High-precision surface tension measuring method and device based on liquid drop forced vibration

Abstract

The invention belongs to the technical field of fluid mechanics testing, and particularly relates to a high-precision surface tension measuring method and device based on liquid drop forced vibration. Comprising the following steps: dropping to-be-detected liquid on a transparent detection table, and shooting a picture of the liquid drop from the lower part of the detection table; obtaining a contact line and a wetting area of the liquid drop on the detection table according to the picture; exciting the liquid drop to vibrate by exciting a vibration signal with gradually increased frequency, and continuously collecting an image in the liquid drop vibration process to obtain a curve of the amplitude of the liquid drop changing along with the frequency; the frequency corresponding to the first peak value of the curve is the viscous first-order resonance frequency fv of the liquid drop, calculating to obtain the non-viscous first-order inherent frequency fi; and obtaining the surface tension according to the density of the liquid to be measured, the volume of the liquid drop and the non-viscous first-order inherent frequency fi. The influence of viscosity, contact angle and contact line shape is considered, the liquid surface tension testing method is obtained based on forced vibration of the liquid drop, and the method has the characteristics of simplicity and convenience in operation, high measurement precision, capability of measuring various types of liquid and the like.

Description

Technical Field

[0001] The present invention belongs to the technical field of hydrodynamic testing, and particularly relates to a high-precision surface tension measurement method and device based on forced vibration of droplets. Background Art

[0002] The surface tension coefficient of a liquid is an important parameter characterizing the properties of the liquid, and this parameter is widely used in various fields such as chemistry, medicine, biotechnology, and materials science. Measuring surface tension is of great significance for understanding the physical properties of liquids, optimizing product performance, and improving processing efficiency. For example: in biomedical engineering, surface tension is used to control the interfacial behavior between cells and liquids, such as the wettability of cell culture media. In microfluidic technology, surface tension is also used for liquid manipulation, such as the generation and transportation of droplets. When liquid drugs are delivered through tiny channels, surface tension determines the fluidity of the liquid and the stability of the liquid in the channels.

[0003] Traditionally, methods for measuring the surface tension of liquids include the maximum bubble method, the sessile drop method, the capillary method, the free vibration method of droplets, etc. The sessile drop method is based on the equilibrium shape of a droplet on a plane. According to the Young-Laplace equation for liquid interface equilibrium, the surface tension is calculated through the contour shape of the droplet. However, the contour shape is generally difficult to obtain accurately and is obtained by fitting. The contour fitting is difficult and the calculation error is large. The free vibration method of droplets calculates the surface tension based on the relationship between the surface tension of the droplet and the first resonance frequency by measuring the first resonance frequency of the droplet. However, this method measures the surface tension of the droplet based on the free vibration of the droplet. When the liquid viscosity is relatively large, the free vibration decays too fast and the measurement error is very large. At the same time, the free vibration method of droplets generally uses the Rayleigh-Lamb formula applicable to spherical droplets, without considering the influence of droplet shape and liquid viscosity. The error in measuring the surface tension of liquids with a small contact angle or a large viscosity is large. In addition, this method does not consider the influence of the contact line shape and defaults the contact line to be circular. Generally speaking, the wetting of a liquid on a solid surface is not uniform, and the contact angle hysteresis phenomenon will occur, resulting in the contact line of the droplet not being circular. For example, some easily contaminated solid surfaces will make the contact line of the droplet non-circular, resulting in insufficient measurement accuracy. Therefore, it is necessary to provide an improved high-precision surface tension measurement method based on forced vibration of droplets to solve the above problems. Summary of the Invention

[0004] The purpose of the present invention is to provide a high-precision surface tension measurement method and device based on forced vibration of droplets, which considers the influence of viscosity, contact angle, and contact line shape, and based on the forced vibration of droplets, solves the disadvantages that the traditional method cannot measure the surface tension of liquids with a relatively high viscosity and cannot achieve accurate measurement in an easily contaminated environment.

