Experimental and theoretical study on the ceasing motion of a droplet manipulated by air-blowing nozzle

In this study, the dynamic process of a droplet moving with a substrate until blocked by air flow is investigated experimentally and theoretically. A sequence of experiments has been conducted to investigate the impacts of wetting properties, droplet volumes, air flow velocities, and droplet velocities. The substrate is driven by a linear motion motor to ensure the droplet moves at a certain velocity alongside the substrate. The air flow that is vertically injected from the nozzles toward the substrate is known as an impinging jet. After the air flow impacts the substrate, it will blow horizontally. When the direction of air flow is opposite to that of the droplet movement, a force will be exerted on the surface of the droplet. This action incurs the deformation of the droplet and the cessation of its movement, eventually resulting in an equilibrium state. The droplet shape and motion processes are recorded by a high-speed camera. A mathematical model considering the effect of droplet contact angle, droplet size, droplet moving velocity, and air flow velocity is established in the state of equilibrium. Correlation factors are used in the model for the drag coefficient and air average velocity acting on the droplet. It is found that the air flow rate required to stop the motion of the droplet increases with the droplet moving velocity and the droplet size but reduces with the increase in the static contact angle. The mathematical model, when equipped with suitable correlation factors, exhibits good agreement with experimental data and


I. INTRODUCTION
The motion of droplets under external force on solid substrates is an important phenomenon in many engineering operations, such as distillation, spray coating, condensation, 1 biological technology, 2 and immersion lithography. 3Due to its importance and unique properties, a lot of authors have investigated the motion of droplets influenced by different external effects, such as vibration, 4,5 gravitation, 6 magnetic and electric fields, 7,8 and shear flow 9,10 in the past.
When a stationary droplet is on a flat surface, three interfaces are observed due to adhesion force and cohesion force.The static contact angle, denoted by θS, is the angle formed between the tangent along the droplet's surface and the substrate surface. 11,12For a hydrophobic substrate, this contact angle typically exceeds π/2, indicative of poor wetting.Conversely, a hydrophilic substrate will have a contact angle less than π/2, signifying better wetting.After introduction of an external force, such as gravity or shear flow, the contact angles of the droplet exhibit contrasting changes.When the droplet adheres to an inclined surface, under the influence of gravity, the upstream contact angle decreases (receding contact angle, θR), while the downstream contact angle increases (advancing contact angle, θA).Contact angle hysteresis refers to the difference between the advancing contact angle and receding contact angle.When a stationary droplet is exposed to shear flow, the contact angle hysteresis phenomenon will also occur.Contact angle hysteresis leads to the generation of adhesion force, which is proportional to the magnitude of the contact angle hysteresis. 9When the inclination angle of the surface is small or the shear flow is small, these external forces may not be sufficient to cause the droplet to move.In such cases, the existence of contact angle hysteresis allows the droplet to maintain its position.
Once the external force exceeds adhesion force, the motion state of the droplet will change.The droplet on the inclined surface would slide along the direction of the external force rather than maintaining its original position.Beyond a critical shear flow rate value, the shear forces acting on the stationary droplet become stronger than the adhesive forces holding it to the substrate.As a result, the droplet cannot maintain at a fixed position and begins to move away due to the shear flow.In other cases, when the droplet slides down along an inclined surface, it can be either stopped or even forced to move in the opposite direction upon encountering a sufficiently strong shear flow. 13The behavior of the droplet is greatly influenced by the nature of the external force. 14ndeed, previous research had heavily focused on understanding how to alter the motion state of a droplet adhered to a stationary substrate.The motion state of the droplet changes when the magnitude of the external force exceeds that of the adhesive force.These different external forces include surface oscillation, gravity, magnetic and electric fields, and shear flow. 15However, in this study, we examine the behavior of the droplet adhered to the moving substrate influenced by wall jet flow.We specifically focus on the droplet capability to halt at a predetermined position, a crucial requirement in immersion lithography.
Immersion lithography is a technique that replaces the air between the lens and the wafer with a high refractive index liquid, such as water, to enhance optical resolution in the image plane.Some new challenges are introduced due to the substitution of the filling medium.When the velocity of the substrate is accelerated beyond the critical velocity, small droplets will form on the substrate at the receding side of the interface. 16These droplet formations may cause problems such as droplet evaporation.When droplets evaporate, they may leave behind impurities on the wafer.These phenomena must be avoided. 17Besides, the droplets that adhere on the substrate and encounter the advancing meniscus again may cause bubble formation. 18Therefore, any residual droplets left on the wafer will potentially lead to defect formation, and it is a critical challenge to restrict and even diminish the droplets on the wafer. 19An effective method to deal with residual droplets is based on gas dynamic sealing technology known as the "air knife."In practical applications, the "air knife" increases the critical velocity required for effective water containment. 20Therefore, by means of air flow, we can constrain droplets that move with the substrate at the internal area of the air knife region.
The aim of this article is to experimentally and analytically study the motion behavior of droplets adhered to the substrate under varying velocities under air flow conditions.An mathematical model is developed based on the air drag force acting on the droplet surface to investigate the essential parameters for the droplet transition from the motion to stop state.The focus of the discussion is the relationship between the magnitude of the air flow rate and the moving velocity of the droplet.In this research, an air dynamic sealing module used to simulate the "air knife" in immersion lithography is constructed to generate air flow in the channel.The behaviors of the moving droplet under the different air flow velocities are systematically investigated.

