CN111912745A - Method for measuring liquid viscosity through dripping experiment - Google Patents
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Abstract
This patent proposes a new method of measuring the viscosity of a liquid. The method comprises the following steps: and carrying out a liquid dripping experiment, and collecting an experiment result of the change of the liquid volume and the liquid tail end displacement along with time in the dripping process. And processing each frame of liquid drop picture, and uniformly subdividing and dispersing the liquid into a plurality of enough micro-segments. And (3) deriving a recursion relational expression of the average speed on the section of any liquid micro-segment by adopting a finite difference method based on a continuity equation. And (5) deriving the displacement and the time by the speed to respectively obtain the strain rate and the acceleration. And simultaneously, carrying out stress analysis to obtain the tensile stress on the thinnest section. And determining a corresponding strain rate result according to the position of the finest section and the time variable, further obtaining a stress-strain rate curve, and finally obtaining the viscosity of the liquid through numerical fitting. The liquid viscosity testing method provided by the invention has the advantages of simple, easy and convenient testing process. In addition, the consumption of instruments and materials used in the test process is low in cost, high in cost performance and strong in practicability.
Description
Technical Field
The present invention relates to a method which has close relation with industrial technologies such as petroleum, chemical industry, etc. And more particularly to a method relating to the measurement of the viscosity of liquids.
Background
The viscosity of a fluid is an inherent physical property of the fluid, and is a property that generates an internal frictional force inside the fluid. The phenomenon of fluid viscosity caused by viscosity is seen everywhere in nature. The viscosity of a fluid is a physical quantity determined by the inherent physical properties of the fluid, and the viscosity is a direct measure of the viscosity of the fluid and a measure of the resistance of the fluid to shear deformation in the flow. All real fluids have viscosity, and knowing the viscosity of a fluid is critical to understanding and using the fluid.
At present, the conventional and novel methods for measuring the viscosity of a liquid are mainly vibration method measurement, capillary viscosity measurement, falling ball method, rotation method, and the like. They have respective applicability and advantages and disadvantages, for example, the capillary viscometry has advantages in that it is inexpensive, convenient in experimental operation and temperature control, and its measurement accuracy is high, absolute measurement of viscosity can be performed, but the capillary is easily clogged with small particles, the handling process is troublesome, and the density of the liquid is accurately determined in advance before measurement; the falling body type continuous viscometer manufactured by adopting a falling ball method can continuously measure the viscosity of fluid flowing in a pipe, and can carry out remote control instruction and record, but a fixed displacement pump is required to convey a sample; the method for measuring the viscosity by using the rotation method is suitable for all liquids, particularly suitable for fluids with higher viscosity or non-Newtonian fluids, but the stability and the reading precision of the method are limited to a certain extent, and the measurement result is very sensitive to the temperature; the vibration method for measuring viscosity has the advantages of convenient measurement of vibration period and attenuation, small sample consumption and convenient temperature control, but has no recognized ideal viscosity calculation formula. Meanwhile, considering cost factors, the problem to be solved at present is to develop a liquid viscosity measurement method which is simple, low in cost, strong in practicability and the like.
Disclosure of Invention
In the above background, the present invention proposes a method for measuring the viscosity of a liquid by a dripping experiment. The method for measuring the liquid viscosity is simple and easy to implement, low in cost and strong in practicability, and can overcome some defects in the conventional liquid viscosity measurement.
In order to achieve the purpose, the invention provides the following technical scheme:
1. a method of measuring the viscosity of a liquid by a drip test, the method comprising:
step 1: and (4) building a test table, adjusting the visual angle of the high-speed camera, and adding a proper amount of liquid to be detected into the needle tube. At the beginning of the experiment, the camera was turned on and the needle port opened and the liquid dripping process was recorded with the camera.
