First, the self-reinforcing mechanism of the actuation pressure of the PIJ printhead under the influence of the positive crosstalk effect is investigated. Self-reinforcing refers to achieving reinforcement of the actuation pressure through the self-modulation of the crosstalk effect, in which the only change concerns the actuation waveform shape rather than any other external conditions. The crosstalk effect involved in this section is the multi-pulse crosstalk effect, generated by the interference between the ink inside the printhead and the solid structure of the printhead.

The actuation pressure in the pump chamber of the PIJ printhead is in the form of an oscillating pressure wave, which is generated by the deformation of the piezoelectric actuator under the excitation of an external actuation electric field. There is a special damping ratio design between the ink supply channel and the nozzle in the structural geometry of the printhead. During the positive phase of the actuation pressure, the ink in the pump chamber produces an acceleration of flowing toward the outside of the nozzle, causing the formation of a jet flow near the nozzle area. During the negative phase of the actuation pressure, the ink in the ink supply channel produces an acceleration of flowing toward the pump chamber, replenishing the ink in the pump chamber. Generally speaking, the peak of positive pressure determines the droplet velocity, while the peak of negative pressure determines whether ink can be supplied in a continuous manner, i.e., whether the droplet jetting process can be continuous. Under the same actuation waveform, the actuation pressure amplitude is almost linearly correlated with the actuation voltage. However, due to the limitations related to the characteristics of piezoelectric ceramic materials, the actuation voltage is often very limited in practical applications, resulting in a very limited actuation pressure amplitude [1,43]. Actuation waveform optimization provides an opportunity to improve the actuation pressure by modulating the multi-pulse crosstalk effect. Previous studies have reported that the multi-pulse crosstalk inside the PIJ printhead under high actuation frequency exhibits periodicity and is controlled by a constructive/destructive interference inherent mechanism [46]. In this article, the positive crosstalk effect is further expanded, i.e., the amplitude of the constructive interference is expanded, achieving self-reinforcing of the actuation pressure.

As shown in Fig. 2, simulation studies have been conducted to analyze the influence of the pulse shape of the actuation waveform on the crosstalk effect and the actuation pressure. The key parameters include the leading edge time T_l, pulse duration T_d, and pulse period T_f (reciprocal of the pulse frequency f). The trailing edge time is set equal to T_l.

Figure 2A shows the evolution process of the actuation pressure under the modulation of leading edge time T_l. Under a waveform with a single leading edge, the actuation pressure inside the printhead reaches the first positive pressure peak quickly, and then begins to enter a residual oscillation stage, i.e., pressure crosstalk. Table S1 statistically compares the peak values and peak arrival time under different T_l. When T_l is decreased from 1.1 μs to 0.2 μs, the value of the first positive pressure peak, corresponding to point A₀ in Fig. 2A (i to iv), increases gradually from 49.54 kPa to 55.23 kPa, i.e., increased by 12%. In the subsequent pressure crosstalk stage, the values of the pressure peaks, corresponding to point B₀ and A₁ in Fig. 2A (i to iv), exhibit no obvious increase. Nevertheless, the peak arrival time tends to occur earlier, with t_B0 advancing from 3.9 μs to 3.5 μs and t_A1 advancing from 7.4 μs to 7 μs, which helps to increase the actuation frequency. Obviously, a smaller T_l is beneficial to produce a higher droplet velocity. In practice, considering the limitation of charging and discharging time of piezoelectric elements, the minimum T_l is limited to 0.1 μs.

