TWI289661B - Method for the surface tension measurement of melting glasses at high temperature - Google Patents

Abstract

This invention is a method for the surface tension measurement of melting glasses at high temperature, especially is a method of creating a silhouette of a pendant drop of melting glass, of video-imaging the silhouette, of digitizing the image, of best-fitting the edge-coordinates with theoretical Young-Laplace equation in order to result an accurate surface tension of the melting glasses at high temperature.

Description

1289661 IX. Description of the Invention: [Technical Field] The present invention relates to a method for measuring the surface and surface tension of a glass droplet in a molten state at a high temperature, in particular, by calculating the shape of a droplet image and the equation by the Y〇ung Laplace equation. The obtained droplet shape is obtained by optimally aligning the surface tension value of the molten glass droplet at a high temperature. [Prior Art] Product quality has a considerable impact. The change in density and surface tension due to temperature changes is related to the flow of molten glass in the glass paste bath, as well as the uniformity, fineness, blistering and cracking of the molten glass. In order to provide the basic interface properties of high-temperature molten glass liquid, explore the dynamic interface characteristics, wet behavior investigation, and the change of surface tension of high-temperature molten glass in different gas environments, such as Αγ, Ή2, N2, dry air and humid air, Surface tension measurement of high temperature molten glass plays an important role. The method for measuring the tensile strength of the high-temperature molten glass currently used is drop weight and maximum pull method (maximum pull » ^ ^ Μ Ψ > ίτ dipping cylinder) ^ 3⁄4 Λ Μ ^ (maximum Bubble pressure), and sessile drop, and fiber elongation. [See A. Kucuk, A.G. Clare, L.E Jones, "An Estimation of the Surface Tension for

Silicate Glass Melts at 1400 〇C Using Statistical Analysis,” Glass Technol·, 40(5), 149-53 (1999)·] 1289661 / However, the current method for measuring high-temperature molten glass is known to be accurate, low' or Only the energy measurement lower Φ tension value is limited in measurement applications. Therefore, the main object of the present invention is to provide a method for measuring the surface tension of glass droplets in a high temperature molten state to solve the above problems. SUMMARY OF THE INVENTION The method of surface tension develops a measuring system that can be applied to the surface tension of molten glass under a fox, except that the measured high temperature molten glass is more accurate and can measure a higher range of surface tension values. 'The measurement temperature can be as high as 165〇〇c. f The invention uses the method of digital image capture to measure the surface tension of high-temperature molten glass by capturing the profile of the suspended molten glass droplets. The following steps: (1) A stable suspension of molten glass droplets can be obtained by self-designed platinum _ 铑 needle at the temperature of 咼 (2) filming its molten glass drape The image of the drop and digitize the image to obtain the coordinate position of the complex point on the boundary of the overhanging droplet; w~ (3) Calculate the theoretical curve of the droplet boundary of the molten glass, including (8) setting X〇, Z(), R 〇 and β value, where Zq is the horizontal and vertical coordinate position of the apex apex (apex), R ❹ is the radius of curvature of the apex of the droplet, and β is the capillary constant, p = 1289661 △p is the high temperature melting glass The difference in density between the air and the air, g is the gravitational acceleration, γ is the surface tension of the molten glass droplets; and (b) integrates the following differential equation cos diagnosis dx ds dz .. —=sm φ ds άφ — 2 ·' Apg二ύηφ ds R γ x