Step 2: and processing the video obtained by the experiment to obtain the picture result of the liquid dripping experiment of each frame. And processing the pictures in batch by using data acquisition software. And selecting the position of the liquid outlet as a coordinate origin, and establishing a cylindrical coordinate system by taking the vertical downward dripping direction as the x-axis forward direction. According to the symmetry of liquid dropping, the shape of the liquid during dropping can be regarded as a rotating body which is obtained by rotating r ═ d/2 around the x axis, wherein d is the cross-sectional diameter of the liquid filament, and r is the radius. The pixel grid of the picture naturally forms an Euler domain of liquid in a plane, and the two-dimensional grid is rotated around an x axis for one circle to obtain the Euler grid in a three-dimensional space. The liquid in the euler domain is approximately divided into a sufficient number of truncated cone micro-segments of height h (pixel size). x is the number ofiThe coordinates of the position of the lower surface of the ith segment of liquid are shown, i is 0,1 and …. x is the number of0＝0，xNIndicating the displacement of the end of the dripping liquid, N changes due to the change in the liquid dripping height over time. Meanwhile, the selected time step length delta t is 1/f, wherein f is the video frame rate, and t is the video frame ratejIndicating the jth time, j is 0,1, …, M being a sufficiently large number.
And step 3: according to the scale and the pixel point coordinates, the liquid volume and the liquid terminal displacement (x) in the dripping process are obtainedN) Over time tjThe result of the change of (c).
And 4, step 4: deriving t by using finite difference method based on fluid mechanics continuity equationjRecursion relation u of average velocity of cross section normal direction of ith liquid micro-segment (i is 0,1, …, N)i，j(xi,tj). Wherein u isN，j(xN,tj) Is tjThe speed of dripping the liquid end at the moment, and the liquid end displacement x obtained in the step 3NDerived from the time.
And 5: t is tjAt the moment, willVelocity ui，j(xi,tj) Deriving the displacement to obtain each position xiVelocity gradient, i.e. strain rate
Will speed ui，j(xi,tj) Derivative the time to obtain tjAcceleration a of the motion of the ith micro-segment liquid at the momenti，j(xi,tj)。
Step 6: at a certain time tjSelecting the thinnest cross section (x) of the liquid dropkPosition) and drip end (x)N) The fluid in between is the research object, and the stress analysis is carried out. The tensile stress sigma on the finest section is obtained by the dynamic equilibrium equationk，j(xk,tj)。
And 7: the corresponding time t in the step 6jAnd the position x of the finest sectionkSubstituting the strain rate expression in the step 5 to obtain tjTime of day, position x of the thinnest cross sectionkStrain rate of (C)
Combining the stress obtained in the step 6 to obtain a stress-strain rate curve
And finally obtaining the viscosity of the liquid through numerical fitting.
Wherein, the experimental device comprises a common medical needle-free injector, an iron stand, a high-speed camera and the like. When the experiment table is set up, the iron support is placed on a table top, and the needle tube is fixed on the support, so that the axis of the needle tube is vertical downwards. The camera bracket is fixed on the ground, so that the camera shooting direction is horizontally vertical to the axis of the needle tube.
Wherein, the experimental video is clipped to obtain a single-drop video, and the operation steps are as follows: first, each frame of picture in the experimental video is extracted, and the scale in the video is determined. Then the picture is cut properly, the colors in the picture are simple as much as possible, and the fluids have obvious differences. Then, the image is processed by binarization and morphological methods to make the edge clearer, and an edge detection method based on wavelet transformation is adopted to obtain the liquid boundary.
And respectively dispersing the space coordinates and the time according to the picture pixels and the video frame rate. The picture is composed of a large number of pixel points, the position of a liquid outlet is selected as an original point, and a cylindrical coordinate system is established in the forward direction by taking the vertical downward dripping direction as an x axis. According to the symmetry of liquid dropping, the shape of the liquid during dropping can be regarded as a rotating body which is obtained by rotating r ═ d/2 around the x axis, wherein d is the cross-sectional diameter of the liquid filament, and r is the radius. The pixel grid of the picture naturally forms an Euler domain of liquid in a plane, and the two-dimensional grid is rotated around an x axis for one circle to obtain the Euler grid in a three-dimensional space. And (3) dispersing the space coordinate x of the liquid image in the dropping direction (x-axis direction) according to the pixel point coordinates, and uniformly subdividing the liquid in the Euler domain into a plurality of enough micro-segments, wherein each segment is h in length. For any fluid micro-segment between the ith pixel point and the (i + 1) th pixel point, the length h of the micro-segment is the difference value of the coordinates of the i pixel point and the (i + 1) th pixel point in the x direction, namely xi+1-xiWherein x isiThe coordinates of the position of the lower surface of the ith segment of liquid are shown, i is 0,1 and …. x is the number ofNIndicating the displacement of the end of the dripping liquid, and N changes as the liquid dripping height changes with time. Meanwhile, selecting a certain experimental picture result starting timing, recording the result as 0 moment, then selecting the time step delta t, and dispersing the time variable according to the video shooting frame rate. The time step Δ t is the time difference between corresponding times of any two frames of pictures, i.e., tj+1-tjWherein, tjThe j is 0,1, …, M is a sufficiently large number, or Δ t is 1/f, where f is the video frame rate.