Figure 2B presents the evolution process of the actuation pressure under the modulation of pulse duration T_d and pulse period T_f. Table S2 statistically compares the peak values and peak arrival time under different waveforms. Under a waveform with a single leading edge of T_l = 0.1 μs (Fig. 2B, i), the obtained point A₀ is (0.3 μs; 57.42 kPa), which means that the peak arrival time is 0.3 μs and the pressure peak value is 57.42 kPa. In the subsequent pressure crosstalk stage, the obtained point B₀ is (3.6 μs; −35.31 kPa) and point A₁ is (7 μs; 19.85 kPa). Under a waveform with a modulated pulse duration T_d (Fig. 2B, ii), where T_d is set to be equal to t_B0 (obtained by Fig. 2B, i) minus T_l, the actuation effect generated by the trailing edge is synchronously superimposed with the pressure crosstalk induced by the leading edge, obtaining the maximum value of the first negative pressure peak (B₀) and pressure crosstalk (A₁). The obtained point B₀ is (3.9 μs; −90.25 kPa), and the value of the pressure peak is 2.56 times higher compared to that in Fig. 2B (i). In the subsequent pressure crosstalk stage, the obtained point A₁ is (6.9 μs; 55.33 kPa), and the value of the pressure peak is 2.79 times higher compared to that in Fig. 2B (i). Under a waveform with a modulated pulse period T_f (Fig. 2B, iii), where T_f is set to be equal to t_A1 (obtained by Fig. 2B, ii), the actuation effect generated by the new the leading edge of the second pulse period is synchronously superimposed with the pressure crosstalk induced by the first pulse period, obtaining the maximum value of the second positive pressure peak (A₁) and pressure crosstalk (B₁). The obtained point A₁ is (7.2 μs; 112.82 kPa), and the value of the pressure peak is 2.04 times higher compared to that in Fig. 2B (ii). In the subsequent pressure crosstalk stage, the obtained point B₁ is (10.5 μs; −62.11 kPa), and the value of the pressure peak is 2.07 times higher compared to that in Fig. 2B (ii). A comprehensive comparison of Fig. 2B (i to iii) suggests that under the modulation of pulse duration T_d and pulse period T_f, the values of the positive pressure peak, negative pressure peak, and pressure crosstalk are all greatly enhanced. As presented in Fig. 2B (iv), by increasing the number of pulses, a modulation process similar to that in Fig. 2B (i to iii) will continue to take place, reaching and stabilizing at a high value state after 6 pulses (about 41.4 μs).

Figure 2C exhibits the working pressure states and evolution curves of the pump chamber under the 3 waveforms used in Fig.1. Under the Basic Waveform and Waveform A, the pressure in pump chamber and the deformation of the actuator are all zero at the initial moment before the leading edge of the waveform is applied; subsequently, the actuator begins to compress the pump chamber, generating an oscillating pressure wave. The maximum values of the positive pressure peaks are 52.74 kPa and 57.42 kPa, respectively. Under Waveform B, the pressure in the pump chamber reached 112.82 kPa at the initial moment before the leading edge of the waveform is applied, and the actuator is in an expanding state. Then, as the actuator compresses the pump chamber, the pressure in the pump chamber increases rapidly, reaching the maximum value of 186.68 kPa. The maximum value of the negative pressure peaks is −183.89 kPa.

By comparing the positive pressure peak values under the 3 different waveforms, it can be seen that the maximum value increased by 1.09 times from Basic Waveform to Waveform A, and by 3.25 times from Waveform A to Waveform B. These basically match the experimental results in Fig.1, and the self-reinforcing mechanism of the actuation pressure under the influence of the positive crosstalk effect has been well explained and verified. In addition, as regards PIJ printheads with other structural forms, e.g., shear mode, push mode, and squeeze mode, simulation results indicate that the actuation pressures are usually increased by 2 to 4 times (Fig. S1), suggesting that the self-reinforcing mechanism of the actuation pressure proposed in this article is universal for different PIJ printheads.