II. MATH AND EQUATIONS
We derive an empirical mathematical model with important parameters such as the critical velocity, gas flow velocity, and droplet size to describe the behavior of the droplet adhered to the moving substrate upon encountering a gas impinging jet.The gas jet is created by sustaining a gas flow Q g through the circular hollow nozzle with an inner diameter d 0 (0.1 mm).Its orifice is located above the substrate at a distance h (0.5 mm). Figure 1 shows the gas flow force acting on the distorted droplet adhered to the moving bottom substrate in the channel.The gas flow is generated through a row of small nozzles connected to a gas source at the top of the air dynamic sealing module.
It was discovered in the present study using a high-speed camera that when the droplet is positioned away from the small nozzles, the droplet moves at a constant velocity V along with the substrate, i.e., the droplet will not deform and the contact angle between the substrate and droplet will be the static contact angle θS before the force of gas acts on the droplet.
As the substrate moves, the droplet gets closer to the small nozzles.Gas is injected through the small nozzles into the gap at a certain flow rate.The gas flow will generate gas drag force FD on the windward side of the droplet, which will impede the movement of the droplet.As the droplet nears the nozzles, the gas drag force increases, leading to the droplet decelerate on the substrate.Relative sliding occurs between the substrate and the droplet.
The velocity difference between the substrate and droplet leads to the viscous force Fs at the contact interface.At the same time, as a result of gas flow influence, the droplet experiences deformation, transitioning from a symmetrically distributed static contact angle to a distinct advancing contact angle and receding contact angle.Therefore, there is a force, which is called the adhesion force FCL, acting on the main body of the droplet, pushing against the upstream of the gas flow to resist the shear impact of the gas flow.
The droplet achieves an equilibrium state and ceases motion due to the balance of forces acting upon it.The force equilibrium in the x-direction yields where FCL is the adhesion force, FD is the gas drag force, and FS is the viscous force.

A. Droplet geometric model
When a stationary water droplet is adhered on a flat substrate, it typically assumes a spherical cap shape due to the balance of forces acting on it, and its contact patch area is exclusively dictated by the characteristics of the material.To estimate the characteristic sizes of the droplet adhered on a substrate, which has been deformed due to the effect of air flow, the mean static contact angle is defined as 21,22 The height of the droplet is where VD is the volume of the droplet and the radius of the wetting area is The area of the droplet wetting the substrate, i.e., the area determined by the three phase contact line, can be calculated as The windward area of the droplet is calculated using the following formula:

B. Adhesion force
When the stationary droplet adheres to a moving substrate and is influenced by air flow, the drop shape deforms significantly under the action of a strong enough airflow.However, when the droplet size is smaller than the capillary length, it is valid to use characteristic sizes to calculate the adhesion force FCL.In order to achieve a more physically realistic yet simplified assumption, it is considered that the contact angle hysteresis through a linear relationship between the advancing contact angle θA and receding contact angle θR.Based on the linear variation assumption, it will result in the representation of FCL denoted as 23,24 FCL = 2γkRDπ(θA − θR)(sin θA where γ denotes the surface tension of liquid and k is the adhesion force factor that depends on contact angle variation and the droplet shape under complex droplet deformation conditions.Researchers generally concur that the adhesive force is proportional to the contact angle hysteresis.However, there are some variations in the values of the proportionality constant k. 9 The deformation of the droplet adhered to the moving substrate exposed to air flow is complex.Because the present study's approach is different from the earlier studies under the influence of a different air flow (i.e., different correlation for the air drag coefficient), it is needed to get an appropriate value to ensure that the theoretical model matches experimental data. 25

C. Drag force
The issue of the force exerted on the droplet by the shear flow is highly complex, involving the hydrodynamics of fluid-fluid interaction.Under typical conditions, the drag force applied to the droplet surface by the gas flow can be characterized as where ρ g is the gas density, u d is the gas velocity averaged over the height of the droplet, CD is the drag coefficient, and E d is the droplet cross-sectional area.

