Device and method for fitting flight liquid drop track

Abstract

The invention discloses a device for fitting a flight liquid drop track. The device comprises a waveform generator and a power amplifier, the liquid drop excitation system is connected with the power amplifier; the liquid drop collection substrate is arranged above the liquid drop excitation system; the industrial camera and the LED light source system are used for shooting the flight path of the liquid drop; and the computer is in communication connection with the image processing system and the industrial camera, receives the image, processes and analyzes the image and fits a flight path, and the fitting step comprises the steps of carrying out stress analysis on the flying liquid drop, considering gravity and air resistance, and then fitting a liquid drop flight path equation according to a stress analysis result and experimental data. According to the invention, the flight liquid drop trajectory can be accurately fitted, efficient and accurate liquid drop trajectory fitting is realized from liquid drop excitation to trajectory shooting and analysis processing through cooperation of all parts of the system, and an effective technical means is provided for related research and application.

Description

Technical Field

[0001] The present invention relates to the technical field of ultrasonic pipetting, and more specifically, to a device and method for fitting the trajectory of flying droplets. Background Art

[0002] Acoustic Droplet Ejection (ADE) is a technology that uses sound waves to generate droplets and precisely eject them from the liquid surface to a specific position. Its core principle is that through the action of the pressure field generated by ultrasonic waves, the local deformation of the liquid surface occurs, and then the droplet is driven to separate from the liquid. Then the droplet will move upward with a certain initial velocity, and finally the droplet will be collected on the collection substrate.

[0003] During the process of ultrasonic - excited micro - liquid transfer, the droplet should move vertically upward. However, in the experiment, the actual movement trajectory of the excited droplet often deviates from the theoretical trajectory. Since the ultrasonic pipetting technology needs to transfer the liquid from the source liquid pool to the collection plate in a non - contact manner, it is necessary to accurately know whether the droplet can be precisely collected by the collection plate after leaving the source liquid pool.

[0004] The volume of the excited droplet is usually at the nanoliter (nL) or picoliter (pL) level. Due to the extremely small size of the droplet, its motion state is difficult to directly observe. Therefore, it is necessary to use an experimental device to monitor and record it in real - time, obtain the motion trajectory of the droplet, and record its flight state and speed. However, there is currently no dedicated device for recording the motion trajectory of the droplet, its flight state, and speed. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the purpose of the present invention is to provide a device that can effectively record the motion trajectory of the droplet, its flight state, and speed. Then, based on these data, it can accurately determine whether the droplet is successfully collected on the collection plate, further optimize the experimental parameters, improve the accuracy and repeatability of ultrasonic pipetting, and ensure the reliability and stability of the experimental results.

[0006] To achieve the above - mentioned purpose, the present invention provides the following technical solution: A device for fitting the trajectory of flying droplets, comprising:

[0007] A waveform generator and a power amplifier, used to generate and amplify a pulse signal with a specific amplitude and duration;

[0008] A droplet excitation system, connected to the power amplifier, used to receive the pulse signal output by the power amplifier and then excite the droplet to make the droplet fly;

[0009] A droplet collection substrate, arranged above the droplet excitation system, used to collect the excited droplets;

[0010] An industrial camera and an LED light source system for photographing the flight trajectory of droplets;

[0011] A computer and an image processing system, communicatively connected to the industrial camera, receiving the images captured by the industrial camera, and performing subsequent image processing, analysis, and fitting of the flight trajectory.

[0012] As a further improvement of the present invention, the droplet excitation system includes:

[0013] A concave focusing transducer, connected to a power amplifier, for receiving the output pulse signal, converting the pulse signal into high-frequency ultrasonic waves and then outputting them;

[0014] A source liquid pool, installed above the concave focusing transducer, filled with a solution, for receiving the high-frequency ultrasonic waves output by the concave focusing transducer to form a capillary wave on the liquid surface of the solution, and then forming micro-droplets with a certain initial velocity;

[0015] A coupling medium, arranged between the concave focusing transducer and the source liquid pool to transmit high-frequency ultrasonic waves to the source liquid pool. Based on the above device, on the other hand, the present invention provides a method for fitting the trajectory of flying droplets, which is as follows: using the waveform generator and power amplifier in the device and the droplet excitation system to excite droplets, collecting droplets through a droplet-based collection substrate, using an industrial camera and an LED light source system to collect flight images, and performing subsequent image processing, analysis, and fitting of the flight trajectory through a computer and an image processing system. Performing subsequent image processing, analysis, and fitting of the flight trajectory includes the following steps:

