet, and the capillary pressure Pc at the bottom of the droplet. The capillary pressure Pc at the bottom of the droplet is calculated by using the surface tension γ and the radius of curvature R at the bottom of the droplet.

[0015]

[Equation 3]

It can be expressed as Furthermore, the density difference Δρ between the two phases inside and outside the droplet is calculated by using the capillary constant q

[0017]

[Equation 4]

It can be expressed as The difference between the coordinate position obtained from the experiment and the coordinate position obtained from the theoretical value is

[0019]

[Equation 5]

Then, the least square method is used to find q, R, Δz, Δx and the angle ω at the time of coordinate conversion for minimizing this φ. In Equation 5, Xi is

[0021]

[Equation 6]

And Zi is

[0023]

[Equation 7]

It is That is, the droplet curve (Xi, Zi) obtained experimentally (i = 1,2, ...
Can be obtained by integrating the curve Xi = Xi (Zi: q, R, Δz, Δ
x, ω), the difference between the experimental and theoretical values φ (q, R, Δz, Δ
x, ω) to minimize q, R, Δz, Δx, and ω
To decide.

The theoretical curve contains Δz, Δx, ω in addition to the parameters of the capillary constant q and the radius of curvature R because the coordinate system (x ', z') defining the droplet experimental curve and the coordinate system of the theoretical curve are included. This is to correct the deviation of (x, z), and has the correspondence relationship as shown in FIG. The experimental measurement points are set at about 50 to 100 (n = 50 to 100), and the left side φ is minimized while changing the five parameters of q, R, Δz, Δx, and ω in the equation 3. (II) Analytical method In the above general principle, the integral of Equation 1 and Equation 2 is z = 0,
If you start from the lowest point of x = 0, θ = 0, the integral will generally diverge, making the analysis generally difficult. Therefore, Equation 1
And the method of preventing the divergence by starting the integration of Expression 2 from a place other than θ = 0 is adopted.

For example, where θ is small, for example, θ =
Substituting equations 3 and 4 into equations 1 and 2 with π / 12 as the integration endpoint, the analytical approximation equations of equations 1 and 2 are

[0027]

[Equation 8]

[0028]

[Equation 9]

It becomes Where ψ is

[0030]

[Equation 10]

It is The expression 8 is approximated by a sixth-order expression for qR, and the expression 9 is approximated by a fourth-order expression for qR. Of course, the present invention is not limited to this. . The nonlinear least squares method selects five parameters that minimize Equation 5, and among them, for example, R. Hook and TAJeaves, (J. A.
ssn. Comp. March., 8 (1961) 212) etc. is effective.

Five parameters (q, R, Δz, Δ in φ
As an initial value of (x, ω), q = 5.5 cm−1, R is the droplet equatorial radius, and ω = 0, and Δx and Δz are x ′ and y ′ as shown in FIG. The one measured in association with each other is used. From these initial values, ψ (q, R, Δz, Δx,
ω) is minimized, and q at that time is substituted into Equation 4 to obtain the surface tension γ.

The pendant droplet type surface tension measuring method of the present invention will be described in more detail below.

[0034]

[Example] As an apparatus for experimentally obtaining the coordinates (Xi, Zi) of a droplet curve (i = 1, 2 ,,,, n is a measurement point), it is possible to automatically measure the surface tension. In addition, for example, the configuration illustrated in FIG. 3 can be shown as one aspect. As illustrated in FIG. 3, droplets injected from a syringe with a micro screw pass through a tube and form droplets in a laboratory tank. The experiment tank is preferably made of transparent material such as glass or plastic, and a sufficient amount of liquid or gas as compared with liquid droplets is put in the experiment tank in advance.

The droplet is irradiated with a light source through a white screen, the shape of the droplet is captured by a CCD camera,
The drop shape is analyzed using a video recorder and a computer for image analysis. By using such an apparatus, it becomes possible to measure the surface tension quickly and with high accuracy.

Further, in the present invention, in addition to the surface tension, the adsorption amount P, the surface charge σ, and the surface tension over time can be measured from the obtained surface tension. In addition to the surface tension, in order to obtain this adsorption amount P and surface charge σ, a reference electrode is installed in the experimental tank as a counter electrode of the liquid droplet, and a voltage is applied to the liquid droplet and the reference electrode. A voltage of several volts is applied by the external power supply device.

Using this device, the amount of solution adsorbed on the liquid droplets
P is

[0038]

[Equation 11]

It becomes Where C is the solution concentration, R is the gas constant, and T is the temperature. In addition, using this device, the surface charge σ on the surface of the solution droplet is

[0040]

[Equation 12]

It becomes Where E is the external voltage. Also, from the change of surface tension γ with time, the equilibrium surface tension is

[0042]

[Equation 13]

It can be obtained by Where γ ₀
Is the initial value and P is the adsorption amount. Further, P is the adsorption amount obtained from Equation 11, and D is the translational diffusion constant of the solution. Next, using the surface tension measuring method of the present invention, mercury droplets were dropped in a solution of pure water and sewage, and the time course of the surface tension was determined. FIG. 4 shows the result. High-accuracy and quick measurement was possible.

Furthermore, the voltage dependence of the surface tension of pure and 0.15 mol saline solutions was measured. The result was as shown in FIG.

[0045]

As described in detail above, according to the method of the present invention, the surface tension can be measured quickly in a short time, and the monitoring at the site of production or the like becomes possible. Further, from the measurement of the surface tension, the electrocapillary force measurement can be measured very easily.

[Brief description of drawings]

FIG. 1 is a sectional view showing the basic principle of the present invention.

FIG. 2 is a sectional view showing the basic principle of the present invention.

FIG. 3 is a schematic diagram showing a measuring method as an embodiment of the present invention.

FIG. 4 is a relationship diagram showing a result of an example of the present invention.

FIG. 5 is a relationship diagram showing a result of an example of the present invention.

[Explanation of symbols]

 1 liquid drop 2 thin tube

Claims (3)

[Claims] 1. A droplet is hung on the tip of a thin tube, and the coordinate value of the surface of the pendant type droplet is observed and determined.
Obtain the surface tension from the parameters at this time by minimizing the difference from the calculated coordinate values of the droplet surface using the capillary constant, the radius of curvature of the pendant droplet, the coordinate position during measurement, and the angle during coordinate conversion as parameters. A pendant droplet type surface tension measurement method characterized by: 2. The measuring method according to claim 1, wherein the droplet shape is optically read and calculated and analyzed. 3. The measuring method according to claim 1, wherein the difference is minimized by the method of least squares.