Automatic discharge compensation pneumatic dispensing system and method

Abstract

A pneumatic dispensing system and method that applies a pressure pulse to the headspace inside a syringe of a pneumatic dispenser to measure the rise time (τ_rise) when the compressed air reaches a plurality of set pressure stages and the decay time (τ_decay) when the applied compressed air dissipates to a plurality of set pressure stages in multiple stages, and estimates V_air and the liquid height H_liquid inside the syringe in real time using a physical relationship (under critical flow conditions) in which both time constants are linearly proportional to the headspace volume V_air, and then automatically corrects the discharge pressure or discharge time of the next discharge cycle according to the estimated liquid height. The measurement cycle consists of four stages: rise (F), decay (E), average (A), and difference (D), and by utilizing the ratio of the time constants of the F and E measurements, R_τ = τ_decay / τ_rise, as a self-diagnostic variable, disturbances such as syringe leakage, nozzle clogging, and gas temperature change are automatically diagnosed and corrected within a single measurement cycle. In addition, by utilizing the same H_liquid estimate, the absolute value |P_vac| of the suction vacuum pressure applied during the idle interval between discharges is automatically corrected in proportion to the change in liquid hydrostatic pressure according to |P_vac(H)| = γ_vac· ρ·g·H_liquid + |P_vac_offset|, thereby simultaneously resolving the first discharge defect caused by natural fall at the nozzle tip and excessive backflow suction on the syringe side with a single H_liquid estimate.

Description

Technology Field

[0001] The present invention relates to a pneumatic liquid dispenser, particularly a time-pressure type precision dispensing device that dispenses liquid material by applying compressed air inside a syringe, and more specifically, to an automatic dispensing correction dispensing system and method based on syringe liquid height estimation that can estimate changes in the remaining liquid amount in real time by precisely measuring the arrival time and dissipation time of the compressed air in the headspace inside the syringe in multiple stages, and dynamically correct the discharge parameters and the vacuum pressure of the idle section based thereon. Background Technology

[0002] Pneumatic dispensing technology is a method of dispensing a precise amount of liquid material through a nozzle by applying compressed air at a constant pressure for a certain period of time to a liquid material in a syringe, and is used in a wide range of fields such as semiconductor packaging, display modules, assembly of electronic components, and dispensing of bio-reagents. However, this method has an inherent limitation in that the actual amount dispensed varies even at the same applied pressure and time as the remaining amount of liquid in the syringe decreases.

[0003] The following literature is known as a conventional technique to solve this residual amount dependency problem.

[0004] EP 1795270 A1 of Musashi Engineering provides a solenoid valve for pressure adjustment, a pressure-regulating pressure reducing valve, and a negative pressure mechanism in a syringe, and allows a controller to supply a pressure setting signal corresponding to the remaining amount of liquid in the syringe. However, the above document does not disclose a specific measurement method regarding how the remaining amount is detected.

[0005] Nordson’s US 7,314,598 measures the absolute value of the vacuum pressure inside the syringe and determines liquid depletion if the vacuum is lower than normal, and blockage if the vacuum rises abnormally. Since this method is a binary determination based on critical comparison of absolute pressure values, it is difficult to apply to the continuous estimation of remaining volume and proportional discharge volume correction.

[0006] US 6,065,335 applies a pressure change to a large tank, such as an automobile fuel tank, and estimates the filling level from the pressure change gradient (dP / dt) within a certain time interval. However, this method is difficult to apply because (a) the dynamic characteristics of the time-pressure response change drastically in the small headspace of a syringe dispenser because it targets macroscopic large tanks, and (b) it lacks an integrated control structure that directly feeds the measurement results back to the discharge correction of precision dispensing.

[0007] The applicant's registered patents KR 10-2330271 (Comprehensive correction of pressure, temperature, and time), KR 10-2466306 (Integrated correction of syringe pressure-temperature multivariables), KR 10-2681795 (Remaining amount detection based on the ideal gas equation PV=nRT), and KR 10-2681799 (Liquid height estimation based on changes in compressed air heat quantity) each disclose a technology for detecting remaining amounts or dispensing correction using measurement values ​​in a pressure domain or a heat domain. The present invention is a multi-stage measurement technology in a time domain that is different from these technologies in terms of measurement domain.

[0008] Furthermore, the applicant’s registered patent KR 10-2330271 utilizes pressure, temperature, and time as comprehensive correction variables, but is limited to pressure and time correction of the discharge itself and does not disclose automatic correction dependent on the residual amount of sound pressure applied during idle intervals between discharges. The present invention has a technical concept that is essentially different from KR 10-2330271 in that (i) the residual amount is estimated through multi-stage measurement in the time domain, and (ii) the estimated residual amount is simultaneously utilized as a single estimated value for correction of idle vacuum pressure as well as discharge pressure and time.

[0009] In conclusion, in the field of syringe dispensers, an integrated system that measures the arrival and dissipation times of compressed air in multiple stages across multiple pressure levels and performs self-diagnosis and self-correction for leakage, nozzle clogging, and temperature change by combining and utilizing two time constants, and an integrated control system that simultaneously utilizes the liquid height estimated therefrom for discharge correction and idle vacuum pressure correction, have never been presented in the prior art. Prior art literature

[0010] EP 1795270(2021. 01. 19.)US 7,314,598(2008. 01.01.)US 6,065,335(2000. 05.23.)KR 10-2330271(2021. 05.31.)KR 10-2681795(2024. 07.01.)KR 10-2681799(2024. 07.01.) The problem to be solved

[0011] The present invention aims to solve the problem (objective) of estimating the liquid level inside a syringe in a non-contact and non-destructive manner by utilizing only the existing pneumatic line and pressure sensor of the dispenser itself, without additional optical, ultrasonic, or mechanical sensors.

[0012] Another objective of the present invention is to clearly present a method for detecting residual amounts that is not specified in the prior art (EP 1795270 A1), and to significantly improve the precision of detection and robustness against disturbances.

[0013] Another objective of the present invention is to minimize the effects of absolute pressure offset and sensor drift by adopting multi-stage characteristic values ​​in the time domain as measurement variables, moving away from simple absolute pressure or threshold comparison methods.

[0014] Another objective of the present invention is to simultaneously achieve cross-verification of measurement reliability, syringe leakage, nozzle blockage, and gas temperature self-diagnosis within a single cycle by combining four-step (F·E·A·D) measurements into a single cycle.