And calibrating the actual length corresponding to the difference value between the coordinates of two arbitrary pixel points according to the actual length between the scales in the scale in the shot picture. Therefore, the liquid volume and the liquid end displacement (x) in the dripping process are obtained on the basis of the discrete of the front space coordinate and the timeN) Over time tjAs a result of the change in (c) of (c),and obtaining xiDiameter d of the corresponding liquid cross sectioni，j(xi,tj)。
Wherein t is derived by using a finite difference method central difference format based on a continuity equation and the incompressibility of the liquidjRecursion relation u of average speed on section of ith liquid micro-segment (i is 1, …, N) at momenti，j(xi,tj). Wherein u isN，j(xN,tj) Is tjThe velocity of the liquid end at the moment is measured as the displacement x of the liquid endNAnd after the change result along with the time, the displacement is obtained by derivation of the time. The liquid micro-segment is simplified into a round table. Assuming that the liquid is incompressible and the density of the liquid in the micro-element liquid round table is unchanged, the continuity equation of the integral form is as follows:
center differencing of time:
substituting the expression (2) into the expression (1) to obtain a recurrence relation of the speed as follows:
wherein the content of the first and second substances,
Φ＝(2di，j+di+1，j)(di，j+1-di，j-1)+(2di+1，j+di，j)(di+1，j+1-di+1，j-1) (4)
the liquid dropping terminal speed u can be known by the recursion (3)N，j(xN,tj) Under the premise of (1), the average flow velocity u of the liquid cross section at any discrete time and at all discrete space positions in the liquid filament is recurredi，j(xi,tj). For theAnd obtaining a speed result by a difference method according to the average flow speed of the liquid section at any time and space position in the time and space range of the experiment but not on the discrete grid nodes.
Wherein, t isjAt the moment, the velocity ui，j(xi,tj) Deriving the displacement, and obtaining each position x by adopting a numerical differentiation method of a central difference formatiVelocity gradient, i.e. strain rate
Will speed ui，j(xi,tj) T is obtained by time derivation and numerical differentiation method of central difference formatjAcceleration a of the motion of the ith micro-segment liquid at the momenti，j(xi,tj). Both results are obtained by the formulae (5) and (6):
wherein the certain time tjSelecting the thinnest cross section (x) of the liquid dropkPosition) and drip end (x)N) The fluid between the two sections is used as a research object, the stress analysis is carried out, and the tensile stress sigma on the finest section is obtained by a dynamic equilibrium equationk，j(xk,tj). The liquid is acted by gravity, pulling force and surface tension and has an acceleration aj(tj) Where σ is the surface tension coefficient, ρ is the liquid density, and g is the gravitational acceleration. At the aforesaid diameter d of the determined liquid cross-sectioni，j(xi,tj) On the basis, the minimum d is found by comparisoni，j(xi,tj) Then by finding the smallest di，j(xi,tj) Corresponding x coordinate, finally determining xk。xkSurface tension and x-axis negative in stress analysisThe included angle of the directions is 0 degree.
Volume V of liquidj(tj) Obtained from the following formula (7):
acceleration a of the liquidj(tj) Obtained from the following formula (8):
the dynamic equilibrium equation is:
thus, t can be obtainedjAt the moment, the tensile stress acting on the finest liquid section:
wherein the stress-strain rate curve is obtained
Then, the viscosity of the liquid is finally obtained by numerical fitting. Due to sigmak，jFor tensile stress, the viscosity obtained by dividing the tensile stress by the strain rate is the extensional viscosity. Since the viscosity of a liquid is usually said to be shear viscosity and one third of extensional viscosity, the viscosity of a liquid is obtained by dividing the elongational viscosity by 3.
