JP4922633B2 - Droplet falling behavior analysis method and apparatus - Google Patents

Description

The present invention is a tumble behavior of droplets on the substrate choice, which can be measured with higher accuracy, to analyzing method and apparatus for droplet falling behavior.

  Control of wetting of solid surfaces is a technical issue located at the boundary between physics and chemistry, and its application range is the most fundamental and important research area covering all engineering fields such as surface functions and production processes. Conventionally, wetting of solid surfaces is based on Young's equation, and the relationship between changes in composition and structure and macro wetting obtained from contact angle measurement, etc. has been studied both theoretically and experimentally. It is known that surface roughness, surface shape, electric field, and the like are involved in a complicated manner.

  In addition, “static” wetting by contact angle measurement has been mainly evaluated in the past, but in recent years, the importance of “dynamic” wetting has begun to be recognized in various engineering fields such as construction and transportation machinery. . This “dynamic” wetting does not mean the rate of wetting and spreading on the hydrophilic surface, but mainly “removability of droplets” on the water-repellent surface. The most commonly evaluated dynamic wettability today is the falling angle and contact angle hysteresis. This contact angle hysteresis is the difference between the advancing contact angle and the receding contact angle. FIG. 1 shows the relationship between the drop angle α, the advancing contact angle θa, and the receding contact angle θr for the droplet 2 (for example, a water droplet) on the solid surface 1. Indicates. However, these are used to gradually tilt the horizontally supported sample surface and read the falling angle, forward and backward contact angles when the droplet started to fall, and do not include any information on the droplet removal speed. Not. For example, even if the drop angle of the droplet is 1 degree, it is known that it falls on a super water-repellent surface in an instant, but is extremely slow on a smooth polymer surface.

  On the other hand, in actual industrial materials, the inclination angle of the surface is mostly determined by the size, function, design, etc., and not `` how many times the inclination angle falls '' but `` how fast at a certain inclination angle '' The information “whether it will fall down” is becoming more important. For example, measurement examples can be seen in Patent Document 1, Patent Document 2, Patent Document 3, Patent Document 4, and the like. Also, in academic journals, Miwa et al. Reported that water on a super-water-repellent surface falls by non-patent document 1 with a uniform acceleration motion. Glycerol has been reported to fall with constant velocity motion due to viscous resistance. In Non-Patent Document 3 and Non-Patent Document 4, the tendency of acceleration may change depending on the falling condition for water on a smooth water-repellent surface, and the droplet may vibrate while falling. Has been reported.

However, the measurement method is not constant. There are various combinations of types and shapes of solid surfaces and types of droplets. Furthermore, it is known that the acceleration of droplets on the solid surface varies depending on the size and inclination angle of the droplets and the material of the solid surface. Yes. The drop-down behavior of the droplet cannot be comprehensively evaluated unless the shape change of the droplet is also evaluated at the same time as the acceleration measurement. For example, considering the case of a drop falling on a solid surface, as described above, there are various combinations of the type and shape of the solid surface and the type of the droplet, and the acceleration of the droplet on the solid surface is It is known that it varies depending on the size and inclination angle of the droplet and the material of the solid surface. For example, when a droplet falls while “rotating”, the falling speed is said to be fast, but there is no report that has been demonstrated by actually visualizing the internal flow of the droplet. Further, the degree of deformation of the droplets at the time of falling is not necessarily uniform, and may be accompanied by periodic fluctuations depending on the conditions of falling, which may affect the falling acceleration. In order to analyze the periodic fluctuation simultaneously with the measurement of the falling acceleration, the advancing contact angle of the droplet viewed from the side with respect to the falling direction, the receding contact angle of the droplet viewed from the side with respect to the falling direction, The length of the contact portion of the droplet with the solid as viewed from the side with respect to the falling direction, the height of the droplet as viewed from the side with respect to the falling direction, and the falling of the two points where the outer periphery of the droplet intersects with the solid surface It is effective to continuously measure at least one of the accelerations at the point opposite to the direction side along with the falling acceleration. These are illustrated in FIG. In FIG. 2, a _a is the acceleration at the point on the falling direction side at the point where the outer periphery and the solid surface intersect, a _r is the acceleration at the point on the opposite side to the falling direction at the point where the outer periphery and the solid surface intersect, and V _a is the outer periphery. speed of points falling direction of the point of intersection is the solid surface, V _r is the outer circumference and that the solid surface intersects the opposite side speed of the points falling direction of, theta _a is the advancing contact angle of the point of intersection is the outer periphery and the solid surface , Θ _r is the receding contact angle at the point where the outer periphery and the solid surface intersect, h is the height of the droplet, and d is the distance between the two points where the outer periphery and the solid surface intersect.