In addition, the self-reinforcing phenomenon similar to Fig. 2 may also be obtained at different frequencies, as shown in Fig. S2. When only considering the frequency, as the jetting frequency gradually increases from 1 kHz to 144.928 kHz, the actuation effect generated by the next leading edge will be superimposed with the previous pressure crosstalk at a different position (Fig. S2A), theoretically resulting in the phenomenon of the droplet jetting state oscillating regularly with the increase of the pulse frequency [46]. The supplementary experimental results (Fig. S2B) at different frequencies match the theory well. The droplet jetting state is stable at a jetting frequency of superimposing near the positive peak point of pressure crosstalk, such as 144.928 kHz (6.9 μs), 166.667 kHz (6 μs), 133.333 kHz (7.5 μs), 72.464 kHz (13.8 μs), and 48.309 kHz (20.7 μs). By contrast, nothing could be observed at a jetting frequency of 100 kHz (10 μs), where the actuation effect is superimposed near the negative peak point of pressure crosstalk. As shown in Fig. S2C and D, the modulation of the pressure crosstalk inside the printhead can be adjusted by adjusting the actuation pulse waveform parameters, such as leading edge time T_l, pulse duration T_d, and trailing edge time T_t, to achieve stable droplet jetting at any desired frequency [46]. One case is that droplet jetting cannot be performed at 100 kHz under the waveform of 0.1 μs–3.5 μs–0.1 μs, while a stable droplet jetting state is achieved at 100 kHz under the waveform of 1 μs–5 μs–1 μs (Fig. S2C). Another case is that the limit jetting frequency for stable jetting is 166.667 kHz (6 μ s) under the waveform of 0.1 μs–3.5 μs–0.1 μs, while the limit jetting frequency for stable jetting is 181.818 kHz (5.5 μs) under the waveform of 0.3 μs–1.3 μs–0.7 μs (Fig. S2D). The Helmholtz oscillation period T_o of the printhead system itself (equals to t_A2 − t_A1 in Fig. 2B, ii), which is mainly influenced by the printhead design and the viscosity of the ink, ultimately determines the limit jetting frequency. In general, for a waveform with a given leading edge time T_l, pulse duration T_d, and trailing edge time T_t, at its limit jetting frequency, the period of the waveform T_f (i.e., the reciprocal of the frequency) is approximately equal to the sum of the pulse length (T_l + T_d + T_t) and 1/2 T_o [46]. Based on experimental results and theoretical estimation, the stable droplet jetting at any frequency within 181.818 kHz (5.5 μs) could be achieved for the used ink with a viscosity of 9.2 cp. As shown in Fig. S2E, the variation of droplet velocity with increasing actuation voltage at different frequencies are analyzed, considering that the core of this work is to achieve stable droplet jetting with UHDV. Obviously, only when the actuation effect is synchronously superimposed with the pressure crosstalk (Fig. 2B), i.e., 144.928 kHz (6.9 μs), is the self-reinforcing effect of the actuation pressure most strong and has the droplet velocity the most sensitive response to the actuation voltage, making it easiest to achieve droplet jetting with UHDV. At other frequencies, the self-reinforcing effect of the actuation pressure will be weakened, and a larger actuation voltage is required to achieve the same droplet velocity.

Second, the self-restraining mechanism of satellite droplets under the influence of the positive crosstalk effect is investigated. Self-restraining refers to eliminating the impact of satellite droplets on printing quality through the self-modulation of the crosstalk effect. In this case, satellite droplets actively merge with subsequent main droplets during the droplet flying process, without any other external conditions. The crosstalk effect involved in this part is the interference between droplet and droplet.

As depicted in Fig. 3, the generation law of satellite droplets and the self-restraining phenomena are discussed. Figure 3A compares the change of droplet morphology with increasing droplet velocity under low frequency. In Fig. 3A (i to iv), under low frequency (Waveform A; 1 kHz), 4 different droplet morphology types appear with increasing droplet velocity, including without satellite droplets (Fig. 3A, i), satellite droplets merge with the main droplets (Fig. 3A, ii), the critical state (Fig. 3A, iii), and ineffaceable satellite droplets (Fig. 3A, iv). Under the type in Fig. 3A (i), the droplet velocity is about 5.83 m/s at 0.5 mm at an actuation voltage of 19 V and droplet jetting maintains a monodisperse state (34 to 94 μs) without the appearance of satellite droplets. Under the type in Fig. 3A (ii), the droplet velocity is about 7.08 m/s at 0.5 mm at an actuation voltage of 21 V and 2 satellite droplets are formed (34 μs); however, they quickly merge into the main droplet (34 to 54 μs) and then maintain the monodisperse droplet morphology (64 to 94 μs). Under the type in Fig. 3A (iii), the droplet velocity is about 7.92 m/s at 0.5 mm at an actuation voltage of 23 V and many satellite droplets are formed (34 μs), which merge into a larger satellite droplet (44 μs) that has a velocity close to that of the main droplet. For a long time to come (54 to 94 μs), this satellite droplet maintains the same distance from the main droplet and does not fade way. Under the type in Fig. 3A (iv), the droplet velocity is about 8.67 m/s at 0.5 mm at an actuation voltage of 25 V and many satellite droplets are also formed (34 μs), which also merge into a larger satellite droplet (54 μs); nevertheless, the velocity of the satellite droplet is lower than that of the main droplet, resulting in an increasing distance between the main droplet and the satellite droplet (54 to 94 μs).