Boundary condition: x'(9)=z'(9)= s(0)=0 where x' = x/R〇,z' = z/R〇,s,= s/R〇, where 乂 and 2 are boundary points respectively The coordinate position in the horizontal and vertical directions, s is the long distance from the apex of the droplet, Lu is the turning angle, R 〇 is defined as above; (4) Calculating the coordinate position and step of the complex point of step (2) 3) the closest distance of the theoretical curve; and (5) repeat steps (3) and (4) until the sum of squares of the nearest distances is less than a desired value, and then calculate γ = ΔPgR 〇 2 by R 〇 and β set in step (3) Therefore, the method for measuring the surface tension of the glass droplets in the high-temperature molten state by the present invention develops a measuring system which is applicable to the surface tension of the molten glass at a high temperature, and utilizes the design of a unique platinum-ruthenium needle. In combination with the application of T-shaped alumina tubes, in addition to the accurate measurement of high-temperature smelting glass, and the measurement of the surface tension value in the higher range, the measurement temperature can be as high as 1650. The advantages and spirit of the present invention can be further understood from the following detailed description of the invention and the drawings of 1289661. [Embodiment] The appropriately cut glass 30 is filled into a self-designed platinum, acoustic needle (20% 铑 and 80% platinum) 32 (see Figure 5), and is hanged on the upper end of Platinum _ 钱 奸 32 A glass block 30 has a weight of about 1 〇 to 5 〇 mg, and the remaining glass block 30 is filled into the platinum-money needle 32 from the rear end, so that the total weight _ is 100 to 300 mg. After heating to the selected measurement temperature, the platinum slanting head 32 can form a stable molten drape glass droplet 34, and the image of the molten sag droplet 34 is captured by the digital image capture system, and then transmitted through The theoretical droplets of the Yoimg-Laplace equation are optimally aligned to obtain the surface tension of the drape glass droplets 34. The high-temperature melting county __ 34 its apparent gravity curve can be represented by the traditional Laplace equation where M: the pressure difference between the two phases on the gas-liquid interface, γ: the surface tension, m2: the two main radii of curvature at any point on the liquid-gas interface ( The principal radius) ° influences the equation because the pressure difference of the molten drape glass droplet 34 by gravity (1) can be expressed by the following formula: Δρ = Δρ〇 + Apgz · ········(2) The pressure of the apex (Δex) is ΔΡ〇 which is the difference in the suspension force between the liquid and gas interfaces ΔΡ〇=2γ/Κ0. 1289661 where R〇 is the radius of curvature of the apex of the molten drape 34, γ is defined as above, Λρ is the difference between the two phases of liquid-vapor, g is the acceleration of gravity, and z is the vertical distance from the apex of the droplet 34. Referring to the coordinate system of the molten drape 34 shown in Figure 1, it is known from the plane geometry -= cos^ ^ = sin^·-...----(3)

U 丄一(四) r4V A ds , ~ a x.........(eight)

Where X and Z are the horizontal and vertical coordinate positions, s is the arc length of the apex of the droplet 34, and 彡 is the turning angle. ° Substituting equations (2), (3) and (4) (1) A can be obtained, APSZ sin^ On the A--...(3)^ Further definition for the dimensionless / = /= especially / see, ν = ζ / exhaust, substituted into equation (3) and (5) And got

2 ! A^gR〇- sin^ ,..,.... ,(7) ds γ χ ...(8) f= A numerical method is used for the known boundary condition X, (9)=z'(9)=s(9)=0 The theoretical equations for the boundary points of the suspended droplets 34 are obtained by integrating the equations (7), (8) and (9), for example using the fourth-order Runge-Kutta method [see Carnahan, B; Luther, H. A.; J· 〇 · Applied Numerical 1289661

Methods; John Wiley & Sons: New York, 1969] and start with the following approach [see Huh, c.; Reed, Reed, RLJ of colloid Interface Sci. 1983, 91? 472]: This approach The answer applies to the case of φ«1, where: [do], Bessel function of the first kind °

Figure 2 shows the results obtained by using the numerical method to integrate equations (7), (8), and (9) for R^l and different β values. When the image of the molten drape glass droplet 34 is digitized, we can take enough boundary points from it and compare the coordinate position data with the above theoretical curve, which can be quickly obtained by appropriate numerical analysis methods. A set of optimal alignment results, and then calculate the surface tension r from the R〇 and β values in the best comparison result.

A specific method for calculating the surface tension of a molten glass includes setting an objective function defined as the sum of the squares of the vertical distances between the measurement point Un and the above theoretical curve v, that is, e= Σ二i [dn(Un,v)]2 ; N is the total number of measurement points. This objective function is affected by four unknown variables (qi, i = 1, 2, 3, 4) | the actual position (X〇 and Z〇) of the apex of the overhanging droplet, the radius of curvature of the vertex (仏) and the capillary constant (β). In order to obtain the best alignment between the measurement point and the theoretical curve, the objective function must have a minimum of these four variables (^: / Qiu, I = 1, 2, 3, 4). The solution to minimize the equation is directly borrowed from the Newton-Raphhson method [see Carnahan, B; Luther, Η·A·; 1289661