[0016] Step 1, perform a force analysis on the flying droplets. The forces acting on the droplets during flight include gravity and air resistance;

[0017] Step 2, according to the force analysis result and experimental data in Step 1, fit the flight trajectory equation of the droplets. As a further improvement of the present invention, the specific steps for performing a force analysis on the flying droplets in Step 1 are as follows:

[0018] Step 1-1, perform a gravity analysis on the flying droplets, and calculate the magnitude of the gravity of the flying droplets according to the following formula:

[0019] F gravity＝ m×g

[0020] where m is the mass of the droplet and g is the acceleration due to gravity;

[0021] Step 1-2, perform an air resistance analysis on the flying droplets, and calculate the magnitude of the air resistance according to the following formula:

[0022]

[0023] Among them, Cd is the drag coefficient, ρ is the air density, A is the cross-sectional area of the droplet, and V is the velocity of the droplet; Step 1-3: Establish the differential equations of motion according to the X-axis, Y-axis, and Z-axis, and then solve the differential equations of motion and take the derivative of the analytical solution.

[0024] As a further improvement of the present invention, the specific steps for establishing the differential equation of motion according to the X-axis direction in Step 1-3 are as follows:

[0025] The droplet is only affected by air resistance in the X-axis direction, and the direction of the resistance is opposite to the direction of the velocity. Therefore, the resistance expression is obtained as:

[0026]

[0027] From Newton's second law:

[0028]

[0029] It is obtained that:

[0030]

[0031] After simplification, it is obtained that:

[0032]

[0033] Among them: As a further improvement of the present invention, the specific steps for establishing the differential equation of motion according to the Y-axis direction in Step 1-3 are as follows: The force analysis in the Y-axis is similar to that in the X-axis, but attention should be paid to the influence of the initial velocity direction on the resistance sign:

[0034]

[0035] As a further improvement of the present invention, the specific steps for establishing the differential equation of motion according to the Z-axis direction in Step 1-3 are as follows: The Z-axis needs to additionally consider the gravitational acceleration, and its equation of motion is:

[0036]

[0037] Among them, Kx = Ky = Kz, reflecting the isotropic drag coefficient.

[0038] As a further improvement of the present invention, the specific method for solving the differential equation of motion and taking the derivative of the analytical solution in Step 1-3 is that for the second-order nonlinear differential equations in the X and Y directions, they are integrated and solved by the method of separating variables, and for the Z-axis equation, the fourth-order Runge-Kutta method is used for numerical solution.

[0039] As a further improvement of the present invention, the specific method for fitting the flight trajectory equation of the droplet in Step 2 is as follows:

[0040] Using a quadratic polynomial to fit the droplet motion trajectory in the X-axis direction, the following trajectory equation can be obtained:

[0041] x(t) = At 2 + Bt + C;

[0042] Using a quadratic polynomial to fit the droplet motion trajectory in the Y-axis direction, the following trajectory equation can be obtained:

[0043] y(t) = At 2 + Bt + C;

[0044] Using a quartic polynomial to fit the droplet motion trajectory in the Z-axis direction, the following trajectory equation can be obtained:

[0045] z(t) = At^4 + Bt^3 + Ct^2 + Dt + E;

[0046] Wherein, A, B, C, D, and E are the polynomial coefficients obtained by fitting.

[0047] Advantages of the present invention: The device for fitting the flight trajectory of ultrasonic droplets in the present invention takes into account the directional influence of air resistance during the droplet flight process, and combines the numerical integration method to more accurately predict the flight trajectory of the droplet. By using the drag coefficients in different directions and the modified analytical solution, this method can more accurately simulate the flight process of the droplet in three-dimensional space and has a high calculation efficiency. Compared with the existing methods, it can effectively realize the motion trajectory of the droplet, record its flight state and speed, and then know whether the droplet can be accurately collected by the collection plate after leaving the source liquid pool. Description of the Drawings

[0048] Figure 1 It is a module schematic diagram of the device for fitting the flight droplet trajectory of the present invention;

[0049] Figure 2 It is a schematic diagram of the droplet captured in the X and Y directions;

[0050] Figure 3 It is a fitting diagram of the droplet flight trajectory. Detailed Embodiments

[0051] The following will further elaborate on the present invention in combination with the embodiments given in the drawings.