  Various measuring devices and measuring principles for the contact angle and the falling angle as described above are known, and as disclosed in Patent Document 5, a method for comprehensively measuring and evaluating the appearance of falling droplets, Although an apparatus has been developed, an algorithm for calculating a measurement item that assumes a dynamic droplet behavior, for example, a dynamic droplet movement behavior, has not yet been developed.

  In analyzing the droplet behavior, since the coordinates are acquired in units of one pixel in the captured image, the accuracy of the measurement item is governed by the resolution of the element. In other words, at a resolution of 500 × 500 pixels, if there is a 5 mm square subject in a 40 mm vertical and horizontal area, the subject is represented by a square of 62 × 62 = about 3844 pixels (1 pixel = 0.08 mm). Therefore, in one pixel unit, the measurement items that characterize the falling behavior of the droplet (the advancing contact angle of the droplet viewed from the side with respect to the falling direction, the receding contact angle of the droplet viewed from the side with respect to the falling direction, The length of the contact portion of the droplet with the solid surface as viewed from the side with respect to the falling direction, the height of the droplet as viewed from the side with respect to the falling direction, and two points where the outer periphery of the droplet intersects with the solid surface When calculating the acceleration of the point on the opposite side to the falling direction, etc.), the data may vary due to insufficient accuracy. In particular, the angle calculation for applying a circle approximation from the coordinate value has a large variation.

In addition, there is no moving image analysis algorithm that can withstand simultaneous measurement of the above-described measurement items in a moving (falling) droplet. In particular, in the method of obtaining the pixel position of the droplet contour that is separated by a certain distance, the fluctuation of the Y coordinate of the measurement point is large, and the measurement value of the contact angle cannot obtain sufficient accuracy. This is because there is a problem in the conventional method for acquiring measurement points, and there is a need to develop an acquisition algorithm for appropriate measurement points (pixel coordinates).
JP 2001-259509 A JP 2002-29783 A JP 2002-97192 A Japanese Patent Laid-Open No. 11-116973 Japanese Patent Application 2005-231801 Miwa, M., Nakajima, A., Fujishima, A., Hashimoto, K. and Watanabe, T., Langmuir, Vol 16, p. 5754-5760 (2000) Richard, D. and Quere, D., Europhys. Lett., Vol. 48, p. 286-291 (1999) Nakajima, A, Suzuki, S., Kameshima, Y., Yoshida, N., Watanabe, T. and Okada, K., Chem. Lett., VoL32, P.1148-1149 (2003) Suzuki, S., Kameshima, Y., Nakajima, A and Okada, K., Surf. Sci., Vo1.557 / 1-3.p.L163-L168 (2004)

For example, when analyzing the droplet falling behavior, a measurement error occurs when the measurement object moves between pixels. That is, one pixel means not a point coordinate but a coordinate area having an area, and a measurement error occurs because a coordinate change less than one pixel unit cannot be expressed. To solve this problem, hard to a method to increase the process on gel resolution, the significant digits of the coordinate value per pixel by software image processor (sub-pixel processing).

Therefore, in the present invention, in order to calculate a measurement item (for example, FIG. 2) in the analysis of the droplet falling behavior, a coordinate value is calculated in units of, for example, 1/100 pixels using subpixel processing, and measurement points are acquired. An object of the present invention is to introduce a geometric condition for developing an optimal analysis algorithm, and to provide a method and an apparatus for analyzing a droplet falling behavior that meets this problem.

In order to solve the above-described problems, a droplet falling behavior analysis method according to the present invention is a method of analyzing a droplet falling behavior with respect to a reference line by capturing an image including a large number of pixels and analyzing the droplet and the reference line. Concentration distribution of an end point-containing pixel including an end point of a droplet as an intersection with the pixel, and two pixels adjacent to the end point-containing pixel on the reference line, or a plurality of pixels separated by a certain distance from the end point From this, an algorithm for calculating the end point coordinates of the droplet in less than one pixel unit by performing sub-pixel processing in the end point-containing pixels is used, and the droplet end point on the reference line is parallel to the reference line. the intersection of the two straight lines and the droplets are disposed at regular intervals n and 2n extends, using the algorithm calculated as coordinates of less than 1 pixels, the coordinates of the calculated three-point The curve is interpolated to obtain a tangent with the end point of the droplet, which is the intersection of the reference line and the droplet, as the contact point of the curve, and the angle between the tangent and the reference line is calculated as the contact angle of the droplet It consists of the method characterized by doing.