Wilkes, J. 0. Applied Numerical Methods; John Wiley & Sons: New York, 1969] 'The molten glass tension value γ is calculated from the best heart and p value. To use the above method to obtain the surface tension value of high-temperature molten glass, the starting values of four appropriate parameters (3), %, 仏, ρ) must be given first. If the starting value is too far from the true value, then Newt〇n- The Raphs〇n method cannot converge. The starting value of XG can be obtained by taking the average value of the horizontal seat=private point of all boundary measurement points. The starting value of Zg can be taken as the lowest of the three lowest (or highest) measuring point coordinates; and the starting point of ^ and ^ The administration of the initial value must be calculated using the droplet shape factor defined by the present invention. The present invention provides a measuring system for measuring the surface tension of a high temperature glass. The system can also be used to measure the change in surface tension of high temperature molten glass at different temperatures. The reason why the drape droplet measurement system can obtain the surface tension value of the molten glass at a high temperature depends on the close cooperation of the following five devices: 1 (8) Parallel light source device for stabilizing light intensity. (b) sophisticated camera, image processing and droplet contour search devices. (4) High temperature constant temperature system, the temperature change is within the Shidai. Platinum and money needles 32 of construction and size. 1289661 (6) Tension meter nose software program. The capillary constant (β) of the molten pendant glass droplet 34 and the radius of curvature value (仏) of the apex of the molten glass liquid 34 can be accurately determined by the definition of the droplet 34 forming function. The system device of the present invention is shown in Figure 3. The device contains 5 subsystems. (1) Parallel light source device (see Figure 3) (2) Image processing and processing device (see Figure 3) (3) High temperature thermostat system 42 (see Figure 4) (4) Overhang Droplet generating device 40 (see Fig. i) (5) Tension calculation software program. The light source system contains a visible light source 2 of a certain light intensity, a set of plano-convex lenses 3' pinholes 4 and an achromatic lens 5. The above components are all fixed to the optical lens holder and the base 20 which can be raised, lowered or rotated. This parallel light is projected onto the signal sensor of camera 16 by melting the glass droplets 34. The image capturing and processing device comprises an objective lens 13, a set of lens groups 14 and blue filters 15, a camera 16, an image digital interface card 21, a computer screen 17 and a computer for searching the contours of the molten glass droplets 34. Program (stored in computer 17). The camera 16 is mounted on a rotating, tilting, lifting, front and rear, left; & secret optical 2G ±. Parallel wire overhangs the molten glass _ 34 and is imaged in the field of the job 16 idiot, the image digital interface card 21 digitizes the signal of the camera 16, and records it on the brain 17. The computer screen displays the image on the camera 16. The droplet profile looks for the number of liquids in the job. The high temperature strange temperature system 42 contains - high temperature furnace body 6, - temperature control box 1 〇, - f control computer 11 and - strange temperature water tank 12. The high temperature furnace body 6 contains a type: Ming tube 22 (see Figure 4), one tube outer temperature measuring rod 7, "in-tube temperature measuring rod 8 and 12 hanging droplet feeding rod 9". The T-type oxidation of the molten glass droplet 34 to be tested is a closed system (ci〇se SyStem). The high temperature furnace body 6 is connected to a constant temperature water tank 12 for reducing the temperature of the tail end of the T-tube 22 when the system is warmed up. The temperature control box 10 is connected to the high temperature furnace body 6, and the program for raising and lowering the temperature is set in the control box 10. When the start of the start, the temperature measuring rod 7 and the temperature measuring rod 8 in the tube can be used to know the high temperature furnace body 6 and the molten glass. Temperature, and its temperature can be controlled within ±1〇C. The temperature control computer η can record the temperature changes in each time period. The two ^-type alumina tubes 22 are respectively provided with quartz plates 23, so that the bismuth-type alumina tube 22 system in the high-temperature furnace body 6 is a closed system. The glazed glass drape liquid helium generating device 40 comprises a self-developed platinum-ruthenium needle 32 (see Figure 5) and an alumina tube feed rod 9. Its function as a platinum 铑 pin 32 is to obtain a stable molten drape droplet 34 at high temperatures. After the platinum-head 32 is filled with glass, it is placed in the hanging liquid droplet feeding rod 9, inserted into the heating furnace, adjusted to the appropriate focal length, and then heated to the selected temperature, and the glass block 3 is turned into a molten droplet shape to start taking For example, the image of the molten glass droplet 34 formed by it is projected onto the sensor of the camera 16 via parallel light, and begins to cool down when the temperature reaches the selected temperature rise end point. In addition to the temperature control box 1 , the constant temperature water tank 12 and the temperature control computer u are installed and fixed on an inflatable shockproof table (vibrati〇n Is〇lati〇n