[0015] Another objective of the present invention is to estimate the liquid height in real time immediately before or during the measurement cycle between discharges, and to automatically correct the pressure (P) and discharge time (t) for the next discharge based on this.

[0016] Another objective of the present invention is to utilize the same estimated liquid height H_liquid to automatically correct the negative pressure (suction vacuum pressure) P_vac applied to the headspace during the idle interval between discharges in proportion to the remaining liquid amount, thereby simultaneously preventing liquid drooling at the nozzle tip and excessive suck-back into the syringe, and to eliminate the first-dot defect. means of solving the problem

[0017] An automatic discharge correction pneumatic dispensing system according to one aspect of the present invention for solving the above problem comprises a syringe (110) containing liquid, a dispenser drive unit (120) including a first line (122) for supplying compressed air to a headspace (115) inside the syringe and a second line (123) for discharging compressed air from the headspace (115) or connecting the headspace to a vacuum source (124), a pressure sensor (130) for measuring the pressure of the headspace, a first valve (V1) and a second valve (V2) for controlling the opening and closing of the first line and the second line, a discharge unit (150) through which liquid is discharged through a nozzle (112), and a system controller (140).

[0018] The system controller (140) (i) measures the rise time τ_rise, during which the pressure reaches a plurality of set values ​​while supplying compressed air through the first line, in multiple stages; (ii) measures the decay time τ_decay, during which the pressure decreases to a plurality of set values ​​while discharging compressed air through the second line, in multiple stages; (iii) estimates the headspace volume V_air by averaging the F-stage and E-stage measurements (A-stage); (iv) self-diagnoses disturbance conditions such as syringe leakage, nozzle blockage, or gas temperature change from the difference or ratio R_τ of the F-stage and E-stage measurements (D-stage); (v) calculates the liquid height H_liquid from the estimated V_air and automatically corrects the discharge pressure or discharge time of the next discharge cycle; and (vi) sets the idle vacuum pressure |P_vac| applied during the idle interval between discharges in proportion to the same H_liquid to |P_vac(H)| By automatically correcting according to = γ_vac· ρ · g · H_liquid + |P_vac_offset|, natural liquid dripping from the nozzle tip and excessive suction on the syringe side are simultaneously prevented. Effects of the invention

[0019] According to the present invention, the following effects can be achieved.

[0020] First, by utilizing only the dispenser's original pressure sensor (130) and pneumatic line configuration without adding a separate external sensor, the height of the liquid in the syringe can be continuously estimated without increasing the complexity of the system or manufacturing costs.

[0021] Second, by adopting time as a measurement variable rather than the absolute value of pressure, the estimation resolution of the liquid height can be significantly improved by utilizing the precise resolution (μs class) of the time measurement without being affected by the absolute accuracy (offset or gain drift, etc.) of the pressure sensor (130).

[0022] Third, through a four-stage combined measurement consisting of stages F, E, A, and D, it is possible to simultaneously perform (i) cross-verification of measurement reliability, (ii) self-diagnosis of leakage in the syringe seal, (iii) self-diagnosis of blockage in the nozzle or exhaust line, and (iv) self-correction due to temperature changes of the pneumatic gas within a single measurement cycle.

[0023] Fourth, since the total measurement cycle takes very little time in the range of 50 ms to 500 ms, it can be performed within the idle interval (non-discharge interval) between consecutive discharge operations, so it does not affect the production tact time of the process.

[0024] Fifth, the cross-sectional area of ​​the syringe can achieve repeatability of the discharge volume compared to conventional pneumatic dispensers in a constant remaining volume range (e.g., 100% to 20% of the remaining volume range), thereby stably maintaining high-precision quantitative dispensing performance.

[0025] Sixth, the algorithm of the present invention can be easily applied by performing only a firmware upgrade on an existing time-pressure dispenser without changing the existing hardware system.

[0026] Seventh, by automatically correcting the absolute value of the idle vacuum pressure |P_vac| applied during the idle interval between consecutive discharge operations in real time according to the change in the liquid hydrostatic pressure (ρ·g·H_liquid), the stability of the nozzle tip meniscus can be maintained consistently throughout the entire range of the syringe's remaining volume, and the natural dripping of liquid when the remaining volume is large and the excessive suck-back phenomenon when the remaining volume is small can be simultaneously resolved through a single control variable. Brief explanation of the drawing

[0027] FIG. 1 is an overall configuration diagram of an automatic dispensing correction pneumatic dispensing system based on syringe liquid height estimation through multi-stage measurement of compressed air arrival time and dissipation time according to one embodiment of the present invention. FIG. 2 is an internal cross-sectional view of a syringe according to the present invention, showing the arrangement of the headspace, pressure line, and pressure sensor. Figure 3 is a time-pressure graph of the FEAD 4-step measurement cycle according to the present invention. Figure 4 is a graph of the multi-stage arrival time / dissipation time calibration curve according to the headspace volume V_air according to the present invention (average of 5 measurements each for empty syringe / full syringe). Figure 5 is a graph of an automatic discharge pressure and time correction value lookup map according to the liquid height H_liquid according to the present invention. FIG. 6 is a flowchart of a D-stage disturbance self-diagnosis algorithm according to the present invention. Figure 7 is a graph comparing the rate of change in discharge volume by syringe remaining amount between the application of the present invention and a conventional time-pressure dispenser. FIG. 8 is a graph showing the idle vacuum pressure P_vac automatic correction graph according to the liquid height H_liquid and the nozzle (112) end meniscus stabilization region (under-vacuum → drooling, appropriate vacuum → stable, over-vacuum → backflow suction). Specific details for implementing the invention

[0028] Hereinafter, embodiments disclosed in this specification will be described in detail with reference to the attached drawings.

[0029] 1. Configuration of automatic discharge correction pneumatic dispensing system (100)

[0030] FIG. 1 is an overall configuration diagram showing an automatic dispensing correction pneumatic dispensing system (100) based on syringe liquid height estimation through multi-stage measurement of compressed air arrival time and dissipation time according to one embodiment of the present invention.

[0031] Referring to FIG. 1, an automatic discharge correction pneumatic dispensing system (100) according to one embodiment of the present invention includes a syringe (110) containing liquid (L), a dispenser drive unit (120) that supplies or discharges compressed air to the upper head space (115) of the syringe (110), a pressure sensor (130) that detects the pressure of the head space (115), and a system controller (140). The dispenser drive unit (120) includes a first line (122) that connects a compressed air supply source (121) to the head space (115) and a second line (123) that selectively connects the head space (115) to an atmosphere or vacuum source (124), and a first valve (V1) and a second valve (V2) are provided in each line. A nozzle (112) is attached to the lower part of the syringe (110) to discharge liquid (L) to the discharge part (150).