[0005] To achieve the above object, the present invention provides a method for measuring surface tension based on the forced vibration of droplets, comprising the following steps:

[0006] S1. Drop the liquid to be measured on a transparent detection table, and take pictures of the droplet from below the detection table;

[0007] S2. Obtain the contact line and wetting area of the droplet on the detection table according to the picture;

[0008] S3. Excite the droplet to vibrate through a vibration signal, and gradually increase the excitation frequency. Continuously collect images of the droplet vibration process from above the detection table to obtain a curve of the droplet amplitude varying with frequency;

[0009] S4. The frequency corresponding to the first peak that appears in the curve of the droplet amplitude varying with frequency is the viscous first-order resonance frequency f v of the droplet. According to the viscous first-order resonance frequency f v obtain the inviscid first-order natural frequency f i :

[0010] S5. Obtain the surface tension of the liquid to be measured according to the density, droplet volume and inviscid first-order natural frequency f i of the liquid to be measured.

[0011] Further, the inviscid first-order natural frequency f i is obtained through the following formula:

[0012]

[0013] where the damping ratio f1 and f2 are respectively the two frequencies corresponding to 0.707 times the amplitude of the first peak;

[0014] Further, the surface tension of the liquid to be measured is obtained through the following formula:

[0015] where σ is the surface tension of the liquid, with the unit of N / m; f i is the inviscid first-order natural frequency of the droplet, with the unit of Hz; ρ is the density of the liquid, with the unit of kg / m 3 ; V is the droplet volume, with the unit of m 3 ; k and C are two dimensionless parameters, where k is obtained by fitting the equivalent contact angle of the droplet, and C is obtained by fitting the shape parameter and equivalent contact angle of the droplet.

[0016] Further, the parameter k is obtained according to the following formula:

[0017] k = -1.361 + 0.2673θ - 0.002631θ 2+6.938×10 -6 θ 3

[0018] Among them, θ is the equivalent contact angle of the droplet; the calculation formula for the equivalent contact angle θ is:

[0019]

[0020] S is the wetting area, with the unit of m 2 , and the unit of V is m 3 .

[0021] Furthermore, the calculation formula for the parameter C is:

[0022]

[0023] Among them, the fitting formula for the parameter ζ and the equivalent contact angle θ of the droplet is:

[0024] ζ = 7.518 - 0.02859θ - 500.4θ -1 +32330θ -2 -2.068×10 5 θ -3 .

[0025] The shape parameter γ = b / a, where b is the minimum width on the wetting area and a is the maximum length on the wetting area.

[0026] Furthermore, a calibration block with known dimensions is also placed on the detection table. The camera is used to simultaneously capture pictures of the droplet and the calibration block from below the detection table, and the wetting area of the droplet is calibrated according to the dimensions of the calibration block.

[0027] Furthermore, the preset volume of the droplet is 5uL - 25uL.

[0028] Furthermore, the transparent detection table is a transparent glass plate.

[0029] Furthermore, the maximum value of the excitation frequency is greater than the first-order resonance frequency of the droplet; the sampling frequency of the image during the vibration process of the droplet is 2 - 10 times the maximum value of the excitation frequency.

[0030] The present invention also provides a surface tension measurement device based on the forced vibration of a droplet, including:

[0031] A detection table for carrying the droplet to be measured;

[0032] A vibration module for exciting the vibration of the droplet to be measured;

[0033] An image acquisition module for acquiring the contact pictures of the droplet to be measured and the detection table and the images during the vibration process of the droplet;

[0034] A signal processing module for processing the contact picture of the liquid droplet to be measured and the detection stage and the image of the liquid droplet vibration process to obtain the non-viscous first-order natural frequency f i Then, according to the density of the liquid to be measured, the volume of the liquid droplet, and the non-viscous first-order natural frequency f i The surface tension of the liquid droplet to be measured is obtained by the calculation formula.

[0035] Furthermore, the vibration module includes a signal generator, a power amplifier, a vibration stage, and a carrier stage connected in sequence; the carrier stage is arranged on the vibration stage, and the detection stage is arranged on the carrier stage.