On Table 20, another small air compressor provides the high-pressure air required for the shockproof table. The tension calculation device consists of a personal computer 17 and a self-written computing program. The image of the high-temperature molten glass droplet 34 is obtained by a continuous image capturing program written by itself, and the boundary point of the 13 1289661 molten droplet 34 is obtained by the automatic search of the droplet boundary, and then the Y〇ung-Laplace equation is used. The optimal blending of the molten glass shaft boundary can be used to obtain the surface tension of the nano-cell droplets. The related embodiments are described below. First, the surface tension of the high temperature molten glass is measured by the drape droplet image digitization measuring instrument (shown in Fig. 2) of the system of the present invention. The tension measurement steps are as follows: (a) The drape drop method puts the cut glass block 30 into the platinum-money needle 32, and a glass block 3 〇 10 to 50 mg is attached to the front end of the platinum-ruthenium needle 32. The glass block 30 is filled with a glass block 3, and the outer glass block 30 is about 1 〇〇 to 3 〇〇 mg. The platinum _ money needle 32 is placed in the hanging liquid droplet feeding rod 9 and inserted into the heating furnace. After heating, a stable suspended molten glass droplet 34 is obtained, and the image is taken after the selected temperature is reached, and then borrowed. The program, the droplet boundary automatic search program, and the optimization of the boundary point of the molten glass droplets 34, and the change of the surface tension with temperature at different temperatures of the suspended molten glass droplets 34 are measured. (b) Fixing the glass block by the fixed droplet method, taking about 1〇~8〇mg, placing it on the refractory monument, and then placing the refractory monument and the glass block on the hanging pot and the horizontal feeding rod, wherein The crucible should be placed on a horizontal feed bar. Pushing the horizontal feed rod into the heating furnace body, after heating, the glass block will form molten droplets, and the selected temperature will start to take the image, and then borrow the image program, the droplet edge 1288961 boundary automatic search program, and the molten glass liquid The optimization of the drop boundary point is compared with the program, and then the change of the surface tension with temperature is measured under the condition that the molten glass is not melted. Dirty and using the present invention to measure the surface tension of the glass drop, compared with the fixed drop method 'has a higher accuracy, please refer to Figure 6, Figure 6 is a fixed droplet of Pyrex glass on the refractory brick, The optimal ratio of the droplet boundary point to the theoretical curve is 'T=85 degrees Celsius, the different curves represent different surface tensions, and the molten glass droplet weight = 24.75 mg. Figure 6 shows that the surface tension measured by the tamping droplet method is optimally compared with the boundary point of the Boma droplet through the theoretical curve, and the difference in surface tension value is large, so that the accuracy is lower. . The surface tension is measured by the drape drop method (see Figure 7 for the optimal alignment of the theoretical curve and the droplet boundary point), and the surface tension value is better or more accurate. Therefore, the surface tension of the drape drop method is high. Figure 7 is a comparison of the droplet boundary point of a pyrex glass melted drape droplet with the theoretical curve, 850 degrees Celsius, different curves representing different surface tensions, and the weight of molten glass droplets = 3258 mg. Figures 6 and 7 show the optimal alignment of the surface tension of the molten glass when T=85G π is used to measure the surface tension of the molten glass. The two droplets on Figures 6 and 7 are approximately the same weight. By optimizing the alignment, it is known that a more accurate Beta shape factor can be obtained by using the suspension method. The measurement of the two methods is the standard deviation (S.D·) age paste, and the comparison between the eight methods is the comparison of the tension accuracy of the drop method and the fixed droplet method. The data from Figure 8 and Table 1 show that when using the vertical drop method, the surface force is accurate depending on the domain method. By labeling 15 f difference ^ and optimizing the alignment curve, we found that when the SD. value exceeds 0 45, the surface tension between the optimal alignment curve and the droplet boundary point is clearly set at 5 o'clock. It is the value of the tensile force measured by the drape drop method (± 8mN/m), which is better than the fixed droplet method (± 58mN/m). The circumference is obviously small, that is, the surface tension of the molten glass is measured by using the drape droplets, and the accuracy is high. At present, the industry often makes Lai|Lai County high-temperature molten glass to humiliate the tension. The value of the value is poor. The present invention uses the drape drop method to obtain a more accurate tension value. Table 1 shows the comparison between the accuracy of the drape method and the sessile drop method.