Compared with the prior art, the technical scheme provided by the invention provides a novel method for measuring the viscosity of the liquid. The method comprises the following steps: and carrying out a liquid dripping experiment, and collecting an experiment result of the change of the liquid volume and the liquid tail end displacement along with time in the dripping process. And processing each frame of liquid dripping picture, and uniformly subdividing and dispersing the liquid into a plurality of enough micro-segments in the vertical and downward dripping direction according to picture pixels. And selecting a time step length, and dispersing the time variable according to the video shooting frame rate. And (3) deriving a recursion relational expression of the average speed on the section of any liquid micro-segment by adopting a finite difference method based on a continuity equation. And (3) deriving the speed on displacement and time to respectively obtain the strain rate of each position and the acceleration of the movement of the liquid micro-segment, and selecting the fluid between the thinnest section of the liquid drop and the drop tail end as a research object to perform stress analysis. The tensile stress on the finest cross section is found from the dynamic equilibrium equation. And determining a corresponding strain rate result according to the position of the finest section and the time variable, further obtaining a stress-strain rate curve, and finally obtaining the viscosity of the fluid through numerical fitting. The fluid viscosity testing method provided by the invention has the advantages of simple, feasible and convenient testing process. In addition, the consumption of instruments and materials used in the test process is low in cost, high in cost performance and strong in practicability.
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For a clearer explanation of the embodiments of the present invention or the technical solutions in the prior art, the following is a brief description of the drawings used in the description of the embodiments or the prior art, and it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings provided without creative efforts.
FIG. 1 is a schematic diagram of experimental measurements according to the present invention;
FIG. 2 is a schematic view of a liquid micro-segment according to the present invention;
FIG. 3 is a flow chart of the velocity measurement of the present invention;
FIG. 4 is a liquid diagram of the present invention;
FIG. 5 is a flow chart of a method for measuring fluid viscosity according to an embodiment of the present disclosure.
Detailed description of the invention
The technical solutions in the embodiments of the present invention will be described clearly below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only some embodiments, not all embodiments, of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without inventive step, are within the scope of the present invention.
The invention provides a novel method for measuring the viscosity of liquid. The method comprises the following steps: and carrying out a liquid dripping experiment, and collecting an experiment result of the change of the liquid volume and the liquid tail end displacement along with time in the dripping process. And processing each frame of liquid dripping picture, and uniformly subdividing and dispersing the liquid into a plurality of enough micro-segments in the vertical and downward dripping direction according to picture pixels. And selecting a time step length, and dispersing the time variable according to the video shooting frame rate. And (3) deriving a recursion relational expression of the average speed on the section of any liquid micro-segment by adopting a finite difference method based on a continuity equation. And (3) deriving the speed on displacement and time to respectively obtain the strain rate of each position and the acceleration of the movement of the liquid micro-segment, and selecting the fluid between the thinnest section of the liquid drop and the drop tail end as a research object to perform stress analysis. The tensile stress on the finest cross section is found from the dynamic equilibrium equation. And determining a corresponding strain rate result according to the position of the finest section and the time variable, further obtaining a stress-strain rate curve, and finally obtaining the viscosity of the fluid through numerical fitting. The fluid viscosity testing method provided by the invention has the advantages of simple, feasible and convenient testing process. In addition, the consumption of instruments and materials used in the test process is low in cost, high in cost performance and strong in practicability.
The instruments and materials used in the process of the method of the invention are: an iron stand, a high-speed camera, silicon oil, silicon rubber, a common medical syringe without a needle, and the like.
Referring to fig. 5, a method for measuring the viscosity of a liquid by a dripping experiment is disclosed in the present invention, the method comprises:
step 101: and (4) building a test table, adjusting the visual angle of the high-speed camera, and adding a proper amount of liquid to be detected into the needle tube. At the beginning of the experiment, the camera was turned on and the needle port opened and the liquid dripping process was recorded with the camera.
Step 102: processing the video obtained by the experimentAnd obtaining the liquid dripping experiment picture result of each frame. And processing the pictures in batch by using data acquisition software. And selecting the position of the liquid outlet as a coordinate origin, and establishing a cylindrical coordinate system by taking the vertical downward dripping direction as the x-axis forward direction. According to the symmetry of liquid dropping, the shape of the liquid during dropping can be regarded as a rotating body which is obtained by rotating r ═ d/2 around the x axis, wherein d is the cross-sectional diameter of the liquid filament, and r is the radius. The pixel grid of the picture naturally forms an Euler domain of liquid in a plane, and the two-dimensional grid is rotated around an x axis for one circle to obtain the Euler grid in a three-dimensional space. The liquid in the euler domain is approximately divided into a sufficient number of truncated cone micro-segments of height h (pixel size). x is the number ofiThe coordinates of the position of the lower surface of the ith segment of liquid are shown, i is 0,1 and …. x is the number of0＝0，xNIndicating the displacement of the end of the dripping liquid, N changes due to the change in the liquid dripping height over time. Meanwhile, the selected time step length delta t is 1/f, wherein f is the video frame rate, and t is the video frame ratejIndicating the jth time, j is 0,1, …, M being a sufficiently large number.