Drag coefficient
The drag coefficient CD is a crucial parameter for resistance calculation.The fluid dynamics problem depicted in Fig. 1 belongs to the category of "flow around obstacles".Many simple geometric shapes with symmetrical flow configurations are provided in the literature.However, due to the deformation of the droplet, the fluid dynamic characteristics in this work are not entirely applicable. 26n addition, the drag coefficient CD cannot be simply regarded as a function of Reynolds number and cannot be expressed simply by a formulation. 27,28Referring to and drawing upon research methods in previous literature, the correction factor ξ is introduced to address the issue of droplet deformation, where a similar approach has been used to simplify the problem's complexity.The correct drag coefficient can be corrected as 26 Promoting the scope of the application to Re < 10 5 , C undef D can be written as 29 The Reynolds number is defined by where μ g is the gas viscosity.

Gas average velocity
There is a significant difference in the average gas velocity impacting the droplet when comparing the gas velocity averaged solely over the droplet height hD with the gas velocity averaged across the entire channel height h.This difference arises from variations in the gas velocity distribution within the channel.Consequently, diverse gas velocity profiles yield distinct gas average velocities that influence the behavior of the droplet.
A row of nozzles is employed to generate the gas flow rate in this paper.The gas flow is vertically injected from the nozzles into the substrate.Therefore, when analyzing the gas flow profile in the channel, the impinging jet and wall jet methods should be used instead of the Poiseuille flow described in other literature studies. 11,23,24s shown in Fig. 1, the gas velocity distribution varies across the channel height.The velocity near the channel substrate tends to be lower due to the presence of boundary layers.In order to calculate the drag force exerted on the windward surface of the droplet more accurately, the velocity profile of the gas flow inside the channel needs to be known.The gas flow that is vertically injected from the nozzle into the substrate is known as an impinging jet.The flow field of an impinging jet can be delineated into three zones: (1) the free jet prior to impingement, (2) the impingement region, and (3) the wall jet region. 30he free jet prior to impingement refers to the region immediately after the gas is ejected from the nozzle until it reaches the impingement substrate.In this zone, the gas flows freely and forms a well-defined jet with a relatively high velocity.The impingement region is where the impinging jet strikes the substrate.At the point of impingement, the gas abruptly changes its direction, causing a significant deceleration and resulting in a high-pressure zone.After impingement, the gas spreads out along the substrate and forms a thin, spreading jet known as the wall jet.In this zone, the gas continues to move along the substrate while gradually losing kinetic energy.In this paper, we only focus on the velocity profile in the wall jet region.
The profile of the gas flow velocity ug in the x-direction in the wall jet region as shown in Fig. 1 is where um is the maximum velocity of cross section 31 and z m/2 is taken as the vertical length scale, that is, the z coordinate where the velocity has a value half of um, where u 0 is the gas flow velocity at the nozzle and d 0 is the diameter of the nozzle.Equation ( 13) accurately captures the experimental findings for x/h values 32 up to ∼0.4.
The equation for z m/2 is written as It is seen that z m/2 increases linearly with x, and the empirical coefficients 32 C b ≈ 0.042 and C 1 ≈ 0.60.
The average gas flow velocity within the range of droplet height u d is calculated as the integral of ug from 0 to h d , yielding the following equation: where ug is the gas velocity.At the same time, the presence of a distance between the impinging jet nozzles results in the nonuniformity of the gas curtain.The circumferential region of the channel between the air dynamic sealing model and the substrate is an open boundary, meaning it is exposed to the atmospheric environment.The gas flow is open to the surrounding boundaries.When considering the relationship between the gas flow rate Q g and gas flow velocity ug in the channel, it is necessary to consider the gas flow losses caused by the movement of gas flow in other directions.
To simplify the fitting process, we use an empirical constant C to approximate the relationship between the actual flow rate and the flow rate acting on the droplet.