[0032] FIG. 2 is an internal cross-sectional view of a syringe (110), showing the arrangement of the headspace, pressure line, and pressure sensor.

[0033] Referring to FIG. 2, the headspace (115) inside the syringe (110) is a gas space formed above the liquid (L) and is a fluctuating volume in which the volume V_air increases as the remaining liquid decreases, and a pressure sensor (130) is directly connected to the headspace (115) to detect the pressure P(t) inside the headspace (115) at a high-speed sampling interval of 1 ms or less.

[0035] 2. Physical Model of Time of Arrival and Time of Dissipation

[0036] The definitions of symbols used in this specification are as shown in Table 1 below.

[0037] sign definition unit note R - Universal gas constant J / (mol·K) 8.314 T Headspace gas absolute temperature K ― V_air Headspace volume m³ change Q_in molar flow rate of supplied compressed air mol / s Oil volume CD Exhaust orifice discharge coefficient Dimensionless 0.6~0.85 A_o Exhaust orifice cross-sectional area m² ― γ Air Specific Heat Ratio (Cp / Cv) Dimensionless 1.40 c* Critical cross-section sound speed m / s 313 (room temperature) R_τ Time constant ratio (= τ_decay / τ_rise) Dimensionless Self-diagnosis variables P_atm Atmospheric pressure (absolute) kPa(abs) 101.3 ρ Liquid density kg / m³ ― g gravitational acceleration m / s² 9.81 H_liquid Liquid height in syringe (estimated value of the present invention) m ― P_vac Idle vacuum pressure (headspace gauge pressure) kPa (gauge) negative value

[0039] In this specification, all pressure values ​​are gauge pressures (gauges) unless otherwise noted. The notation (abs) is used to denote absolute pressure.

[0040] When compressed air with a constant molar flow rate Q_in is supplied to the volume V_air of the headspace (115), the pressure change in the headspace (115) under isothermal assumptions is described by the following differential equation:

[0041] dP / dt = (R- · T) / V_air × Q_in

[0042] Integrating this equation, the time to reach τ_rise between two pressures P_a and P_b is linearly proportional to the headface volume V_air as follows:

[0043] τ_rise(P_a → P_b) = V_air · (P_b - P_a) / (R · T · Q_in) = k_F · V_air

[0044] Similarly, when compressed air is discharged under choked flow conditions through an exhaust orifice (discharge coefficient C_d) of cross-sectional area A_o, the dissipation time τ_decay, during which the absolute pressure decreases from P_b to P_a, is linearly proportional to V_air as follows:

[0045] τ_decay(P_b → P_a) = V_air / (C_d · A_o · c*) × ln(P_b / P_a) = k_E · V_air

[0046] Here, P_a and P_b are absolute pressures, and c* represents the speed of sound at the critical cross-section. Since both equations are linearly proportional to V_air, V_air can be calculated from measurements at any pressure level by predetermining the calibration functions (or constants) k_F and k_E through prior experiments, and since the syringe cross-sectional area A_s is known:

[0047] H_liquid = H_total - V_air / A_s

[0048] 2-1. Specification of Critical Flow Condition (Choked Flow Condition)

[0049] In order for the arrival time and dissipation time equations of the present invention to maintain a first-order proportional relationship with respect to the volume V_air, the critical flow (choked flow) condition must be satisfied in the compressed air supply line and exhaust line. The critical flow condition is established when the ratio of the upstream absolute pressure to the downstream absolute pressure is greater than or equal to ((γ+1) / 2)^(γ / (γ-1)) - approximately 1.893 for air. Accordingly, in the automatic discharge correction pneumatic dispensing system (100) according to the present invention, the absolute pressure P_supply of the compressed air supply source is set to satisfy the following relationship relative to the maximum value P_n of the measured pressure step:

[0050] P_supply ≥ 1.893 × (P_n + P_atm)

[0051] For the exhaust line, the absolute pressure (P_n + P_atm) of the syringe headspace (115) is required to be at least 1.893 times the atmospheric pressure P_atm. If the critical flow condition is broken in some sections within the range of measurement pressure steps P_1 to P_n, the measurement value in that section is processed separately as a non-linear region by the correction function k_E(P_i) at the end of the measurement cycle or is excluded from the measurement target.

[0053] 3. Detailed sequence of the FEAD 4-step measurement cycle

[0054] Referring to FIG. 3, the measurement cycle of the present invention consists of the following four steps. FIG. 3 is a time-pressure graph of the F(Fill)-E(Empty)-A(Average)-D(Differential) four-step measurement cycle.

[0055] F-step (multi-stage rise time measurement): (s2-1) The system controller opens the first valve (V1) to supply compressed air to the headspace (115), and the pressure sensor (130) measures the pressure P(t) at a high-speed sampling interval of 1 ms or less. (s2-2) Whenever a predetermined plurality of measured pressures P_1 < P_2 < … < P_n (e.g., 100, 200, 300, 400 kPa (gauge)) are reached, the corresponding time is recorded, and the rise times τ_rise(P_1) ~ τ_rise(P_n) based on the start time are calculated respectively.

[0056] E-step (multi-stage decay time measurement): (s3-1) The system controller (140) closes the first valve (V1) and, after a stabilization pause (e.g., 10 ms), opens the second valve (V2) to discharge compressed air from the headspace (115). (s3-2) Each time the pressure decreases sequentially from the maximum pressure P_n to P(n-1), …, P_1, the time is recorded to calculate the decay time τ_decay(P_(i+1) → P_i) for each stage.

[0057] A-stage (average verification of volume estimation): The F-stage estimate V^_F and E-stage estimate V^_E, calculated for supply in the same pressure range, are calculated, and weights (w_F, w_E) that are dynamically adjusted according to the signal-to-noise ratio (SNR) are applied to determine the final estimate of the headspace (115) volume as the weighted average V^_air = w_F · V^_F + w_E · V^_E.

[0058] D-Stage (Disturbance Self-Diagnosis): Time constant ratio, which is the ratio of the dissipation time to the arrival time in the same pressure range (P_a, P_b):

[0059] Calculates R_τ(P_a, P_b) = τ_decay(P_b → P_a) / τ_rise(P_a → P_b).