[0036] Furthermore, the image acquisition module includes a first camera arranged below the detection stage and a second camera arranged above the detection stage, and the second camera is located on the side of the liquid droplet to be measured; a calibration block with a known size is also fixed on the detection stage.

[0037] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the following technical advantages are mainly possessed:

[0038] 1. The high-precision surface tension measurement method based on the forced vibration of liquid droplets provided by the present invention fully considers the influence of the contact angle, contact line shape, and viscosity of the liquid droplet. Based on the forced vibration of the liquid droplet (i.e., by continuously applying an excitation to make the liquid droplet vibrate continuously), by accurately measuring the first-order resonance frequency of the liquid droplet, the surface tension of the liquid can be accurately obtained. The present invention can measure the surface tension of liquid droplets with non-circular contact lines and liquid droplets with high viscosity, and can solve the problem of insufficient measurement accuracy caused by the existing methods not considering the influence of the contact angle and viscosity, as well as the problem of insufficient measurement accuracy in many easily contaminated environments. It has the characteristics of simple operation, high measurement accuracy, and a wide variety of liquids that can be measured.

[0039] 2. The present invention is convenient for collecting the bottom image of the liquid droplet through the transparent detection stage and the micro camera arranged below the detection stage, so as to obtain its contact line shape and wetting area, providing effective parameters for the calculation of the surface tension.

[0040] 3. The present invention considers the problem of damping due to the action of viscosity when the liquid droplet vibrates. The damping ratio is obtained according to the two frequencies corresponding to 0.707 times of the maximum amplitude, and the non-viscous first-order natural frequency is obtained according to the damping ratio and the viscous first-order resonance frequency, improving the accuracy of the surface tension calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a schematic structural diagram of an apparatus for high-precision surface tension measurement based on the forced vibration of liquid droplets of the present invention.

[0042] Figure 2Another perspective structural schematic diagram of the device for high-precision surface tension measurement based on forced vibration of droplets in the present invention.

[0043] Figure 3 Curves of droplet vibration (left) and amplitude varying with frequency (right).

[0044] Figure 4 Curve of the relationship between the equivalent contact angle and the wetted area of a droplet with a volume of 22 uL.

[0045] Figure 5 Curve of the relationship between k and the equivalent contact angle.

[0046] Figure 6 Curve of the relationship between ζ and the equivalent contact angle.

[0047] In all the drawings, the same reference numerals are used to represent the same elements or structures, where:

[0048] 1 - High-speed camera, 2 - Constant-volume dropper, 3 - Droplet, 4 - Calibration block, 5 - Detection table, 6 - Micro camera, 7 - Carrier table, 8 - Vibration table, 9 - Power amplifier, 10 - Signal generator. Specific implementation mode

[0049] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0050] As Figure 1 and 2 shown, the present invention provides a surface tension measurement device based on forced vibration of droplets, including:

[0051] A detection table for carrying the droplet to be measured; a constant-volume dropper for dripping a specified volume of droplet onto the detection table;

[0052] A vibration module for exciting the vibration of the droplet to be measured;

[0053] An image acquisition module for acquiring the contact picture of the droplet to be measured and the detection table and the images during the vibration process of the droplet;

[0054] A signal processing module for processing the contact picture of the droplet to be measured and the detection table and the images during the vibration process of the droplet to obtain the non-viscous first-order natural frequency f i , and then according to the density of the liquid to be measured, the volume of the droplet and the non-viscous first-order natural frequency f iThe surface tension of the liquid droplet to be measured is obtained by the calculation formula.

[0055] Specifically, the image acquisition module includes a high-speed camera 1 obliquely above the detection stage 5 for taking and recording images of the vibration of the liquid droplet 3, and a micro camera 6 below the detection stage 5 for taking pictures of the liquid droplet 3 from below the detection stage 5. The calibration block 4 is located near the liquid droplet on the detection stage 5 for calibrating the scale of the picture of the liquid droplet 3 taken by the micro camera 6, and then using a computer to process the picture to obtain the wetting area S of the contact line and the shape parameter γ. The detection stage 5 is preferably a transparent glass plate.