[0052] Referring to Figure 1 as shown, a device for testing the contact position of a flying droplet in this embodiment includes: an ultrasonic pipetting part, a droplet observation part, and a droplet image processing part.

[0053] The ultrasonic pipetting part is used to excite and generate micro-droplets moving upward, including an arbitrary waveform generator 1, a power amplifier 2, a concave focusing transducer 3, a coupling medium 4, a source liquid pool 5 and a droplet collection substrate 7. Among the above, the arbitrary waveform generator 1 is used to output a sine pulse signal with a specific amplitude and duration. After being amplified by the power amplifier 2, it drives the concave focusing transducer 3 to convert the amplified electrical signal into high-frequency ultrasonic waves. The high-frequency ultrasonic waves are transmitted to the source liquid pool 5 through the coupling medium 4. The high-frequency ultrasonic waves will focus on the liquid surface of the source liquid pool 5. When the acoustic power is high enough, the focused energy will overcome the constraint of surface tension and form a capillary wave on the liquid surface, and then form micro-droplets with a certain initial velocity. The micro-droplets will finally be collected on the droplet collection substrate 7.

[0054] The droplet observation part is used to capture images of flying droplets, including two industrial cameras 8 and two LED light sources 6. Among the above, by setting two industrial cameras 8 in the X and Y directions and then using two LED light sources 6 for supplementary lighting, when the micro-droplets fly upward away from the source liquid, the flying trajectories of the micro-droplets will be recorded by the two industrial cameras 8.

[0055] The droplet image processing part is used to preprocess the images of flying droplets and fit the motion trajectory curve of the droplets, including a computer 9 and a software program preset in the computer. Among the above, the computer 9 receives the images taken by the industrial camera 8 and screens out the images containing droplets. The images containing droplets are screened out through the droplet image processing module. As Figure 2 shown in the droplet images in the X and Y directions, the specific processing steps are as follows:

[0056] First, preprocess the droplet images, including: image denoising to remove interference caused by factors such as ambient light sources; edge detection to ensure clear droplet boundaries; centroid extraction to use image analysis algorithms to extract the centroid position of the droplets and fit to obtain the flight trajectory of the droplets. Finally, record the flight state and speed of the droplets. The specific steps to fit the flight trajectory of the droplets are as follows:

[0057] Step 1, perform force analysis and establish a motion differential equation using the experimental data obtained by the above device.

[0058] First, perform force analysis. It can be known that the flying droplets are affected by multiple forces, mainly including gravity and air resistance:

[0059] Gravitational force: The droplets will be affected by gravitational force during flight, causing them to fall vertically.

[0060] The magnitude of the gravitational force is

[0061] F gravity＝ m×g

[0062] where m is the mass of the droplet and g is the acceleration due to gravity.

[0063] Effect of air resistance: When the droplet is flying in the air, the air resistance decelerates the droplet. The magnitude of the air resistance is given by the hydrodynamics equation:

[0064]

[0065] where Cd is the drag coefficient, ρ is the air density, A is the cross-sectional area of the droplet, and V is the velocity of the droplet.

[0066] The motion of the droplet in three-dimensional space is affected by both gravity and air resistance. According to Newton's second law, the acceleration in each direction is determined by the resultant force. Considering the non-linear characteristics and direction dependence of air resistance, the following differential equations of motion are established:

[0067] Establish a differential equation in the X-axis direction

[0068] The droplet is only affected by air resistance in the X-axis direction, and the direction of the resistance is opposite to the direction of the velocity. The resistance expression is:

[0069]

[0070] From Newton's second law:

[0071]

[0072] We get:

[0073]

[0074] After simplification, we get:

[0075]

[0076] where:

[0077]

[0078] Establish a differential equation in the Y-axis direction

[0079] The force analysis in the Y-axis is similar to that in the X-axis, but note the influence of the initial velocity direction (such as a negative initial velocity) on the sign of the resistance:

[0080]

[0081] Establish a differential equation in the Z-axis direction

[0082] The acceleration due to gravity (negative downward) needs to be additionally considered in the Z-axis. Its equation of motion is:

[0083]

[0084] where \(K_x = K_y = K_z\), representing the isotropic drag coefficient.