[0060] This value becomes a constant system intrinsic constant R_τ,nom, independent of V_air under normal conditions. If R_τ deviates from the normal range of R_τ,nom (R_τ,nom ± δ), the occurrence of disturbances, such as leakage or nozzle blockage, is diagnosed. (For a detailed diagnostic algorithm, refer to FIG. 6 and Section 7 of this specification.)

[0062] 4. Multi-stage Calibration Curve - Average of 5 measurements each for empty syringe and full syringe

[0063] FIG. 4 illustrates the multi-stage calibration curves of the time to reach and the time to dissipate according to the headspace (115) volume V_air as a multi-stage calibration curve (average of 5 measurements each of empty syringe / full syringe). It can be seen that at all pressure stages, the two time constants are linearly proportional to V_air.

[0064] In the present invention, five repeated measurements are performed under the same conditions at each calibration measurement point (empty syringe V_air = V_total, full syringe V_air = V_min), and the average value is used to determine the calibration function, thereby minimizing the effects of pressure sensor (130) noise, valve response delay jitter, and minute fluctuations in gas flow rate that may occur during a single measurement.

[0066] 5. Discharge Compensation Algorithm

[0067] Based on the estimated liquid height H_liquid, the discharge pressure and discharge time of the next discharge cycle are automatically adjusted using the following correction function:

[0068] P_dispense(H) = P_base + α · (H_ref - H_liquid)

[0069] t_dispense(H) = t_base × [1 + β · (H_ref - H_liquid) / H_ref]

[0070] Here, α and β are correction coefficients predetermined according to the liquid viscosity, nozzle diameter, and application pattern. FIG. 5 is a graph of automatic correction values ​​for discharge pressure and time according to the liquid height H_liquid, and FIG. 5 shows an example of a correction lookup table under conditions of a 50 cc syringe, 5,000 cP viscosity, and 0.41 mm nozzle.

[0071] In another embodiment of the present invention, P_dispense and t_dispense may be directly output by inputting a time series (τ_rise, τ_decay, H_liquid, previous discharge result) into a pre-trained artificial intelligence (machine learning) model.

[0073] 6. Automatic correction of idle vacuum pressure (suck-back) based on remaining capacity

[0074] 6-1. Definition of the symbol P_vac in this specification

[0075] In this specification, idle vacuum pressure P_vac is defined as the gauge pressure of the headspace (115), and a negative value indicates vacuum (less than atmospheric pressure). That is, when P_vac < 0, |P_vac| is the degree of vacuum, and the greater the absolute value, the higher the degree of vacuum. In the following section, all values ​​described simply as 'P_vac' or '|P_vac|' represent absolute values ​​(i.e., the magnitude of the degree of vacuum), and the correction formula |P_vac(H)| = γ_vac · ρ · g · H_liquid + |P_vac_offset| defines the magnitude of the degree of vacuum itself.

[0076] 6-2. Limitations of Conventional Fixed P_vac

[0077] In pneumatic dispensing, during the idle period between discharges, the liquid (L) in the syringe (110) tends to drool through the nozzle (112) due to its own weight. To prevent this, the automatic discharge correction pneumatic dispensing system (100) of the present invention stabilizes the meniscus at the tip of the nozzle (112) by applying a fine negative pressure (hereinafter referred to as 'idle vacuum pressure' or P_vac) to the headspace (115) immediately after discharge by switching the second valve (V2) to the vacuum source (124) side path of the dispenser drive unit (120).

[0078] However, conventional dispensers apply an idle vacuum pressure P_vac as a fixed value regardless of the remaining amount in the syringe, resulting in the following two conflicting defects.

[0079] (a) When there is a large amount of liquid remaining in the syringe (large liquid), the liquid hydrostatic pressure is high, so the fixed P_vac alone cannot suppress the natural fall of the liquid, causing drooling to occur at the end of the nozzle (112).

[0080] (b) Conversely, when the remaining amount of the syringe is small (H_liquid is small), the liquid hydrostatic pressure is small while the same idle vacuum pressure P_vac is applied, so suck-back occurs in which the liquid inside the nozzle (112) flows excessively back toward the syringe side, causing an air meniscus to enter the nozzle (112) and a first-dot defect in which the first discharge amount is insufficient during the next discharge.

[0081] 6-3. Derivation of Meniscus Force Balance and Correction Formula

[0082] In the present invention, the balance of meniscus forces at the tip of the nozzle (112) is described as follows. The balance condition of the liquid hydrostatic pressure P_hyd(H) acting on the meniscus at the tip of the nozzle (112), the meniscus holding force P_st due to surface tension, and the idle vacuum pressure |P_vac| applied to the headspace (115) is:

[0083] P_hyd(H) - |P_vac(H)| = P_st ± ΔP_meniscus

[0084] It is expressed as P_hyd(H), where P_hyd(H) = ρ · g · H_liquid (ρ is liquid density, g is gravitational acceleration, and H_liquid is the liquid height estimated from the FEAD measurement of the present invention), and ΔP_meniscus is the static stability allowable range of the nozzle (112) end meniscus, which is determined by the nozzle diameter, liquid surface tension, and contact angle. If the left side exceeds +ΔP_meniscus, drooling occurs, and if it falls below -ΔP_meniscus, suck-back occurs.

[0085] From the above balance conditions, an automatic correction formula for idle vacuum pressure to maintain the nozzle (112) end meniscus within a stable region throughout the entire liquid residue range is derived as follows:

[0086] |P_vac(H)| = γ_vac · ρ · g · H_liquid + |P_vac_offset|

[0087] Here, γ_vac is a liquid-nozzle compensation coefficient that is predetermined according to the liquid viscosity, nozzle diameter, and application pattern, and P_vac_offset is a correction offset for balancing the surface tension of the meniscus at the end of the nozzle (112). As H_liquid decreases, |P_vac(H)| also decreases automatically, so a large vacuum is applied in a full syringe (large P_hyd) to suppress natural fall, and as it approaches an empty syringe (small P_hyd), the vacuum is weakened to prevent backflow caused by excessive suction.

[0088] 6-4. Viscosity-Nozzle Matrix of γ_vac Compensation Factors

[0089] The viscosity-nozzle matrix of γ_vac values ​​determined based on the measurement results of Section 9 of Example is as shown in Table 2 below (based on a 50 cc syringe).