In the droplet falling behavior analysis method according to the present invention, the coordinates of two end points as intersections of one droplet and the reference line can be calculated in units of less than one pixel.

  It is also possible to calculate the length of the bottom surface of the droplet from the coordinates of the two end points calculated in units of one pixel.

  Further, the coordinates of the end points calculated in units of less than one pixel are obtained from the captured image of each frame in the imaging, and the movement speed and / or acceleration of the droplet is determined from the movement distance of the end points and the time interval of each frame. Can be calculated.

  In addition, a point that is farthest from the reference line of the droplet is calculated as a coordinate of less than one pixel unit using the algorithm, and a distance between the point and the reference line is calculated as the height of the droplet. You can also.

Furthermore, the present invention also provides a droplet falling behavior analysis apparatus including means using at least one of the methods as described above.

According to the present invention, it is possible to analyze the falling behavior of a droplet with high accuracy that could not be achieved in the past. In particular, as shown in the examples described later, when analyzing the behavior of falling droplets, it is possible to acquire coordinates in units of 1/100 pixels by acquiring appropriate measurement points based on geometric conditions and subpixel processing. Calculated items (for example, the advancing contact angle of a droplet viewed from the side with respect to the falling direction, the receding contact angle of the droplet viewed from the side with respect to the falling direction, and the liquid viewed from the side with respect to the falling direction. The length of the contact portion of the droplet with the solid surface, the height of the droplet viewed from the side with respect to the falling direction, and the acceleration at the point on the opposite side of the falling direction out of the two points where the droplet outer periphery and the solid surface intersect Etc.) can be effectively achieved. As a result, we were able to pioneer a new path in the method for evaluating and analyzing the dynamic behavior of droplets.

Hereinafter, the droplet sliding behavior analysis method and apparatus according to the present invention will be described in detail with preferred embodiments.

(Preprocessing)
In the calculation of the measurement item when the liquid droplets are falling moved over the surface of the substrate as a solid surface, introducing a unique geometrical conditions, by using an algorithm that combines sub-pixel processing, the droplets falling behavior Measurement items can be calculated. Before the measurement item calculation process, it is desirable to perform the pre-process according to the following procedure. The luminance setting (binarization threshold) of the boundary condition for extracting the droplet portion is preferably 5 to 100 (as shown in FIG. 3) so that the droplet portion is not scraped in the difference image of the droplet. preferably and a child of about between the case portion of the droplets 2 is white against a solid surface 1) as a reference line.

Examples of pre-processing include the following processing.
Pre-processing 1: Trajectory and background image acquisition pre-processing 2: Inter-screen calculation (difference) Background luminance-Brightness setting of each frame image
After differential processing: low brightness (black); fixed object
High brightness (white); moving object (droplet and part of reflected light)
Preprocessing 3: Frame range specification
Specify the area to process 4-7 below Pre-processing 4: Binary
A certain luminance or higher is defined as a droplet. → Extracted from boundary conditions (for example, Fig. 2)
Pretreatment 5: hole filling
Fill the cavity of the droplet part.
Pre-processing 6: Particle deletion
Pre-deletion process 7: deletion of outer edge part other than the liquid droplet part (part not contacting the liquid droplet part)
Deleting the outer edge of the processing area

  After the above pre-processing, the interval n of the Y coordinate for obtaining the peripheral coordinates of the droplet other than the end point which is the intersection of the geometric condition (the reference line as the boundary between the droplet and the solid surface) and the droplet After the setting, the following algorithm can be used to simultaneously calculate the drop (acceleration) speed, contact angle, bottom length, height, and the like of the droplet. FIG. 4 shows an example of the flow of this algorithm.