[0085] Step 2: Equation Solving and Derivation of Analytical Solution

[0086] For the second-order nonlinear differential equations in the X and Y directions, they are solved by integration using the method of separation of variables. Taking the X-axis as an example:

[0087]

[0088] By separating variables and integrating, we get:

[0089]

[0090] We obtain:

[0091]

[0092] Substituting the initial condition \(V\) x (0) = \(V\) x0 , we solve to get:

[0093]

[0094] Integrating again gives the displacement equation:

[0095]

[0096] Similarly, the solution for the Y-axis is:

[0097]

[0098] For the Z-axis equation, due to the coupling of gravity and resistance, there is no closed-form analytical solution. The fourth-order Runge-Kutta method is used for numerical solution:

[0099]

[0100] Step 3: Generation of Theoretical Trajectory

[0101] For the X-axis, \(\ln(1 + K\) x \(V\) x0 \(t)\) can be Taylor-expanded when \(t\) is small as Truncated to the quadratic term approximation. Therefore, by fitting the droplet motion trajectory in the X-axis direction with a quadratic polynomial, the following trajectory equation can be obtained: \(x(t)=At\) 2 +\(Bt + C\)

[0102] Similarly for the Y-axis, the analytical solution with a negative initial velocity is still dominated by the quadratic term after expansion. Therefore, by fitting the droplet motion trajectory in the Y-axis direction with a quadratic polynomial, the following trajectory equation can be obtained: \(y(t)=At\) 2 +\(Bt + C\)

[0103] For the trajectory with high-order dynamic characteristics caused by the coupling of Z-axis gravity and non-linear resistance, a fourth-order term is required to capture the curvature change. Therefore, by using a fourth-degree polynomial to fit the droplet motion trajectory in the Z-axis direction, the following trajectory equation can be obtained: z(t) = At 4 + Bt 3 + Ct 2 + Dt + E

[0104] where A, B, C, D, and E are the polynomial coefficients obtained by fitting.

[0105] In this way, through the above device and the corresponding image processing method, the fitting of the droplet flight trajectory can be effectively realized, and the flight state and speed of the flying droplet can be recorded.

[0106] The following examples are provided in this embodiment to further illustrate the progress of the solution of the present invention.

[0107] Using distilled water as the solution in the coupling medium 4 and the source liquid pool 5, adjust the position and focal length of the industrial camera 8, adjust the voltage amplitude and frequency of the electrical signal of the arbitrary waveform generator 1, and adjust the power of the power amplifier 2 to continuously and stably excite the droplet by the concave focusing transducer 3. Turn on the industrial camera 8 and the computer 9 for experiments. During the experiment, the flying droplet is tracked and photographed by the industrial camera 8 and the LED light source 6. The computer 9 records the whole process of the droplet from excitation to collection, and processes the collected data to obtain the three-dimensional coordinate data (x(t), y(t), z(t)) during the droplet movement. The results are shown in Table 1:

[0108] Table 1 Records a set of droplet coordinates

[0109]

[0110] In summary, according to the experimental data and the force analysis of the droplet, a dynamic model of droplet flight is constructed. Through the mathematical analysis of the forces acting on the droplet, the motion equation of the droplet in three-dimensional space is obtained. The motion of the droplet is comprehensively affected by gravity, air resistance, and air torque. Combining the above steps and the data in Table 1, the experimental data is fitted with the force model using the least squares method, and the coefficients of each term of the droplet flight trajectory equation are calculated. The purpose of the least squares method is to minimize the error between the actual data and the fitting equation to obtain the optimal flight trajectory equation. Finally, the fitted trajectory image is obtained as Figure 3 shown, and the following trajectory equation set:

[0111] x(t) = -0.00010102t2 + 0.023t + 3.213e-10

[0112] y(t) = 0.00022055t2 -0.034t - 1.0366e-09

[0113] z(t) = -0.024425t 4 +0.38989t 3 -5.0335t 2 +1.1063t + 2.7531e-05。

[0114] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements should also be regarded as within the protection scope of the present invention.

Claims

1. A device for fitting the trajectory of a flying droplet, characterized in that: include: A waveform generator (1) and a power amplifier (2) are used to generate and amplify a pulse signal with a specific amplitude and duration; A droplet excitation system is connected to the power amplifier (2) and is used to excite the droplets after receiving the pulse signal output by the power amplifier (2), so that the droplets are excited to fly; A droplet collecting substrate (7) is arranged above the droplet excitation system and is used to collect the excited droplets; An industrial camera (8) and an LED light source system (6) for photographing the flight trajectory of the droplets; The computer and image processing system (9) are connected to the industrial camera for communication, receive images taken by the industrial camera, and perform subsequent image processing, analysis and flight trajectory fitting.