[0090] Viscosity \ Nozzle Diameter 0.20 mm 0.41 mm 0.84 mm 1,000 cP 0.62 0.78 0.95 5,000 cP 0.71 0.85 1.05 30,000 cP 0.85 0.98 1.18

[0091] From the above matrix, the idle vacuum pressure compensation coefficient γ_vac is determined as a positive real number that increases monotonically by the liquid viscosity and nozzle (112) diameter in the range of 0.5 to 1.2. After being determined once in the pre-calibration step for the same syringe / liquid, it is automatically updated by closed-loop learning.

[0092] 6-5. Simultaneous Utilization of a Single H_liquid Estimator

[0093] In the present invention, H_liquid is estimated as a single measurement value through the same FEAD measurement cycle used for discharge correction in Section 5 without separate devices such as external weight sensors or optical sensors. Therefore, the automatic idle vacuum pressure correction in this section is performed simultaneously with the automatic discharge pressure and time correction in Section 5 by sharing the single H_liquid estimate value in real time without additional hardware configuration. That is, the system controller (140) of the present invention updates (i) P_dispense and t_dispense of the next discharge cycle and (ii) |P_vac| of the next idle section simultaneously based on the same H_liquid estimate value at the end of each measurement cycle.

[0094] FIG. 8 is an automatic correction graph of idle vacuum pressure P_vac and a diagram of the meniscus stability region according to the liquid height H_liquid. FIG. 8 shows the automatic correction graph of |P_vac(H)| and the meniscus stability region (drooling region / stable region / suck-back region) under the conditions of a 50 cc syringe, 5,000 cP viscosity, and 0.41 mm nozzle.

[0095] 6-6. Closed-loop learning algorithm for reward coefficients - Details of step (s7)

[0096] In another embodiment of the present invention, the compensation coefficient γ_vac and offset |P_vac_offset| of |P_vac(H)| are learned in a closed loop immediately after each discharge through an optical image at the end of the nozzle (112) or a fine fluctuation of the pressure sensor (130) (a fine pulse of the pressure of the headspace (115) when a droplet is formed), thereby enabling automatic updating of the correction coefficient according to changes in liquid viscosity, temperature, and time. The closed-loop learning of this section includes the following steps (s7-1) to (s7-3).

[0097] (s7-1) Meniscus monitoring step: Immediately after each discharge process, within a short stabilization pause (e.g., 5 ms to 50 ms) between the discharge and the next measurement, (a) extract the radius of curvature r of the meniscus from an optical image of the tip of the nozzle (112), or (b) calculate the dP / dt peak value or the dominant frequency component of the Fourier transform from the micro-pulse response of the headspace (115) pressure detected by the pressure sensor (130).

[0098] (s7-2) Region determination step: The extracted meniscus state indicator is compared with a predetermined threshold value to determine which region it belongs to among (a) a drooling region (e.g., r > r_threshold_d), (b) a stable region (r_threshold_s ≤ r ≤ r_threshold_d), and (c) a suck-back region (r < r_threshold_s). At this time, the threshold values ​​r_threshold_s and r_threshold_d are predetermined in the range of 0.5 to 2.0 times the diameter of the nozzle (112).

[0099] (s7-3) Update correction factor: If determined to be drooling, the absolute value of |P_vac| is increased by Δγ_vac = +0.005 to +0.05 (or Δ|P_vac_offset| = +0.05 kPa), and if determined to be suck-back, the same step is updated in the opposite direction. The update step size is predetermined based on the liquid viscosity and nozzle (112) diameter, and the convergence time constant of this closed-loop learning is typically in the range of 5 to 50 discharge cycles. The updated correction factor is generalized to the time-dependent function |P_vac(H, t_age)| = γ_vac(t_age) · ρ · g · H_liquid + |P_vac_offset(t_age)|.

[0101] 7. D-Stage Disturbance Self-Diagnosis

[0102] FIG. 6 illustrates a flowchart of a D-stage self-diagnosis algorithm. The self-diagnosis of the present invention classifies and diagnoses the following four types of disturbances within a single measurement cycle.

[0103] (i) R_τ is within the normal range (R_τ, nom ± δ) → Determined as normal, V_air estimate adopted

[0104] (ii) R_τ is abnormally small → Determined as syringe seal leakage (reduced dissipation time)

[0105] (iii) If R_τ is abnormally large → It is determined that the nozzle (112) or exhaust line is blocked (extended dissipation time)

[0106] (iv) Simultaneous change of τ_rise and τ_decay in all pressure ranges at a constant rate → Determined as a change in gas temperature

[0107] (v) Non-linearity between pressure steps is inconsistent with the normal calibration curve → determined to be pressure sensor (130) drift or syringe deformation

[0108] 8. Calibration Procedure

[0109] The automatic discharge correction pneumatic dispensing system (100) of the present invention undergoes the following calibration procedure once whenever the syringe type, nozzle type, or liquid type is changed.

[0110] (c1) System initialization: After making the internal pressure of the headspace (115) a complete vacuum (0 kPa (abs)), pressurize it to a reference pressure of 600 kPa (gauge) or higher to synchronize the reference point of the pressure sensor (130).

[0111] (c2) Empty syringe measurement (V_air = V_total): With the syringe empty, the measurement cycles of the F-step and E-step are repeated 5 times for each of the pressure steps P_1, P_2, …, P_n, and the 5 average values ​​of the rise time τ_rise(P_i) and decay time τ_decay(P_(i+1) → P_i) for each pressure step are calculated and recorded as (τ_rise(P_i)_max, τ_decay(P_(i+1) → P_i)_max). Here, the subscript 'max' indicates that the V_air value is maximum (empty syringe).

[0112] (c3) Measurement of a full syringe (V_air = V_min): Immediately after filling the syringe with liquid, the measurement cycle is repeated 5 times for each of the same pressure steps P_1, …, P_n as in (c2) using the same procedure as (c2), and the average value of the 5 measurements for each pressure step is recorded as (τ_rise(P_i)_min, τ_decay(P_(i+1) → P_i)_min). 'min' indicates that the V_air value is at its minimum (full syringe).

[0113] (c4) Determination of calibration function: From the two average measurement points obtained in steps (c2) and (c3), the calibration functions k_F(P_i) and k_E(P_i) for each pressure step are finally determined through first-order linear regression analysis.

[0114] (c5) Determination of self-diagnosis threshold value: From the average measurements of (c2) and (c3), the normal system constant R_τ,nom of the time constant ratio R_τ = τ_decay / τ_rise is calculated and stored as the threshold value for D-stage self-diagnosis.