Step 103: according to the scale and the pixel point coordinates, the liquid volume and the liquid terminal displacement (x) in the dripping process are obtainedN) Over time tjThe result of the change of (c).
Step 104: deriving t by using finite difference method based on fluid mechanics continuity equationjRecursion relation u of average velocity of cross section normal direction of ith liquid micro-segment (i is 0,1, …, N)i，j(xi,tj). Wherein u isN，j(xN,tj) Is tjThe speed of dripping the liquid end at the moment, and the liquid end displacement x obtained in the step 3NDerived from the time.
Step 105: t is tjAt the moment, the velocity ui，j(xi,tj) Deriving the displacement to obtain each position xiVelocity gradient, i.e. strain rate
Will speed ui，j(xi,tj) Derivative the time to obtain tjAcceleration a of the motion of the ith micro-segment liquid at the momenti，j(xi,tj)。
Step 106: at a certain time tjSelecting the thinnest cross section (x) of the liquid dropkPosition) and drip end (x)N) The fluid in between is the research object, and the stress analysis is carried out. The tensile stress sigma on the finest section is obtained by the dynamic equilibrium equationk，j(xk,tj)。
Step 107: the corresponding time t in the step 6jAnd the position x of the finest sectionkSubstituting the strain rate expression in the step 5 to obtain tjTime of day, position x of the thinnest cross sectionkStrain rate of (C)
Combining the stress obtained in the step 6 to obtain a stress-strain rate curve
And finally obtaining the viscosity of the liquid through numerical fitting.
In summary, the present invention provides a new method for measuring the viscosity of a liquid. The method comprises the following steps: and carrying out a liquid dripping experiment, and collecting an experiment result of the change of the liquid volume and the liquid tail end displacement along with time in the dripping process. And processing each frame of liquid dripping picture, and uniformly subdividing and dispersing the liquid into a plurality of enough micro-segments in the vertical and downward dripping direction according to picture pixels. And selecting a time step length, and dispersing the time variable according to the video shooting frame rate. And (3) deriving a recursion relational expression of the average speed on the section of any liquid micro-segment by adopting a finite difference method based on a continuity equation. And (3) deriving the speed on displacement and time to respectively obtain the strain rate of each position and the acceleration of the movement of the liquid micro-segment, and selecting the fluid between the thinnest section of the liquid drop and the drop tail end as a research object to perform stress analysis. The tensile stress on the finest cross section is found from the dynamic equilibrium equation. And determining a corresponding strain rate result according to the position of the finest section and the time variable, further obtaining a stress-strain rate curve, and finally obtaining the viscosity of the fluid through numerical fitting. The fluid viscosity testing method provided by the invention has the advantages of simple, feasible and convenient testing process. In addition, the consumption of instruments and materials used in the test process is low in cost, high in cost performance and strong in practicability.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (9)
1. A method of measuring the viscosity of a liquid by a drip test, the method comprising:
step 1: and (4) building a test table, adjusting the visual angle of the high-speed camera, and adding a proper amount of liquid to be detected into the needle tube. Starting the experiment, starting the camera equipment, opening a needle tube port, and recording the dropping process of the liquid by using a camera;
step 2: and processing the video obtained by the experiment to obtain the picture result of the liquid dripping experiment of each frame. And processing the pictures in batch by using data acquisition software. And selecting the position of the liquid outlet as a coordinate origin, and establishing a cylindrical coordinate system by taking the vertical downward dripping direction as the x-axis forward direction. According to the symmetry of liquid dropping, the shape of the liquid during dropping can be regarded as a rotating body which is obtained by rotating r ═ d/2 around the x axis, wherein d is the cross-sectional diameter of the liquid filament, and r is the radius. The pixel grid of the picture naturally forms an Euler domain of liquid in a plane, and the two-dimensional grid is rotated around an x axis for one circle to obtain the Euler grid in a three-dimensional space. The liquid in the euler domain is approximately divided into a sufficient number of truncated cone micro-segments of height h (pixel size). x is the number ofiThe coordinates of the position of the lower surface of the ith segment of liquid are shown, i is 0,1 and …. x is the number of0＝0，xNIndicating the displacement of the end of the dripping liquid, N changes due to the change in the liquid dripping height over time. Meanwhile, the selected time step length delta t is 1/f, wherein f is the video frame rate, and t is the video frame ratejRepresents the jth time, j is 0,1, …, M is a sufficiently large number;