D. Viscous force
When the droplet slows down to a stationary position due to resistance from the gas flow, the substrate continues to move at the same velocity V.According to the assumption of viscous Newtonian fluid, the bottom liquid in contact with the substrate moves in the x-direction with a velocity V.Because of the mass conservation, the liquid at the upper part of the droplet will move with the same velocity V, but in the opposite direction of the motion of the substrate.As a result, the viscous force, also known as viscous drag or shear force FS, is generated to maintain the droplet attached to the moving substrate at a fixed position under air flow.It is assumed that the flow velocity of the liquid inside the droplet varies linearly from the substrate at the bottom y = 0 to the top of the droplet at y = hD.It is obtained that where μ l is the liquid viscosity.

III. EXPERIMENTAL SETUP
In order to investigate the role of some important experimental parameters, an experimental system was designed, which mimics the basic relationship between the air knife and droplet adhered on a moving substrate, as shown in Fig. 2. A certain size of liquid droplet is generated at position A on a substrate and then moves at a certain speed along the linear motion platform toward position B. At position B, there is an air dynamic sealing module that generates gas shear flow to impede further movement of the liquid droplet.The entire motion process of the droplet at position B was recorded by a high-speed camera.
The final overall experimental system is shown in Fig. 3(a).The linear motion platform was specifically designed to emulate the immersion system utilized in lithographic scanning tools.It consisted of a linear motor capable of performing reciprocating motion in a single direction.In addition, the linear motion platform was equipped with an interchangeable substrate, enabling precise positioning of the substrate or object placed on it.The linear motion  motor can reach a maximum scan velocity of 1.5 m/s with a maximum acceleration of 22 m/s 2 .The substrate can be changed easily with different wetting properties with different surface coatings.
The droplet was created in a controlled manner by using a micro-needle at position A, resulting in droplet volumes in the range of 0.08 and 0.05 μl.When the droplet was prepared to the desired size, we set the platform to move to position B at a certain velocity.Position B is the measurement position where the air dynamic sealing module was fixed at a specific height above the substrate.
The top of the air dynamic sealing module was connected to a gas source, and there was a row of air injection small holes at the bottom surface facing the substrate, as shown in Fig. 3(b).When the substrate passed through the air dynamic sealing module, the substrate and the bottom face of the module would form a channel.The air flow injected through the nozzles would act on the droplet as it moved along the substrate in the channel.
The gap h formed between the air dynamic sealing module and the substrate will generate a horizontal shear air flow that creates resistance against the droplet.By introducing different flow rates of air through the small holes, we can influence the motion and behavior of the droplet.The air flow rate passing through the nozzles was adjusted by the MFC (Mass Flow Controller, ALICAT, ±1 F.S).
The behavior of the droplet was recorded through a high-speed camera (Phantom V9, 1400 f/s) with an optical lens at position B. The magnification of the optical lens is 0.58× ∼ 7.5×.The camera is a high-speed camera capable of acquiring a maximum of 20 000 f/s with an optical resolution (pixel size) of 11 μm.
This camera is capable of capturing images of a vertical cross section of both the advancing and receding meniscus of the droplet.
An LED light source used for illumination adopted red parallel light with adjustable brightness (2.7 W).The initial picture of the droplet was consistently recorded before the air flow started to generate effects in order to ascertain the static contact angle (θS), as shown in Fig. 3(c).Then hundreds of images were acquired and processed in order to obtain meaningful measurement of the advancing and receding contact angle (θA and θR), as shown in Fig. 3(d).At the same time, the motion of the droplet was recorded, whether it stopped at a certain position near position B or continued to pass through position B.

IV. RESULTS
In this section, the results of the experiments are discussed and compared to the corresponding theoretical analysis.In this paper, gas and liquid are air and water, respectively.The physical parameters of the response are as follows: γ = 0.072 N/m, μ l = 1 × 10 −3 Pa ⋅ s, μ g = 1.184 × 10 −5 Pa ⋅ s, and ρ g = 1.26 kg/m 3 .