(Droplet end point extraction)
Peripheral coordinates of the part extracted in the pre-processing 4 (an integer value because the peripheral coordinate values are in units of pixels) are acquired, and the intersection of the peripheral coordinate value of the droplet and the reference line (the boundary line between the droplet and the substrate) is determined as the droplet. The coordinates (xL, yL) of the left end point L and the coordinates (xR, yR) of the left end point R are obtained. For each image, a boundary line (geometric condition) between the solid surface and the droplet surface is set. “When the x coordinate is constant, the y coordinate> y (upper) portion of the reference line is the droplet region. It is extracted. Since L and R are obtained from surrounding coordinate values, they are coordinate values in pixel units (integer values).

(Sub-pixel processing)
For the pixel including the intersection (end point) L (xL, yL) and the intersection R (end point) (xR, yR) and the two adjacent pixels, the luminance pattern of three pixels on each of the left and right (see FIG. 5). The left end portion is exemplified.) Coordinate values (0.01 pixel unit) L ′ (xL ′, yL ′) and R ′ (xR ′, yR ′) of less than one pixel, for example, 0.01 pixel unit are calculated. Luminance information of three consecutive pixels 3 and 4 in the x-axis direction, including the two pixels 4 that are adjacent to the pixel (pixel 3 including the end point) of the droplet peripheral coordinates of the portion extracted in the preprocessing 4 For example, as shown in FIG. 6, the relationship between the coordinate value and the coordinate value is analyzed by a cubic function, and the coordinate value of the x coordinate is obtained from the luminance at the time of binarization. In FIG. 5, by performing sub-pixel processing in the endpoint-containing pixel 3 from the density distribution of the endpoint-containing pixel 3 and two pixels 4 adjacent to the endpoint-containing pixel 3 on the reference line, Although an example in which an algorithm for calculating the end point coordinates of each pixel in less than one pixel unit has been shown, the end point-containing pixel 3 and a plurality of end point-containing pixels 3 separated from the end point by a certain distance on the reference line It is also possible to use an algorithm that calculates the end point coordinates of a droplet in units of less than one pixel by performing sub-pixel processing in the end point containing pixel 3 from the density distribution with the pixel. In this case, as the plurality of pixels that are separated from the end point by a certain distance, for example, two adjacent pixels adjacent to the end point-containing pixel 3 are selected, and two adjacent pixels counted from there are also included. It is possible to select a plurality of pixels.

(Contact angle calculation)
When the shape of the liquid droplet 2 is expressed as a function by curve approximation (circle / ellipse), three points including the end point coordinates are required on each of the left and right sides, and therefore, as shown in FIG. L1 (xL1, yL1) · L2 (xL2, yL2), right side: R1 (xR1, yR1) · R2 (xR2, yR2). By setting geometric conditions (straight lines parallel to the reference line and pixels on a straight line arranged at a constant interval n), the parallel straight line having a distance n and 2n from the reference line and the periphery of the droplet The intersections with the coordinates are L1 (xL1, yL1), R1 (xR1, yR1), L2 (xL2, yL2), R2 (xR2, yR2), respectively. Further, the coordinate values of these four points are obtained in units of 1/100 pixels as in the preprocessing 3 for extracting the droplet end points. Circles (circles: C1 and C2) passing through 3 points each of L ', L'1, and L'2 and R', R'1, and R'2 are obtained (Fig. 8). The perpendiculars of the straight lines passing through the centers of the circles C1 and C2 and the intersections L ′ and R ′ were respectively obtained (FIG. 9), and the angles formed between the perpendiculars and the reference line were defined as the contact angles θL and θR (FIG. 10).

(Calculation of bottom length)
The distance between the two points was calculated from the coordinates of the points L ′ and R ′.

(Height calculation)
When a straight line parallel to the reference line has the droplet peripheral coordinate H acquired in the pretreatment 1 having the largest distance from the reference line, the distance between the H and the reference line is defined as the height of the droplet.

  In this way, by establishing and setting appropriate geometric conditions and performing sub-pixel processing, variation in coordinate values when droplets move between cells is reduced, and endpoints that show sliding properties during movement are reduced. Measurement items that show the shape change at the time of sliding, including velocity (advanced contact angle of the droplet viewed from the side with respect to the falling direction, receding contact angle of the droplet viewed from the side with respect to the falling direction, and the falling direction Thus, the accuracy of the length of the contact portion of the droplet with the solid surface viewed from the side surface, the height of the droplet viewed from the side surface with respect to the falling direction, and the like can be improved. Further, conventionally, there has been an algorithm for measuring a static contact angle. However, measurement of a droplet falling behavior when sliding on a solid surface at high speed can be realized for the first time by this algorithm.