Pendant Drop (32.58 mg) —-----::—Sessile Drop (24.75 meV Tension Surface Tension Tension Surface Tension T==850°C Range (mN/m) Range (mN/m) (mN/m) ( mN/m) 267 ί 275 土 8 205 ί 263 士 5 8 282 320 The invention can be applied to the determination of the interface physical properties of the molten glass, and contributes to the selection of conditions for the flow forming of the molten glass in the glass paste pool, thereby improving the yield of the finished product. The method for measuring the surface tension of glass droplets in a high-temperature molten state by the present invention develops a measuring system which is suitable for the surface tension of molten glass at a high temperature, and utilizes a unique white gold-铑 needle head 1289616 design, which is more compatible with T. The word Wei Weimu's Gu, in addition to measuring the high temperature molten glass is fresh and can measure the surface tension value of a higher range, the measured temperature can be as high as 1650 〇C. The details of the present invention are intended to be more clarified, and the present invention is not limited to the preferred embodiments disclosed above. Instead, the purpose is to cover various Change and The equivalence is arranged within the scope of the patent scope of the invention to be applied for. [Simplified illustration of the drawing] Figure 1 shows the coordinate system of a drape droplet; Figure 1 shows the theory of the drape droplets when different β values are shown. Figure 2 is a schematic view of a measuring system for the surface tension of a high-temperature molten glass used in the present invention; Figure 4 is a design of a surface tension measuring system for a molten glass; and Figure 5 is a white gold-铑 of a drape glass droplet forming. Needle: 20% money + 80 〇 / 〇 white gold; Figure 6 is a fixed droplet of Pyrex glass on the refractory brick, the best comparison between the droplet boundary point and the theoretical curve, T = 875 ° C, different curves represent Different surface tensions; Figure 7 is the optimal alignment of the droplet boundary points of a Pyrex glass melted drape droplet with the theoretical curve, T = 975 ° C, different curves represent different surface tensions; and 17 1289661 Figure 8 is a drape drop Comparison of the tension accuracy between the method and the fixed droplet method

[Main component symbol description] Melt drape droplets 34 Light source 2 Plano-convex lens 3 Pinhole 4 Achromatic lens 5 South temperature furnace body 6 Tube outside temperature measuring rod 7 Tube inside temperature rod 8 Mirror lens 13 Lens group 14 Blue filter 15 Camera 16 Interface card 21 Computer 17 Temperature control box 10 Temperature control computer 11 Thermostatic water tank 12 High temperature thermostat system 42 Suspended liquid droplet feed rod 9 Quartz sheet 23 Platinum - 姥 needle 32 Glass block 30 T-type alumina tube 22 Suspended droplets Generating device 40 18

Claims (1)

1289661 X. Patent Application Range: 1. A method for measuring the surface tension of a glass droplet in a high temperature molten state, comprising the steps of: attaching a cut glass piece to a platinum-ruthenium needle and filling it into the Platinum-姥 needle; heating the platinum-铑 needle to a selected temperature so that the glass block forms a molten drape at the lower end of the platinum ; needle; aligning the melting with a photosensor of a camera Suspending the droplets ' to produce a side view projection image corresponding to the molten glass droplets; extracting the side view projection image of the molten pendant glass liquid and digitizing the side view projection image; and melting the portion by digitization A side view projection image of the suspended glass droplets, searching for the boundary of the molten pendant glass droplets, and performing an optimum regression with the Y〇ung-Laplace theoretical curve of the molten pendant glass droplets, thereby obtaining the smelting suspension glass droplets Surface tension value. 2. The method of claim 1, wherein the side view projection image is generated by placing a parallel light source device and the 1289661 photo sensor on opposite sides of the suspended liquid droplet. And in a straight line distribution, wherein a normal vector of the plane of the light sensor is in the same direction as the parallel light projected by the parallel light source device, by projecting the parallel light on the side of the molten suspension glass droplet, so that , the photo sensor produces a side view projection image of the molten pendant glass droplet. The method of claim 1, wherein the camera extracts a side view projection image of the molten pendant glass droplet from the photo sensor, and outputs the corresponding image signal to an image interface. The card passes through the image interface card to generate a corresponding image digitization signal, and then transmits the image digitization signal to a computer for processing to obtain a boundary of the molten pendant glass droplet. 4. The method of claim 1, wherein the obtaining the molten drape glass droplet comprises the steps of: filling the cut glass block into the platinum-ruthenium needle, when the temperature reaches the selected At a temperature, the molten drape glass droplet is formed in a middle portion of a τ-shaped alumina tube disposed laterally; and two quartz sheets are respectively added to both ends of the τ-shaped alumina tube, thereby causing the molten suspension The glass droplets are in a closed state at a temperature of 20 1289661. % twenty one