2. The device for fitting the trajectory of a flying droplet according to claim 1, characterized in that: The droplet excitation system comprises: The concave focusing transducer (3) is connected to the power amplifier (2) and is used to receive the output pulse signal, convert the pulse signal into high-frequency ultrasonic waves and then output them; A source liquid pool (5), which is installed above the concave focusing transducer (3) and is filled with a solution, and is used to form a capillary wave on the liquid surface of the solution after receiving the high-frequency ultrasonic wave output by the concave focusing transducer (3), thereby forming micro-droplets with a certain initial velocity; The coupling medium (4) is arranged between the concave focusing transducer (3) and the source liquid pool (5) to transmit high-frequency ultrasonic waves to the source liquid pool (5).

3. A method for fitting the trajectory of a flying droplet, using the device as claimed in claim 1 or 2, using the waveform generator (1) and the power amplifier (2) and the droplet excitation system in the device to excite the droplets, collecting the droplets through a droplet-based collection substrate (7), using an industrial camera (8) and an LED light source system (6) to collect flight images, and performing subsequent image processing, analysis and flight trajectory fitting through a computer and an image processing system (9), characterized in that: The subsequent image processing, analysis and flight trajectory fitting include the following steps: Step 1: Perform force analysis on the flying droplets. The forces on the droplets during flight include gravity and air resistance. Step 2: Fit the droplet flight trajectory equation based on the force analysis results of step 1 and experimental data.

4. The device for fitting the trajectory of a flying droplet according to claim 3, characterized in that: The specific steps of performing force analysis on the flying droplet in step 1 are as follows: Step 1, perform gravity analysis on the flying droplets, and calculate the gravity of the flying droplets according to the following formula: F gravity＝ m×g Where m is the mass of the droplet and g is the acceleration due to gravity; Step 1 and 2: Analyze the air resistance of the flying droplets and calculate the air resistance according to the following formula: Where Cd is the drag coefficient, ρ is the air density, A is the cross-sectional area of ​​the droplet, and V is the velocity of the droplet; Step 1 and 3, establish the differential equation of motion according to the X-axis, Y-axis and Z-axis directions, and then solve the differential equation of motion and differentiate the analytical solution.

5. The device for fitting the trajectory of a flying droplet according to claim 4, characterized in that: The specific steps of establishing the motion differential equation according to the X-axis direction in step 1-3 are as follows: The droplet is only affected by air resistance on the X-axis, and the direction of resistance is opposite to the direction of velocity, so the resistance expression is obtained as: From Newton's second law: have to: Simplified: in:

6. The device for fitting the trajectory of a flying droplet according to claim 4, characterized in that: The specific steps of establishing the differential equation of motion according to the Y-axis direction in step 1-3 are as follows: The force analysis of the Y-axis is similar to that of the X-axis, but attention should be paid to the influence of the initial velocity direction on the resistance sign:

7. The device for fitting the trajectory of a flying droplet according to claim 4, characterized in that: The specific steps of establishing the motion differential equation according to the Z-axis direction in step 1-3 are as follows: The Z-axis needs to additionally consider the gravity acceleration, and its motion equation is: Among them, Kx=Ky=Kz, reflecting the isotropic drag coefficient.

8. The device for fitting the trajectory of a flying droplet according to claim 4, characterized in that: The specific method of solving the motion differential equation and deriving the analytical solution in the steps 1 and 3 is to solve the second-order nonlinear differential equations in the X and Y directions by integration through the separation of variables method, and to numerically solve the Z-axis equation by the fourth-order Runge-Kutta method.

9. The device for fitting the trajectory of a flying droplet according to claim 3 or 4, characterized in that: The specific method of fitting the droplet flight trajectory equation in step 2 is as follows: Using a quadratic polynomial to fit the droplet motion trajectory in the X-axis direction, the following trajectory equation can be obtained: x(t) = At2 + Bt + C; Using a quadratic polynomial to fit the droplet motion trajectory in the Y-axis direction, the following trajectory equation can be obtained: y(t) = At2 + Bt + C; Using a fourth-order polynomial fitting for the droplet motion trajectory in the Z-axis direction, the following trajectory equation can be obtained: z(t)=At4+Bt3+Ct2+Dt+E; Among them, A, B, C, D, and E are the fitted polynomial coefficients.

Images