In Fig. 3B, under high frequency (Waveform B; 144.928 kHz), droplet jetting maintains monodisperse states with increasing droplet velocity, without the appearance of satellite droplets. The droplet velocity is 11.91 m/s at 1 mm (Fig. 3B, i), 18.14 m/s at 1 mm (Fig. 3B, ii), 22.94 m/s at 1 mm (Fig. 3B, iii), and 27.53 m/s at 1 mm (Fig. 3B, iv), corresponding to actuation voltages of 10 V, 15 V, 20 V, and 25 V. In all cases, there are tails in front of and behind the main droplet, with the length of the tail increasing with increasing actuation voltage. However, under high frequency, the morphology of the formed droplets is almost opposite to that of droplets formed at a low frequency; that is, there exists a small droplet at the head and a large droplet at the end, connected with a tail in the middle (Fig. S3). The reason for this phenomenon is that the tail and satellite droplets generated by the fracture of the first main droplet are quickly merged with the subsequent main droplets. This process is so rapid that there is no chance to see the formation of any individual satellite droplets. The high frequency of droplet jetting is the reason behind the occurrence of this phenomenon.

In Fig. 3C, a more in-depth discussion was conducted on the mechanism of eliminating satellite droplets under high frequency. Figure 3C (i) illustrates a schematic diagram of the process of satellite droplets being actively merged with subsequent main droplets during the droplet flying process, where f is the droplet jetting frequency, d is the distance between the first and second main droplets, V_S is the velocity of the satellite droplet, V_m is the velocity of the main droplet, and d_S is the distance between a satellite droplet and the first main droplet. Assuming that d is relatively small, the difference of the velocity between the first and second main droplets can be ignored. If the elapsed time after a satellite droplet separates from the first main droplet is t, the relationship between the above parameters can be expressed as:

When d_S is equal to d, the center of the satellite droplet coincides with that of the subsequent main droplet, thus eliminating the impact of satellite droplets on printing quality. Assuming that the corresponding time is T_ms, an approximate equivalence relationship can be obtained:

The key parameter is T_ms, which determines the merging state. In general, the larger the T_ms, the longer the satellite droplet will exist, and vice versa. When T_ms is large enough, the satellite droplet could not merge with the subsequent main droplet within the printing distance, which would affect the printing quality; when T_ms is small enough, there is not enough time to see the formation of satellite droplet, just as seen in Fig. 3B (i to iv).

Considering that the volume of the main droplet is larger than that of the satellite droplet, it can be approximately assumed that, for the same droplet flying duration, the decrease in velocity of the main droplet will be smaller than that of the satellite droplet [22]. Therefore, assuming that V_m and V_s remain constant during the droplet flying process, an approximate value of T_ms slightly larger than the actual value will be obtained:

T_ms mainly depends on the ratio of the satellite droplet velocity to the main droplet velocity V_S/V_m and on the droplet jetting frequency f. When V_S/V_m is close to 1, T_ms is close to infinity, which means that the satellite droplet will never merge with the subsequent main droplet. This situation usually occurs in the CIJ technology, where a constant-pressure source is used to accelerate the ink [42]. Thus, the velocity of the satellite droplet is naturally close to that of the main droplet, and external conditions are needed to assist in changing the direction of the satellite droplet, thereby eliminating its impact on printing quality. In the PIJ technology, V_s is always not equal to V_m, due to the use of a pulse pressure source. The value of V_S/V_m changes with the actuation voltage. The smaller the V_S/V_m and the higher the jetting frequency, the shorter the time needed for the satellite droplet to be actively merged with the subsequent main droplet. In Fig. 3C (ii and iii), experiments were conducted under different frequencies (f_A1, f_A2, and f_A3 correspond to the actuation frequencies obtained at points A1, A2, and A3 in Fig. 2B, where approximately f_A1 = 2f_A2 = 3f_A3) and different droplet velocities (obtained at 20 V, 17.5 V, and 15 V) to verify the effectiveness of the theory described as Eq. 4. Under f_A1 and f_A3, the value of V_S/V_m is small, and the satellite droplets are quickly eliminated. Under f_A2, the value of V_S/V_m is larger, and longer times are needed. Under the actuation voltage of 15 V, V_S/V_m is close to 8/15, and the value of T_ms calculated according to Eq. 4 is 2.1/f_A2, which matches the T_ms of 1/f_A2 − 2/f_A2 obtained experimentally. Under the actuation voltage of 17.5 V, V_S/V_m is close to 7/9, and the value of T_ms calculated according to Eq. 4 is 4.5/f_A2, which matches the T_ms of 4/f_A2 − 5/f_A2 obtained experimentally. Under the actuation voltage of 20 V, V_S/V_m is close to 4/5, and the value of T_ms calculated according to Eq. 4 is 5/f_A2, which matches the T_ms of 5/f_A2 − 6/f_A2 obtained experimentally.