A. The motion of the droplet
Several parametric studies have been conducted to explore the influence of contact angle and air flow rate on droplet motion and deformation.The motion of the water droplet along with the substrate in flowing air can be classified into two outcomes: crossing and stopping.The outcomes are related to the motion velocity of the droplet and air flow rate acting on the droplet.
Figure 4 shows that the air flow velocity is not enough to stop the moving droplet adhered to the substrate.The influence of viscosity, droplet size, and contact angle on this critical air velocity was examined, along with the corresponding shape of the droplet.The position of the red arrow indicates the location of the air nozzles.The blue arrow indicates the direction of substrate motion.When the droplet is far away from the nozzles, and the force exerted by the air jet flow from the nozzles is not sufficient to alter the motion and deformation of the droplet.As a result, the droplet maintains a stable shape as it moves along with the substrate, as shown in Fig. 4(a).
When the droplet reaches near the nozzles, the force generated by the air jet flow begins to affect both the motion and shape of the droplet.At this stage (0.011 s), the droplet velocity decelerates and the deformation is initiated, as shown in Fig. 4(b).However, the air flow velocity is insufficient to halt the motion of the droplet.Thus, the droplet persists in its motion.When the droplet reaches directly beneath the nozzles (0.014 s), the droplet undergoes severe deformation, as shown in Fig. 4(c).Once the deformed droplet passes through the nozzles, the droplet undergoes an opposite change in shape because of the change in the direction of the air jet flow (0.022 s), as shown in Fig. 4(d).
Figure 5 shows pictures of the air velocity required to stop the process of the moving droplet.The blue arrow indicates the direction of substrate motion.The indication of the red arrow is the same as that shown in Fig. 4. When the droplet is far away from the nozzles, the droplet maintains a stable shape as it moves along with the substrate.
As the droplet moves toward the air nozzles, the droplet experiences a gradual increase in the force exerted by the air flow.At this stage (0.007 s), the droplet's velocity decelerates where the deformation starts, as shown in Fig. 5 rate is enough to stop the motion of the droplet and the droplet remains fixed in proximity to the air nozzles.It should be noted that, at the stage (0.013 s) when the droplet stops moving, a portion of the liquid is pulled out of the droplet, as shown in Fig. 5(c).This phenomenon where droplet leakage occurs due to the pulling motion of the substrate is very similar to what is described in Ref.17.Then the droplet will eventually settle into a fixed shape and remain in a stable position, as shown in Figs.5(d)-5(f).

B. Deformation of the droplet
Figure 6 illustrates the variation process of the dynamic advancing and receding contact angle with a substrate velocity of 100 mm/s when the droplet is at equilibrium state.
It is worth noticing that the deformation of the droplet is primarily influenced by drag force, surface tension, and inertial forces.
The deformation of the droplet occurs simultaneously as it comes to a halt.The stopping process of the droplet can be divided into two stages: the deceleration stage and the equilibrium stage.At the deceleration stage, the motion velocity of the droplet gradually decreases, while the dynamic contact angle undergoes drastic changes.The advancing dynamic contact angle gradually increases until reaching the maximum and remains constant thereafter, while the receding dynamic contact angle decreases until it reaches zero.When a portion of the liquid is pulled out from the droplet receding the meniscus due to the receding dynamic contact angle reaching zero, the receding dynamic contact angle begins to gradually increase until reaching the equilibrium stage.
The droplet reaches equilibrium when the drag and surface tension forces balance each other, with the inertial force being zero.At this time, the droplet comes to a stop.At the equilibrium stage, the advancing contact angle and receding contact angle will remain fixed, and the shape of the droplet will no longer change.