and step 3: according to the scale and the pixel point coordinates, the liquid volume and the liquid terminal displacement (x) in the dripping process are obtainedN) Over time tjThe result of the change of (c);
and 4, step 4: deriving t by using finite difference method based on fluid mechanics continuity equationjRecursion relation u of average velocity of cross section normal direction of ith liquid micro-segment (i is 0,1, …, N)i，j(xi,tj). Wherein u isN，j(xN,tj) Is tjThe speed of dripping the liquid end at the moment, and the liquid end displacement x obtained in the step 3NObtaining a derivative of the time;
and 5: t is tjAt the moment, the velocity ui，j(xi,tj) Deriving the displacement to obtain each position xiVelocity gradient, i.e. strain rate
Will speed ui，j(xi,tj) Derivative the time to obtain tjAcceleration a of the motion of the ith micro-segment liquid at the momenti，j(xi,tj)；
Step 6: at a certain time tjSelecting the thinnest cross section (x) of the liquid dropkPosition) and drip end (x)N) The fluid in between is the research object, and the stress analysis is carried out. The tensile stress sigma on the finest section is obtained by the dynamic equilibrium equationk，j(xk,tj)；
And 7: the corresponding time t in the step 6jAnd the position x of the finest sectionkSubstituting the strain rate expression in the step 5 to obtain tjTime of day, position x of the thinnest cross sectionkStrain rate of (C)
Combining the stress obtained in the step 6 to obtain a stress-strain rate curve
And finally obtaining the viscosity of the liquid through numerical fitting.
2. The method of claim 1, wherein the experimental device comprises a common medical needle-free injector, a stand, a high-speed camera, etc. When the experiment table is set up, the iron support is placed on a table top, and the needle tube is fixed on the support, so that the axis of the needle tube is vertical downwards. The camera bracket is fixed on the ground, so that the camera shooting direction is horizontally vertical to the axis of the needle tube.
3. The method for measuring the viscosity of the liquid through the dripping experiment as claimed in claim 1, wherein the editing of the experiment video to obtain the single-drop dripping video comprises the following steps: first, each frame of picture in the experimental video is extracted, and the scale in the video is determined. Then the picture is cut properly, the colors in the picture are simple as much as possible, and the fluids have obvious differences. Then, the image is processed by binarization and morphological methods to make the edge clearer, and an edge detection method based on wavelet transformation is adopted to obtain the liquid boundary.
4. The method of claim 1, wherein spatial coordinates and time are discretized according to picture pixel and video frame rates, respectively. The picture is composed of a large number of pixel points, the position of a liquid outlet is selected as an original point, and a cylindrical coordinate system is established in the forward direction by taking the vertical downward dripping direction as an x axis. According to the symmetry of liquid dropping, the shape of the liquid during dropping can be regarded as a rotating body which is obtained by rotating r ═ d/2 around the x axis, wherein d is the cross-sectional diameter of the liquid filament, and r is the radius. The pixel grid of the picture naturally forms an Euler domain of liquid in a plane, and the two-dimensional grid is rotated around an x axis for one circle to obtain the Euler grid in a three-dimensional space. According to the coordinates of pixel points, the liquid image is dripped in the direction (x-axis direction)Directional) to disperse the spatial coordinates x, uniformly subdividing the liquid in the euler domain into a sufficient number of micro-segments, each segment of length h. For any fluid micro-segment between the ith pixel point and the (i + 1) th pixel point, the length h of the micro-segment is the difference value of the coordinates of the i pixel point and the (i + 1) th pixel point in the x direction, namely xi+1-xiWherein x isiThe coordinates of the position of the lower surface of the ith segment of liquid are shown, i is 0,1 and …. x is the number ofNIndicating the displacement of the end of the dripping liquid, and N changes as the liquid dripping height changes with time. Meanwhile, selecting a certain experimental picture result starting timing, recording the result as 0 moment, then selecting the time step delta t, and dispersing the time variable according to the video shooting frame rate. The time step Δ t is the time difference between corresponding times of any two frames of pictures, i.e., tj+1-tjWherein, tjThe j is 0,1, …, M is a sufficiently large number, or Δ t is 1/f, where f is the video frame rate.