[0056] The vibration module includes a signal generator 10, a power amplifier 9, a vibration table 8 and a carrier table 7 connected in sequence; the carrier table 7 is arranged on the vibration table 8, and the detection stage 5 is arranged on the carrier table 7. The signal generator 10 is used to generate a sine wave signal with a given amplitude and frequency. After being amplified by the power amplifier 9, the signal is input to the vibration table 8 to make the vibration table generate vibrations with the same frequency as the input signal, and the vibrations are transmitted to the liquid droplet 3 through the carrier table 7 to excite the liquid droplet to vibrate.

[0057] Particularly, the vibration table 8, the carrier table 7 and the detection stage 5 are bonded and fixed by a photo-curing UV glue.

[0058] The surface tension measurement method based on the forced vibration of the liquid droplet provided by the present invention uses a high-speed camera to collect the forced vibration image of the liquid droplet and convert it into a vibration signal, which is collected and processed by a computer signal processing module, and based on parameters such as the shape and area of the contact line of the liquid droplet, the surface tension is obtained. Specifically, it includes the following steps:

[0059] (1) Use a fixed-volume dropper 2 to drop a liquid droplet with a fixed volume on the transparent glass plate. For the accuracy of measurement, the volume of the liquid droplet should not be too large and should be between 5 uL and 25 uL. In this embodiment, a liquid droplet with a volume of 22 uL is used for specific illustration.

[0060] (2) Use the micro camera 6 to take a picture of the shape of the contact line of the liquid droplet 3 from below the transparent glass plate, and the calibration block 4 on the transparent glass plate will also be photographed in the picture. The picture is transmitted to the computer processing module. After the computer automatically calibrates the size of the picture using the photographed calibration block 4, the picture is binarized to obtain a grayscale image of the shape of the contact line of the liquid droplet, and the edge detection algorithm is used to detect the contact line, and the wetting area S of the liquid droplet is calculated. The shape parameter γ of the contact line is obtained by calculating the ratio of the minimum width b and the maximum length a of the contact line, γ = b / a.

[0061] (3) Use the signal generator 10 to output a sine wave signal with a fixed amplitude and a frequency that continuously increases over time. After being amplified by the power amplifier 9, the signal is input to the vibration table 8 to cause the vibration table 8 to vibrate. The vibration is transmitted through the carrier table 7 and the transparent glass plate to the droplet 3 to excite the droplet 3 to vibrate. The amplitude of the signal output by the signal generator 10 should not be too large to avoid exciting the high-order modes of the droplet and also to avoid the influence of the large amplitude of the droplet 3 on the first-order resonance frequency due to non-linear vibration.

[0062] (4) The high-speed camera 1 captures the images of the vibration of the droplet 3, and the amplitude of the droplet 3 is extracted through computer machine vision processing. As time changes, the frequency of the signal input from the signal generator 10 to the vibration table 8 gradually increases. As the input vibration frequency increases to approach the first-order resonance frequency of the droplet, the amplitude of the droplet gradually increases. Then, as the input vibration frequency increases to exceed the first-order resonance frequency of the droplet, the amplitude of the droplet gradually decreases. After being processed by the computer processing module, the curve of the droplet amplitude changing with frequency is obtained, as Figure 3 shown. According to the sampling theorem, the sampling frequency needs to be more than twice the highest signal frequency. The image sampling frequency of the high-speed camera 1 is set to 10 times the highest signal frequency to ensure that the waveform of the captured droplet vibration signal is not distorted.

[0063] (5) Figure 3 The frequency corresponding to the first peak in the curve of the droplet amplitude changing with frequency in v is the viscous first-order resonance frequency f v of the droplet. Due to the effect of viscosity during the vibration of the droplet, there will be damping, making the actual viscous first-order resonance frequency f i of the droplet lower than the non-viscous first-order natural frequency f

[0064] where f v is the viscous first-order resonance frequency of the droplet, f i is the non-viscous first-order natural frequency of the droplet, and χ is the damping ratio of the vibration.