[0115] (c6) Determination of vacuum pressure correction factor: Set initial values ​​for γ_vac and |P_vac_offset| by referring to the viscosity-nozzle matrix in Section 6-4, and enable automatic updates with closed-loop learning in Section 6-6.

[0116] (c7) Temperature Correction (Optional): If the viscosity and temperature of the liquid fluctuate within a certain range, repeat the procedures (c2) through (c6) at multiple temperature points to create a temperature correction table.

[0117] The procedure of using the average value after the above 5 repeated measurements minimizes the influence of pressure sensor (130) noise, valve response jitter, and minute fluctuations in gas flow rate that may occur during a single measurement, thereby improving the reliability of the calibration function and the precision of subsequent remaining amount estimation.

[0119] 9. Example - 50 cc syringe, viscosity 5,000 cP, display module encapsulant

[0120] As an embodiment of the present invention, the results of applying a process to which a display encapsulant with a viscosity of 5,000 cP is filled into a 50 cc syringe and a 1 mm diameter dot is applied using a 0.41 mm nozzle (112) are described.

[0121] The measurement pressure levels were set to four stages of 100, 200, 300, and 400 kPa (gauge) (satisfying the critical flow condition with the absolute supply pressure P_supply = 950 kPa (abs)), and the measurement cycle was set to once every 10 discharges. Calibration was performed by using the average value after 5 repeated measurements on each empty syringe and a full syringe.

[0122] As an example of measurement results, when V_air = 5 cc, τ_rise(400) = 28 ms (mean of 5 samples, sample standard deviation σ = 0.6 ms, standard error SE = σ / √5 ? 0.27 ms), τ_decay(400 → 100) = 92 ms (σ = 1.4 ms, SE It was 0.63 ms), and when V_air = 45 cc, τ_rise(400) = 252 ms (σ = 3.2 ms) and τ_decay(400 → 100) = 828 ms (σ = 8.7 ms). The ratio of the two time constants, R_τ, remained constant at 3.28 ± 0.05 in all measurement intervals, so the steady state of the syringe seal was self-diagnosed.

[0123] The vacuum pressure correction coefficients determined in this example were γ_vac = 0.85 and |P_vac_offset| = 0.5 kPa. Immediately after fully filling a 50 cc syringe with 5,000 cP encapsulating material (H_liquid ≈ 80 mm), the appropriate vacuum level was calculated as |P_vac| = 0.85 × 1,050 × 9.81 × 0.080 + 0.5 ≈ 1.20 kPa, and at a remaining amount of 5% (H_liquid 4 mm), |P_vac| It was automatically reduced to 0.53 kPa. The |P_vac(H)| correction curve of this embodiment is shown in FIG. 8.

[0124] FIG. 7 illustrates the results of a comparison of the discharge volume fluctuation rate between an automatic discharge correction pneumatic dispensing system (100) to which the present invention is applied and a conventional time-pressure dispenser. In a conventional time-pressure dispenser to which the present invention is not applied, the discharge volume fluctuation rate accumulated significantly in the syringe remaining volume 90% → 20% range, and a deviation in the discharge volume dependent on the remaining volume was clearly observed. However, when the present invention is applied, the discharge volume repeatability precision in the same range was significantly improved to a level that is difficult to achieve with a conventional pneumatic dispenser without a correction function. In addition, due to the residual volume-based idle vacuum pressure automatic correction of the present invention, the tip meniscus of the nozzle (112) is maintained within a stable region throughout the entire range of syringe remaining volume change, and the occurrence rate of the first-dot defect is also significantly reduced compared to the conventional method. However, the above results were evaluated only in the range of 100% to about 20% of the remaining volume, where the calibration assumption that the syringe cross-sectional area is constant is valid, and the limitations of the application of the present invention in the range of less than about 20% of the remaining volume and the morphological causes thereof are described separately in Section 9-1 of this specification.

[0125] 9-1. Syringe Shape Dependence and Valid Correction Range

[0126] The measurement and calibration algorithm of the present invention is based on the assumption that the internal cross-sectional area A_s of the syringe is constant within the measurement interval. That is, the relationship between the liquid height H_liquid and the headspace (115) volume V_air is linear in the first order, H_liquid = H_total ? V_air / A_s, and the calibration functions k_F(P_i) and k_E(P_i) of the present invention are determined based on this linear relationship.

[0127] However, the lower portion of a standard dispensing syringe (e.g., 50 cc, 30 cc, 10 cc, etc.) has a funnel or cone shape for connection with a nozzle (112), and when the remaining amount of the syringe decreases below a certain percentage, the liquid reaches this shape change section. In the syringe shape change section, the change in V_air increases non-linearly for the same discharge amount, so the first linear calibration of the present invention is no longer valid. Although there are some differences depending on the type and capacity of the syringe, typically, the section where the remaining amount of the syringe is about 20% or less corresponds to this shape change section.

[0128] Accordingly, the effective range for the discharge correction and idle vacuum pressure correction of the present invention is limited to the range of 100% to approximately 20% of the syringe remaining volume. When the syringe remaining volume decreases to less than approximately 20%, operation is processed in any one of the following ways.

[0129] (i) Syringe replacement mode: When the syringe volume decreases to a predetermined threshold (e.g., 20% volume), the system controller (140) generates a syringe replacement alarm, and the syringe is replaced by an operator or an automatic replacement module.

[0130] (ii) Shape-dependent calibration mode: By pre-measuring syringe shape information (cross-sectional area A_s(H) per remaining amount) and generalizing the calibration function into shape-dependent functions k_F(P_i, H_liquid) and k_E(P_i, H_liquid), the correction application range is extended to the shape variation section of the lower part of the syringe.

[0131] (iii) Conventional mode switching: In the range where the syringe remaining amount is less than about 20%, the remaining amount-dependent correction of the present invention is temporarily suspended, and the correction value based on the last effective H_liquid estimate is maintained, or the remaining liquid is discharged according to a preset termination sequence.

[0132] By the above configuration, the present invention ensures the reliability of the entire dispensing process by providing an operating method that clearly recognizes the morphological limitations of the syringe and avoids or compensates for those limitations.