5. The method of claim 1, wherein the actual length corresponding to the difference between the coordinates of two arbitrary pixels is calibrated according to the actual length between the scales in the scale in the photographed image. Therefore, the liquid volume and the liquid end displacement (x) in the dripping process are obtained on the basis of the discrete of the front space coordinate and the timeN) Over time tjAnd obtaining xiDiameter d of the corresponding liquid cross sectioni，j(xi,tj)。
6. The method of claim 1, wherein t is derived by using a finite difference method center difference format based on a continuity equation and the incompressibility of the liquidjRecursion relation u of average speed on section of ith liquid micro-segment (i is 1, …, N) at momenti，j(xi,tj). Wherein u isN，j(xN,tj) Is tjThe velocity of the end of the liquid at that moment being measuredTo the end of the liquid displacement xNAnd after the change result along with the time, the displacement is obtained by derivation of the time. The liquid micro-segment is simplified into a round table. Assuming that the liquid is incompressible and the density of the liquid in the micro-element liquid round table is unchanged, the continuity equation of the integral form is as follows:
center differencing of time:
substituting the expression (2) into the expression (1) to obtain a recurrence relation of the speed as follows:
wherein the content of the first and second substances,
Φ＝(2di，j+di+1，j)(di，j+1-di，j-1)+(2di+1，j+di，j)(di+1，j+1-di+1，j-1) (4)
the liquid dropping terminal speed u can be known by the recursion (3)N，j(xN,tj) Under the premise of (1), the average flow velocity u of the liquid cross section at any discrete time and at all discrete space positions in the liquid filament is recurredi，j(xi,tj). The velocity results are obtained by the difference method for the average flow velocity of the liquid cross section at any time and space position within the time and space range of the experiment but not on the discrete grid nodes.
7. Method for measuring the viscosity of a liquid by means of a dripping experiment according to claim 1, characterised in that said tjAt the moment, the velocity ui，j(xi,tj) The derivation of the displacement is carried out,each position x is obtained by adopting a numerical differentiation method of a central difference formatiVelocity gradient, i.e. strain rate
Will speed ui，j(xi,tj) T is obtained by time derivation and numerical differentiation method of central difference formatjAcceleration a of the motion of the ith micro-segment liquid at the momenti，j(xi,tj). Both results are obtained by the formulae (5) and (6):
8. method for measuring the viscosity of a liquid by means of a dripping experiment according to claim 1, characterised in that the certain time tjSelecting the thinnest cross section (x) of the liquid dropkPosition) and drip end (x)N) The fluid between the two sections is used as a research object, the stress analysis is carried out, and the tensile stress sigma on the finest section is obtained by a dynamic equilibrium equationk，j(xk,tj). The liquid is acted by gravity, pulling force and surface tension and has an acceleration aj(tj) Where σ is the surface tension coefficient, ρ is the liquid density, and g is the gravitational acceleration. At the aforesaid diameter d of the determined liquid cross-sectioni，j(xi,tj) On the basis, the minimum d is found by comparisoni，j(xi,tj) Then by finding the smallest di，j(xi,tj) Corresponding x coordinate, finally determining xk。xkThe included angle between the surface tension and the negative direction of the x axis in the stress analysis is 0 degree;
volume V of liquidj(tj) Obtained from the following formula (7)：
Acceleration a of the liquidj(tj) Obtained from the following formula (8):
the dynamic equilibrium equation is:
thus, t can be obtainedjAt the moment, the tensile stress acting on the finest liquid section:
9. the method of claim 1, wherein the obtaining of the stress-strain rate curve is based on a method of measuring the viscosity of a liquid by a drip test
Then, the viscosity of the liquid is finally obtained by numerical fitting. Due to sigmak，jFor tensile stress, the viscosity obtained by dividing the tensile stress by the strain rate is the extensional viscosity. Since the viscosity of a liquid is usually said to be shear viscosity and one third of extensional viscosity, the viscosity of a liquid is obtained by dividing the elongational viscosity by 3.
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