[0065] (6) The damping ratio χ can be obtained through the half-power bandwidth method in the frequency response curve. From Figure 3 the two frequencies f1 and f2 corresponding to 0.707 times the maximum amplitude in the frequency response curve (the 0.707 times position of the amplitude peak corresponds to two frequencies, namely one is the frequency corresponding to the amplitude rising to 0.707 times and the other is the frequency corresponding to the amplitude falling to 0.707 times), and f1 is less than f2, the damping ratio can be calculated as

[0066] (7) The calculation formula for the surface tension of the liquid is:

[0067] Among them, σ is the surface tension of the liquid, with the unit of N / m; f i is the inviscid first-order natural frequency of the droplet, with the unit of Hz; ρ is the density of the liquid, with the unit of kg / m 3 ; V is the volume of the droplet, with the unit of m 3 ; k and C are two dimensionless parameters determined by the shape of the contact line and the wetting area.

[0068] (8) The calculation of the parameters k and C requires the equivalent contact angle θ of the droplet.

[0069] The calculation formula for the equivalent contact angle θ is:

[0070]

[0071] The unit of S is m 2 , and the unit of V is m 3 .

[0072] Specifically, in the implementation, the droplet volume is fixed at 22 uL. The curve of the equivalent contact angle θ of the 22 uL droplet and the wetting area S of the contact line is as Figure 4 shown. The equivalent contact angle θ can be calculated using the formula for the equivalent contact angle θ, and the operation can be quickly completed by a computer.

[0073] (9) The relationship between the parameter k and θ can be obtained through numerical simulation. The fitting formula for the parameter k and θ is:

[0074] k = -1.361 + 0.2673θ - 0.002631θ 2 + 6.938×10 -6 θ 3

[0075] The curve of the parameter k and θ is as Figure 5 shown. Calculate the corresponding k using the equivalent contact angle θ obtained in step (8).

[0076] (10) The calculation formula for the parameter C is:

[0077]

[0078] Among them, ζ is related to the equivalent contact angle θ. The fitting formula for the parameter ζ and θ is:

[0079] ζ = 7.518 - 0.02859θ - 500.4θ -1 + 32330θ -2 - 2.068×10 5 θ -3 .

[0080] The relationship curve is as Figure 6As shown, the value of ζ can be calculated by the formula using the equivalent contact angle θ, and then the parameter C can be calculated.

[0081] Furthermore, the wetting area S of the droplet contact line and the value of the shape parameter γ obtained in the specific implementation step (2) are calibrated using a calibration block. The shape parameter γ is the ratio of the minimum width b (minor axis length) to the maximum length a (major axis length) of the droplet, i.e., γ = b / a.

[0082] In summary, a method and device for realizing high-precision measurement of liquid surface tension based on forced vibration of droplets provided by the present invention takes into account the effects of the contact angle, contact line shape, and viscosity of the droplets. By accurately measuring the first-order resonance frequency of the droplets, the surface tension of the liquid can be accurately measured. The present invention can measure the surface tension of droplets with non-circular contact lines and droplets with high viscosity. It can solve the problem of insufficient measurement accuracy caused by the existing methods not considering the effects of contact angle and viscosity, and can also solve the problem of insufficient measurement accuracy of the existing methods in many easily contaminated environments.

[0083] Those skilled in the art can easily understand that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for measuring surface tension based on forced vibration of a droplet, characterized in that: The following steps are involved: S1. Drop the liquid to be tested on a transparent testing platform and take a picture of the drop from the bottom of the testing platform; S2. Obtaining the contact line and wetting area of ​​the droplet on the test platform according to the image; S3, exciting the droplet to vibrate by a vibration signal, and gradually increasing the excitation frequency, continuously collecting images of the droplet vibration process from above the detection platform, and obtaining a curve of the droplet amplitude changing with the frequency; S4. The frequency corresponding to the first peak of the curve of droplet amplitude changing with frequency is the first-order viscous resonance frequency f of the droplet. v , according to the first-order resonance frequency f v The inviscid first-order natural frequency f is obtained i : S5, according to the density of the liquid to be tested, the volume of the droplet and the inviscid first-order natural frequency f i The surface tension of the liquid to be measured is obtained.