In theory, as long as the flying distance is long enough, satellite droplets will eventually be eliminated. The value of V_S/V_m is affected by many factors; therefore, in practical applications, increasing the jetting frequency f is the most practical and convenient method to realize self-restraining of satellite droplets.

Third, the self-weakening mechanism of the air resistance under the influence of the positive crosstalk effect is investigated. Air resistance refers to the frictional force that droplets experience during the flying process in the air, which will reduce droplet velocity. Self-weakening refers to weakening the deceleration effect on droplet velocity through the self-modulation of the crosstalk effect. In this case, the air resistance of the droplet can be weakened by the shielding effect caused by the accelerated air flow induced by the moving droplet in front, without any other external conditions. The crosstalk effect involved in this part concerns the interference between droplet and air.

As shown in Fig. 4, the deceleration effect of the droplet velocity caused by air resistance under different jetting conditions is discussed. Figure 4A compares the simulation and experimental results of the droplet jetting process under a high-frequency waveform (Waveform B; 144.928 kHz) and an actuation voltage of 25 V. The position and velocity distribution of droplets obtained by simulation and experiments matched very well, proving the effectiveness of the simulation. The only obvious difference lies in the morphology of the satellite droplets, which is attributed to the insufficient refinement of the mesh. The size of the satellite droplet is only about 1/3 to 1/10 times that of the main droplet; thus, more refined meshes are needed, i.e., an increase of 3 to 10 times to the number of meshes, which would result in excessive computational complexity. To this end, the satellite droplets were ignored in the simulation. Figure 4B and C compare the distribution and evolution process of droplet velocity at low and high frequencies. In Fig. 4B, under low frequency (Waveform A; 1 kHz; 25 V), an approximately single-droplet jetting state is obtained, with a droplet velocity of 9 m/s at 420 μm. As it can be seen within 420 to 480 μm, the flying droplet experiences air resistance in the head area, the air forces the droplet to decelerate, and the droplet pushes the air in front of it to generate forward flow; the velocity of the air is higher than 0. On the jet trajectory, the droplet drags the air behind it, generating an airflow in the same direction. As it can be observed in the area of 0 to 380 μm, the closer the position to the droplet, the higher the velocity of the induced airflow. In Fig. 4C, under high frequency (Waveform B; 144.928 kHz; 25 V), a series of droplets are observed simultaneously, with a droplet velocity of 27.5 m/s at 420 μm. In the stable droplets train, the internal airflow velocity is also accelerated to 20 m/s, as seen in the area of 240 to 600 μm, which is close to 73% of the droplet velocity. The coupling between fast airflow and fast droplets greatly reduces the air resistance experienced by the droplets.

Figure 4D and E provide a more intuitive interpretation of the coupling between airflow and droplets by showcasing the distribution and evolution process of the droplet velocity of 2 consecutive droplets. The 2 consecutive droplets are jetted by 2 identical actuation pulses with a pulse period of 6.9 μs, which have the same shape with the actuation pulse in Waveform A. In Fig. 4D, the droplet velocity of the second droplet is 9.5 m/s at 420 μm. However, when reaching the same position, the droplet velocity of a single droplet is only 9.0 m/s at 420 μm (Fig. 4B); this indicates that the attenuation of the droplet velocity of the second droplet is weakened. More specifically, the air between the 2 consecutive droplets is simultaneously dragged by the first droplet and pushed by the second one, generating an airflow with a velocity close to the droplet velocity. This indicates that a shielding effect of air resistance is applied on the second droplet. In Fig. 4E, the droplet flying process of the 2 consecutive droplets is displayed. The attenuation of the droplet velocity of the first droplet is larger than that of the second droplet, and the distance between them decreases gradually until they eventually merge (30 to 70 μs), which provides a more intuitive demonstration of the shielding effect.

To further evaluate the shielding effect, Fig. 4F compares the air resistance under different initial droplet velocities V₀ for the frequency of 1 kHz (Fig. 3A), 48.309 kHz (Fig. S2B), 72.464 kHz (Fig. S2B), 100 kHz (Fig. S2C), 133.333 kHz (Fig. S2B), 144.928 kHz (Fig. 3B and Fig. S2B), 166.667 kHz (Fig. S2B), and 181.818 kHz (Fig. S2D). The droplet velocity reduction at a distance of 1 mm, denoted as R_V, is proportional to the amount of air resistance experienced by the droplet; therefore, it is used to characterize the air resistance. Theoretically, the air resistance on a droplet is determined by both droplet velocity and droplet jetting frequency. At the same droplet velocity, if the number of the flying droplets is the same, the air resistance is smaller for the droplet with larger frequency. The reason is that at the same droplet velocity, the larger the frequency, the smaller the distance between adjacent droplets and the relative velocity between the droplet and its front air, resulting in a smaller air resistance. The simulation and experimental results showed that under the same droplet velocity, the air resistance will decrease with the increase of the drop jet frequency, further proving that the air resistance with larger frequency is smaller.