  Hereinafter, the present invention will be described more specifically with reference to examples actually measured and evaluated according to the present invention. In addition, these Examples are only illustrations and do not restrict | limit this invention.

Example 1 (subpixel processing + contact angle calculation result after introducing unique geometric conditions)
FIG. 11 shows the calculation result of the contact angle after subpixel processing + introducing unique geometric conditions. In this way, the y-coordinate is fixed and the four points L'1, L'2, R'1, and R'2 are determined. Variation of θL and θR is suppressed.

Comparative example 1 (calculation result of contact angle using conventional technology)
FIG. 12 shows the calculation result of the contact angle measured by an algorithm that does not use subpixel processing.

  Comparing Example 1 and Comparative Example 1, it can be clearly seen that the measurement accuracy is improved by performing the sub-pixel processing and the geometric pattern matching according to the present invention.

The present invention can be applied to all industrial fields in which it is desired to accurately grasp the droplet falling behavior.

It is a schematic explanatory drawing which shows the relationship between a forward and backward contact angle, and a fall angle. It is a schematic explanatory drawing which shows the item measured with a fall acceleration. It is a schematic explanatory drawing when a droplet part is extracted from a background image. It is a schematic explanatory drawing of the work flow of a measurement item calculation algorithm. It is a schematic explanatory drawing when the coordinate value of 0.01 pixel unit is calculated | required from the luminance pattern of three pixels on either side. It is a schematic explanatory drawing when the relationship between the luminance information and coordinate values of three consecutive pixels in the x-axis direction is analyzed with a cubic function, and the coordinate value of the x coordinate is obtained from the binarized luminance. FIG. 5 is a schematic explanatory diagram when two points on peripheral coordinates other than the end point coordinates are set when the droplet shape is expressed as a function by curve approximation (circle / ellipse). It is a schematic explanatory drawing when the circle which passes 2 points | pieces on an end point coordinate and a surrounding coordinate is calculated | required. It is a schematic explanatory drawing when the tangent is calculated | required by making the end point on the calculated | required circle into a contact. It is a schematic explanatory drawing when the angle | corner which the tangent and the line which set the board | substrate set was calculated | required. It is a characteristic view which shows the contact angle calculation result after the subpixel process in Example 1, and original geometric conditions introduction. It is a characteristic view which shows the calculation result of the contact angle measured with the algorithm which does not use the sub pixel process in the comparative example 1.

Explanation of symbols

1 Solid surface (reference line)
2 Droplet 3 Pixel including the end point 4 Adjacent pixel

Claims (6)

In analyzing the falling behavior of the droplet relative to the reference line by capturing an image including a large number of pixels, an endpoint-containing pixel including the endpoint of the droplet as an intersection of the droplet and the reference line, and the endpoint-containing pixel By performing sub-pixel processing in the end point-containing pixels from the density distribution with two pixels adjacent on the reference line or with a plurality of pixels separated from the end point by a certain distance, Using an algorithm for calculating coordinates in units of less than one pixel, the end point of the droplet on the reference line and the intersection of the two straight lines that extend parallel to the reference line and are arranged at constant intervals n and 2n and the droplet Is calculated as coordinates of less than one pixel unit using the algorithm, curve interpolation is performed using the calculated coordinates of the three points, and the liquid is an intersection of the reference line and the droplet Droplet sliding behavior analysis method characterized in that the end points determine the tangent line as the contact of the curve to calculate the angle between the reference line and該接line as the contact angle of the droplet. The droplet falling behavior analysis method according to claim 1, wherein coordinates of two end points as intersections of one droplet and the reference line are calculated in units of less than one pixel. The droplet falling behavior analysis method according to claim 2, wherein the length of the droplet bottom surface is calculated from the coordinates of the two end points calculated in units of less than one pixel. From the captured image of each frame in the imaging, the coordinates of the end points calculated in units of less than one pixel are obtained, and the moving speed and / or acceleration of the droplet are calculated from the moving distance of the end points and the time interval of each frame. The droplet falling behavior analysis method according to any one of claims 1 to 3. The point at the position farthest from the reference line of the droplet is calculated as coordinates of less than one pixel unit using the algorithm, and the distance between the point and the reference line is calculated as the height of the droplet. The droplet falling behavior analysis method according to any one of 1 to 4. A droplet falling behavior analysis apparatus comprising means for using at least one of the methods according to claim 1.

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