2. The surface tension measurement method based on forced vibration of a droplet according to claim 1, characterized in that: The inviscid first-order natural frequency f i Obtained by the following formula: Among them, the damping ratio f1 and f2 are two frequencies corresponding to 0.707 times the amplitude of the first peak.

3. The surface tension measurement method based on forced vibration of a droplet according to claim 1, characterized in that: The surface tension of the liquid to be measured is obtained by the following formula: Where σ is the surface tension of the liquid, in N / m; f i is the inviscid first-order natural frequency of the droplet, in Hz; ρ is the density of the liquid, in kg / m 3 ; V is the droplet volume, in m 3 ; k and C are two dimensionless parameters, where k is obtained by fitting the equivalent contact angle of the droplet, and C is obtained by fitting the shape parameters of the droplet and the equivalent contact angle.

4. The surface tension measurement method based on forced vibration of a droplet according to claim 3, characterized in that: The parameter k is obtained according to the following formula: k=-1.361+0.2673θ-0.002631θ 2 +6.938×10 -6 i 3 Wherein, θ is the equivalent contact angle of the droplet; the calculation formula of the equivalent contact angle θ is: S is the wetted area, in m 2 , the unit of V is m 3 ; The parameter C is obtained according to the following formula: Among them, the fitting formula of parameter ζ and the equivalent contact angle θ of the droplet is: ζ=7.518-0.02859θ-500.4θ -1 +32330θ -2 -2.068×10 5 i -3 ; The shape parameter γ=b / a, where b is the minimum width on the wetted area and a is the maximum length on the wetted area.

5. The surface tension measurement method based on forced vibration of a droplet according to claim 1, characterized in that: A calibration block of known size is also placed on the test bench, and a camera is used to simultaneously take pictures of the droplet and the calibration block from below the test bench, and the wetting area of ​​the droplet is calibrated according to the size of the calibration block.

6. The surface tension measurement method based on forced vibration of a droplet according to claim 1, characterized in that: The preset volume of the droplet is 5uL-25uL; the transparent detection platform is a transparent glass plate.

7. The surface tension measurement method based on forced vibration of a droplet according to claim 1, characterized in that: The maximum value of the excitation frequency is greater than the first-order resonance frequency of the droplet; and the sampling frequency of the image of the droplet vibration process is 2-10 times the maximum value of the excitation frequency.

8. A surface tension measuring device based on forced vibration of a droplet, characterized in that: include: A testing platform, used for carrying the droplets to be tested; A vibration module, used for exciting the droplet to be tested to vibrate; An image acquisition module, used to acquire contact images between the droplet to be tested and the test platform and images of the droplet vibration process; The signal processing module is used to process the contact image of the droplet to be tested and the detection platform and the image of the droplet vibration process to obtain the inviscid first-order natural frequency f i , then according to the density of the liquid to be tested, the volume of the droplet and the inviscid first-order natural frequency f i The surface tension of the droplet to be tested is obtained by the calculation formula.

9. The surface tension measuring device based on forced vibration of a droplet according to claim 8, characterized in that: The vibration module comprises a signal generator, a power amplifier, a vibration platform and a bearing platform which are connected in sequence; the bearing platform is arranged on the vibration platform, and the detection platform is arranged on the bearing platform.

10. The surface tension measuring device based on forced vibration of a droplet according to claim 8, characterized in that: The image acquisition module includes a first camera arranged below the detection platform and a second camera arranged above the detection platform, wherein the second camera is located on the side of the droplet to be detected; a calibration block with a known size is also fixed on the detection platform.

Images