[0133] 10. Examples of Combination Application

[0134] The present invention may be applied in combination with the applicant’s registered patents KR 10-2330271, KR 10-2466306, KR 10-2681795 and / or KR 10-2681799. That is, by fusing the measurement value of the present invention in the time domain (V_air,time) and the measurement values ​​in the pressure domain (KR 10-2681795: V_air,P) and heat quantity domain (KR 10-2681799: V_air,Q) through a Kalman filter or weighted average, a multi-domain integrated estimation system that complements the limitations of a single measurement domain can be constructed.

[0135] The disclosed content is merely illustrative and can be modified and implemented in various ways by a person skilled in the art without departing from the gist of the claim claimed in the patent claims; therefore, the scope of protection of the disclosed content is not limited to the specific embodiments described above. Explanation of the symbols

[0136] 100: Automatic Discharge Compensation Pneumatic Dispensing System 110: Syringe 112: Nozzle 115: Headspace 120: Dispenser drive unit 121: Compressed air supply 122: 1st line 123: 2nd line 124: Vacuum source 130: Pressure sensor 140: System controller 150: Discharge section L: Liquid V1: First valve V2: Second valve

Claims

Claim 1 A syringe (110) containing liquid; a dispenser drive unit (120) comprising a first line (122) for supplying compressed air to a headspace (115) inside the syringe (110) and a second line (123) for discharging the compressed air from the headspace (115); a pressure sensor (130) for measuring the pressure in the headspace (115); at least one valve (V1 and V2) for controlling the opening and closing of the first line (122) and the second line (123); and a nozzle (112) coupled to the syringe (110) for discharging the liquid; The system controller (140) includes a system controller that measures the arrival times τ_rise(P_1), τ_rise(P_2), ..., τ_rise(P_n) at which the measured pressure of the head space (115) reaches each of the plurality of pressure stages (P_1 < P_2 < ..., P_n) while supplying the compressed air through the first line (122), and measures the decay times τ_decay(P_n → P_(n-1), ..., τ_decay(P_2 → P_1) at which the measured pressure of the head space (115) sequentially decreases according to the plurality of pressure stages (P_n, P_(n-1), ..., P_1) while discharging the compressed air through the second line (123); the system controller (140) estimates the height or remaining amount of the liquid based on the measured arrival times and the decay times, and based on the estimated height or remaining amount of the liquid, the next cycle An automatic discharge correction pneumatic dispensing system characterized by automatically correcting at least one of the discharge pressure or discharge time. Claim 2 An automatic discharge correction pneumatic dispensing system according to claim 1, wherein the number of pressure steps n is 3 to 8, each pressure step is predetermined in the range of 50 kPa (gauge) to 800 kPa (gauge), and the absolute pressure (P_supply) of the supply source supplied through the first line (122) is set to satisfy the critical flow condition of P_supply ≥ 1.893 × (P_n + P_atm) with respect to the maximum value P_n of the measured pressure step. Claim 3 An automatic discharge correction pneumatic dispensing system according to claim 1, wherein the measurement cycle performed by the system controller (140) comprises: i) a multi-stage F-step for measuring the arrival time; ii) a multi-stage E-step for measuring the dissipation time; iii) a weighted average estimate of the volume of the head space (115) from the measured values ​​of the arrival time and the dissipation time; and iv) a D-step for self-diagnosing the disturbance state of the system by calculating the difference between the measured values ​​of the arrival time and the dissipation time or a time constant ratio defined as dissipation time / arrival time. Claim 4 In claim 3, the D-step compares the value of the time constant ratio R_τ(P_a, P_b) = τ_decay(P_b → P_a) / τ_rise(P_a → P_b), which is the ratio of the time constant in the same pressure range (P_a, P_b), with a normal reference value (R_τ,nom); if the ratio of the time constant (R_τ) decreases outside the set range relative to the normal reference value (R_τ,nom), it is determined that there is leakage in the seal of the syringe (110); if the ratio of the time constant (R_τ) increases outside the set range relative to the normal reference value (R_τ,nom), it is determined that there is blockage of the nozzle (112) or the exhaust line; if the rise time (τ_rise) and dissipation time (τ_decay) of all pressure ranges change simultaneously at a constant rate, it is determined that there is a temperature change of the pneumatic gas; and if the non-linearity between pressure stages does not match the normal calibration curve, the drift of the pressure sensor (130) or the An automatic discharge correction pneumatic dispensing system characterized by determining each external deformation of the syringe (110). Claim 5 An automatic discharge correction pneumatic dispensing system according to claim 3, wherein the total time required for the measurement cycle is 500 ms or less, and the system controller (140) controls the measurement cycle to be performed within a non-discharge interval between consecutive discharge operations so as not to affect the production takt time. Claim 6 An automatic dispensing correction pneumatic dispensing system according to claim 1, wherein the system controller (140) includes a pre-trained artificial intelligence model, and inputs to the pre-trained artificial intelligence model multi-stage measurement values ​​of the arrival time and the dissipation time, measurement time series data of the previous N (N: natural number) dispensing cycles, and viscosity and temperature information of the liquid as input values, and outputs the liquid height in the syringe (110) and the dispensing pressure or dispensing time which is the dispensing correction value of the next dispensing cycle. Claim 7 In claim 1, the system controller (140) performs a calibration mode for initializing the system, wherein the calibration mode (i) reduces the pressure of the headspace (115) to a vacuum state and then pressurizes it to a preset reference pressure of 600 kPa (gauge) or higher to synchronize the zero point and reference point of the pressure sensor (130), and (ii) in the state of an empty syringe (V_air = V_total) in which no liquid is contained, a plurality of preset pressure steps P_1, P_2, … An automatic dispensing correction pneumatic dispensing system characterized by: (iii) performing a measurement cycle at least 5 times for each of , P_n to calculate the average value of the empty syringe for the arrival time and the dissipation time; (iv) performing the measurement cycle at least 5 times for each of the plurality of pressure steps in the state of the full syringe (V_air = V_min) in which the liquid is contained to the maximum to calculate the average value of the full syringe for the arrival time and the dissipation time; and (iv) determining k_F(P_i) and k_E(P_i), which are calibration functions for each pressure step, and R_τ,nom, which is a normal reference value, based on the average value of the empty syringe and the average value of the full syringe. Claim 8 An automatic discharge correction pneumatic dispensing system according to claim 1, wherein the system controller (140) further calculates at least one of a first