Under low frequency (Waveform A; 1 kHz), i.e., the black line in Fig. 4F, the relationship between initial droplet velocity V_0-low and droplet velocity reduction at a distance of 1 mm, i.e., R_V-low, can be approximated as:

Under high frequency (Waveform B; 144.928 kHz) i.e., the red line in Fig. 4F, the relationship between initial droplet velocity V_0-high and droplet velocity reduction at a distance of 1 mm, i.e., R_V-high, can be approximated as:where a₁, b₁, x1, a₂, b₂, and x2 are constants. According to the change trend of the curves in Fig. 4F, x1 is larger than x2, which suggests that R_V-low increases faster than R_V-high. In other words, the air resistance under high frequency increases slower than that under low frequency. For instance, at an initial droplet velocity of 27.7 m/s, R_V-low is 1.955 ms⁻¹ mm⁻¹, while R_V-high is 0.725 ms⁻¹ mm⁻¹ (only 37% of R_V-low). This indicates that, for the same initial droplet velocity, the theoretical droplet flying distance at high frequency (Waveform B; 144.928 kHz) will be ~2.7 times higher than that at low frequency (Waveform A; 1 kHz).

Obviously, increasing the jetting frequency f helps to form an obvious shielding effect and achieve self-weakening of the air resistance during the droplet flying process.

Finally, considering that the mechanisms of self-reinforcing of the actuation pressure, self-restraining of satellite droplets, and self-weakening of air resistance at the start and stop processes may differ from the stable droplet jetting process in the actual pattern printing process, experimental evaluations (Fig. S4) were conducted on the droplet jetting states of the start and stop processes.

As shown in Fig. S4A, a special waveform was designed to observe the droplet jetting state at the start and stop processes. At the front of the waveform (0 to 0.69 ms), the setting is exactly the same as Waveform B, ensuring that 1,000 droplets are jetted exactly the same as Waveform B in each waveform period. The back of the waveform (0.69 ms to 10 ms) is the idle time, and the waveform period is 10 ms (frequency of 0.1 kHz). The droplet jetting processes in each waveform period are repeated, making the start and stop processes to be cleverly captured by the droplet observation module. The actuation voltage is 22 V.

During the start process, the velocities of the first 5 droplets were lower than that of the subsequent droplets, as the actuation pressure in the first 5 actuation periods were lower than that of the subsequent actuation periods (Fig. 2B, iv). As shown in Fig. S4B and C, the front droplet is constantly overtaken by the subsequent droplets during the flying process at the start stage, merging into a larger “First Main Droplet”. The droplets formed during the start stage, i.e., the stage before the “First Main Droplet” reaches the substrate, cannot guarantee the accuracy of pattern printing. The time of the start stage is usually related to the printing distance, e.g., the time is 85 μs at a printing distance of D = 1 mm (Fig. S4B) and the time is 145 μs at a printing distance of D = 2 mm (Fig. S4C). Within a typical printing distance of several millimeters or even tens of millimeters, the start stage takes several tens of microseconds to a few milliseconds, which is quite brief and has a negligible impact on printing efficiency.

During the stop process, the residual pressure crosstalk and satellite droplet may have an influence on the printing process. After the droplets are ejected from the printhead, there will still be residual pressure crosstalk inside the printhead, such as point A₁ in Fig. 2A and B (i and ii). Under the proposed UHDV-PIJ method, the pressure inside the printhead is very high, resulting in obvious residual pressure crosstalk, even to the level of producing “Residual Droplet” (Fig. S4B and C). In addition, after the “Last Main Droplet” (Fig. S4B and C) is ejected, there are no subsequent droplets to achieve the self-restraining of satellite droplets, thus generating the “Last Satellite Droplets” (Fig. S4B and C). The time of the stop stage also equals to several tens of microseconds to a few milliseconds, and the impact on printing efficiency is also minimal.

As shown in Fig. S4D, in order to eliminate the impact of “First Main Droplet”, “Residual Droplet”, and “Last Satellite Droplets” on printing quality, simple shielding masks should be added outside the substrate to filter out the droplets generated during the start and stop stages.