C. Comparison between the model and experiments
The empirical constant C is used to approximate the relationship between the actual flow rate and the flow rate acting on the droplet because of the gas flow losses caused by the movement of gas flow in other directions.Data taken for a lot of experiments have shown that the empirical constant C should be adjusted from 0.8 to 0.95.
It is important to consider the effects of droplet deformation and its behavior under an impinging jet.For the gas drag coefficient, most droplet dynamics models are overly simplified, typically assuming that droplets remain spherical.This assumption neglects the impact of droplet deformation.Furthermore, it overlooks the complex interactions between the external gas flow field and the internal flow field within the droplet.In order to take these factors into account and simplify the calculations, we have made some simplifying assumptions.
In this paper, the drag coefficient correction factor ξ and adhesion force factor k are introduced to address the issue of droplet deformation under the influence of air flow.ξ is calculated by assuming that the ratio of the drag coefficient CD to the droplet surface remains constant as the droplet shape changes.Specifically, the ratio of the drag coefficient of the undeformed droplet to the surface of the deformed droplet remains consistent.The constant k is initially derived under a uniform force field.However, in practice, droplets are affected by factors such as flow field non-uniformity and dynamic changes in the droplet shape, so the choice of k needs to be adapted to the actual flow conditions.To ensure that the model accurately reflects experimental results, we fit the model using experimental data to minimize the experimental error.
The adhesion force factor k is about 0.1, and the correction factor ξ is about 0.1.These empirical constants are verified over a range of experimental data that demonstrated accuracy to within ∼10% for As the velocity of the droplet motion increases, the amount of air flow rate required to stop the motion of the droplet also increases because the force exerted on the droplet needs to overcome the adhesion between the droplet and the substrate.
It is easy to understand that when the droplet stops moving, the substrate continues to move at its original velocity.Therefore, viscous force arises between the droplet and the substrate and is proportional to the velocity of substrate motion.As a result, a corresponding air flow rate is required to generate enough air drag force to counteract the viscous force.Hence, the faster the droplet motion velocity, the larger the air flow rate required to stop the motion of the droplet.
Besides, as the droplet volume increases, the air flow velocity required to stop the motion increases.An increase in droplet volume will result in an increase in the mass of the droplet, thus leading to a larger inertia force.In addition, the area of the droplet in contact with the substrate also increases, resulting in a larger viscous force.However, due to the influence of the wall jet, the effective action of the air flow is concentrated near the bottom of the channel.Therefore, the increase in droplet volume, which leads to an increase in the exposed windward area, does not significantly impact the drag force exerted by the air flow.
When the droplet is on the substrate with different surface properties, the contact angle will change.This difference will still exist even with the influence of air flow.In order to study the effect of contact angle on the motion performance of liquid droplets, RaxinX (static contact angle 100 ○ ) and PiQnano (static contact angle 120 ○ ) were coated on the substrate.The relationship between the critical velocity and air flow rate for the droplet of the same volume with different contact angles is shown in Fig. 8.It is worth noticing that as the contact angle increases, the air flow rate required to stop the motion of the droplet decreases.Due to its position within the boundary layer and exposure to a velocity gradient, a droplet with a larger contact angle will be elevated relative to the substrate, leading to an increased mean air velocity perceived by the droplet.

V. DISCUSSION AND CONCLUSIONS
In this study, the cessation process of the droplet that adhered to the moving substrate under the influence of air flow has been systematically investigated.The mathematical model has been developed through force balance at the equilibrium state, including drag force, adhesion force and viscous force.To alleviate the computational burden, certain assumptions have been made, such as the relationship between the advancing and receding contact angle.In addition, correction parameters have been introduced to calculate the drag coefficient and average air flow velocity, accounting for deviations caused by droplet deformation and air flow losses due to characteristics of the gas impinging jet.Subsequently, under dynamic equilibrium conditions, the relationship between droplet deformation, air drag force, and viscous forces is systematically studied.
The predicted correlation between the air flow rate and droplet critical velocity aligns with experimental results with the air dynamic sealing model.It can be noticed that the droplet is stopped when the air flow rate reached a certain value.The air flow rate required to stop the motion of the droplet increases with both the droplet moving velocity and the droplet size, while decreasing with the contact angle.
Since the study is limited in the equilibrium state, the dynamic motion of the droplet under the action of air forces is not analyzed.The arrangement and size of nozzles in the gas impact jet are not systematically analyzed and studied with respect to their effects on the motion of the droplet.Considering the important influence of air flow velocity distribution on the dynamic movement process of droplets, it is suggested to further investigate this complicated instability phenomenon.The empirical constants C, k, and ξ in the model are limited to the experimental conditions reported in this study.Their relations have not been further studied and revealed.It is suggested to further perform more experiments with other liquids and surfaces to obtain more data that could be used in generalizing the model.

FIG. 1 .
FIG. 1. Schematic of forces acting on a deformed droplet with moving substrate and air flow.

FIG. 2 .
FIG. 2.Schematic of the experimental system.A droplet of a specific size on a substrate is generated at position A. Then the substrate moves toward position B at a certain velocity.The moving droplet is subjected to the shear flow generated by the air dynamic sealing module, and the entire process is recorded by camera B.

FIG. 3 .
FIG. 3. Experimental system and the scheme of droplet motion: (a) overview of the experimental system; (b) overview of the air dynamic sealing module; (c) the static contact angle of the droplet moving with the substrate; (d) the advancing and receding contact angle of the droplet affected by the air flow.

FIG. 6 .
FIG.6.The change process of the advancing contact angle and receding contact angle as the droplet transitions from motion to stillness.

FIG. 7 .
FIG. 7. The process of the moving droplet stopped by the air flow near the air nozzle region.

FIG. 8 .
FIG. 8.The influence of static contact angle on critical velocity (the volume of the droplet is 0.08 μl).