auxiliary estimate (V_pressure) that estimates the remaining amount from a change in the absolute value of the internal pressure of the syringe (110) or a second auxiliary estimate (V_thermal) that estimates the remaining amount of the liquid from a change in the heat quantity of the compressed air, and calculates a multi-domain integrated liquid remaining amount estimate by fusing the time domain estimate (V_time) based on the arrival time and dissipation time and the first auxiliary estimate through a Kalman filter or a weighted average. Claim 9 In claim 1, the dispenser drive unit (120) is configured to selectively connect the headspace (115) to a vacuum source through the second line (123), and the system controller (140) calculates an idle vacuum pressure (P_vac) determined by a monotonic proportional function with respect to the estimated height of the liquid (H_liquid) during an idle period between consecutive discharge operations, and controls the gauge pressure of the headspace (115) to the idle vacuum pressure (P_vac), wherein P_vac is defined as a negative value, meaning that the greater the absolute value, the higher the vacuum level of the headspace (115); when H_liquid is large, the absolute value of P_vac is increased to suppress liquid drooling at the end of the nozzle (112), and when H_liquid is small, the absolute value of P_vac is decreased so that the liquid inside the nozzle (112) flows toward the syringe (110). An automatic discharge correction pneumatic dispensing system characterized by preventing a first-dot defect caused by excessive suck-back. Claim 10 An automatic discharge correction pneumatic dispensing system according to claim 9, wherein the absolute value of the idle vacuum pressure P_vac is determined according to the following formula: |P_vac(H)| = γ_vac · ρ · g · H_liquid + |P_vac_offset| (where ρ is the density of the liquid, g is the acceleration due to gravity, H_liquid is the height of the liquid, γ_vac is the liquid-nozzle compensation coefficient, and |P_vac_offset| is the absolute value of the surface tension correction offset of the nozzle end meniscus). Claim 11 An automatic discharge correction pneumatic dispensing system according to claim 10, wherein the liquid-nozzle compensation coefficient γ_vac is a positive real number in the range of 0.5 to 1.2, and |P_vac_offset| is a positive real number greater than 0 kPa and less than or equal to 5 kPa, and wherein γ_vac and |P_vac_offset| are predetermined according to the viscosity of the liquid and the diameter of the nozzle. Claim 12 An automatic discharge correction pneumatic dispensing system according to claim 9, wherein the system controller simultaneously updates (i) the discharge pressure (P_dispense) and discharge time (t_dispense) of the next discharge cycle and (ii) the idle vacuum pressure (P_vac) of the next idle period based on a single estimated value H_liquid calculated at the end of each measurement cycle, and wherein the correction of the discharge pressure and time and the correction of the idle vacuum pressure are performed by a single measurement cycle without additional sensors by sharing the same pressure sensor and the same compressed air line configuration. Claim 13 In claim 10, the system controller monitors (s7-1) immediately after each discharge at least one of (a) the radius of curvature (r) of the meniscus based on an optical image of the tip of the nozzle (112), or (b) a peak value of the rate of change of pressure (dP / dt) calculated from the micro-pulse response of the headspace (115) pressure detected by the pressure sensor (130); (s7-2) compares the monitored value with a predetermined threshold value to determine which region the state of the meniscus belongs to among a drooling region, a stable region, and a suck-back region; and (s7-3) if the result of the determination the state of the meniscus deviates to the drooling region, the absolute value of the idle vacuum pressure (P_vac) is increased, and if the state of the meniscus deviates to the suck-back region, the absolute value of P_vac is decreased, in such a manner the liquid-nozzle compensation coefficient (γ_vac) and the An automatic discharge correction pneumatic dispensing system characterized by automatically updating the absolute value (|P_vac_offset|) of the surface tension correction offset by closed-loop learning with a preset step size, wherein, by the automatically updated compensation coefficient and offset, the absolute value of the idle vacuum pressure (P_vac) is controlled by generalizing it to a time-dependent function equation dependent on the operating time (t_age) of the dispensing system: |P_vac(H, t_age)|=γ_vac(t_age)·ρ·g·H_liquid+ |P_vac_offset(t_age)| (where ρ is the density of the liquid, g is the acceleration due to gravity, γ_vac(t_age) is the operating time-dependent liquid-nozzle compensation coefficient, and |P_vac_offset(t_age)| is the absolute value of the operating time-dependent surface tension correction offset of the nozzle tip meniscus). Claim 14 As an automatic dispensing correction method for a pneumatic dispensing system, the method comprises: (s1) a F-step of measuring the rise time τ_rise (P_i) at which the measured pressure of the headspace reaches each of a predetermined plurality of pressure steps (P_1 < P_2 < … < P_n) while supplying compressed air to the headspace inside the syringe; (s2) an E-step of measuring the decay time τ_decay (P_(i+1) → P_i) at which the measured pressure of the headspace (115) sequentially decreases to the plurality of pressure steps (P_n, P_(n-1), …, P_1) while discharging the compressed air of the headspace (115); and (s3) an A-step of calculating a weighted average estimate of the volume (V_air) of the headspace (115) from the measurements of the F-step and the E-step in the same pressure range. (s4) a D-step for self-diagnosing a disturbance state from the difference or time constant ratio of the F-step and E-step measurements; (s5) a step for calculating the height (H_liquid) or remaining amount of liquid from the volume (V_air) of the headspace (115); (s6) a step for automatically correcting at least one of the discharge pressure or discharge time of the next discharge cycle based on the calculated height or remaining amount of liquid, comprising an automatic discharge correction dispensing method. Claim 15 An automatic discharge correction dispensing method according to claim 14, further comprising the step of maintaining a rest period for stabilizing the internal pressure of the headspace (115) for a time of 1 ms to 100 ms between the F-step and the E-step. Claim 16 In claim 14, (s7) based on the liquid height (H_liquid) calculated in step (s5), the absolute value |P_vac| of the idle vacuum pressure applied during the idle interval between consecutive discharge operations is given by the following formula: |P_vac(H)| = γ_vac·ρ·g·H_liquid + |P_vac_offset| The automatic dispensing correction method further includes the step of determining the gauge pressure P_vac of the headspace (115) (wherein γ_vac is a liquid-nozzle compensation coefficient of 0.5 to 1.2, ρ is the liquid density, g is the acceleration due to gravity, and |P_vac_offset| is the absolute value of the nozzle tip meniscus surface tension correction offset) and controlling the gauge pressure P_vac (P_vac < 0, |P_vac| is the degree of vacuum) as the H_liquid decreases, thereby maintaining a nozzle tip meniscus stable region throughout the entire remaining amount of the syringe (110).

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