## Abstract

This experimental work utilizes a newly developed method, curved water jet-guided laser micromachining, to generate microfeatures on metallic surfaces. During the process, material is removed by a high-power nanosecond laser beam, which is transmitted through a high-pressure microwater jet via total internal reflection. To achieve intricate texturing patterns, a secondary motion component is superimposed on the XY motion of the workpiece provided by the motion stage. The secondary motion is generated by deflecting the water jet trajectory by a controllable dielectrophoretic force. The induced secondary motion of the water jet cuts the processing time to one half when generating texture patterns for isotropic wetting as compared to processes with only XY motion. The ability to alter the water jet's trajectory by tens of microns at high frequencies, which is beyond the capability of conventional CNC machines, allows a wide range of different micropatterns to be generated, profoundly increasing the flexibility and efficiency of the process as compared to conventional approaches. As a demonstration, surface textures for isotropic and anisotropic behaviors are generated on stainless steel surfaces. The influence of feature spacing, motion speed (frequency), and texturing patterns on surface wettability is studied.

## 1 Introduction

Water jet-guided laser processing is a novel hybrid manufacturing technique that was proposed to overcome the disadvantages of traditional laser and water jet technologies [1]. The underlying principle is to transmit high-power laser energy through a water jet by total internal reflection [2]. The water jet serves as a multimode waveguide as long as the jet remains stable. This innovative manufacturing method has attracted a great amount of attention in the past couple of decades. Major applications have been developed for water jet-guided laser processing, including microcutting, grooving, slotting, and wafer dicing. Porter et al. [3] and Hock et al. [4] successfully demonstrated that water jet-guided laser processing can be employed to perform different kinds of micromachining processes on metals. Rashed et al. [5] performed a comparative study between micro-electrical discharge machining (micro-EDM) and water jet-guided laser processing in microdrilling in terms of surface quality. It was discovered that water jet-guided laser processing can generate smoother surfaces than micro-EDM. More recently, Sun et al. [6,7] reported on the utilization of water jet-guided laser processing to cut carbon-fiber-reinforced polymers. From a broader perspective, water jet-guided laser processing has also been implemented in the light-emitting diode (LED) screen [8] and jewelry industries [9].

Even though most past research efforts have focused on the development of the water jet-guided laser process, there are no studies related to attempts to manipulate the trajectory of the high-pressure water jet to improve and control the impingement accuracy and flexibility of the process. Dielectrophoresis (DEP), which is a phenomenon where a translational force is exerted on a dielectric object due to polarization when it is subjected to a nonuniform electric field [10], has been proposed in the literature to alter the moving path of liquid jets or streams of droplets. The study of bending a liquid jet by DEP was first introduced and demonstrated by Taylor [11]. The rhythmic motion of a liquid jet in the electric field, as the result of dielectrophoresis and electrophoresis, was studied by Hokmabad et al. [12]. Chiarot and Jones [13] and Doak et al. [14] experimentally observed the dielectrophoretic motion of continuous ink jets in the microdomain and revealed the basic relationships between some experimental parameters and the ink jet's deflection at low water pressures. With the objective to predict the liquid jet's trajectory in different electric field configurations, a preliminary numerical model was developed in comsol by Mohanty et al. [15]. All these early studies were performed on low-pressure and low-speed liquid jets with no machining capabilities. In the author's early work, an attempt was made to fill this gap by studying the behavior of high-pressure microwater jets under both static and dynamic electric fields [16].

Fabrication of functional surfaces by micro- and nano-manufacturing techniques has developed rapidly due to their applications in areas such as reduced friction [1719], antifouling [20,21], anti-icing [22], superhydrophobic [23,24], and other functional surfaces. Various techniques to texture surfaces with modified wettability have been widely researched. Laser texturing [24], chemical etching [25,26], oxidation [27], and vibration cutting [28] are among them. Water jet-guided laser micromachining was also used to achieve superhydrophobic surface properties [29].

Conventionally, simple grid patterns are commonly adopted to achieve isotropic wetting behavior [30]. Guo et al. studied the wetting behavior of surfaces textured with channels generated by vibration cutting instead by grid patterns [28]. It was shown that channel patterns exhibit anisotropic wetting behavior, i.e., the contact angles are significantly different in directions along and perpendicular to the channels. The unanswered question is whether channel patterns that are simpler and faster to manufacture can be used to control wetting behavior. Specifically, whether the proposed curved water jet-guided process has the capability to add intricate features to channel patterns so that both isotropic and anisotropic behavior can be achieved.

The overarching goal of this paper will be to apply the concept of manipulating the water jet's trajectory in water jet-guided laser processing to form a new type of manufacturing processes called curved water jet-guided laser micromachining. The specific major objectives of the experimental study, in turn, will be the: (1) generation of microstructures by curved water jet-guided laser micromachining, (2) achievement of both isotropic and anisotropic wetting on surfaces textured with different microstructure features, and (3) reduction of processing time. Compared to conventional water jet-guided laser micromachining without the assistance of an electric field, as reported in our previous study [29], a tertiary motion component at hundreds of hertz in a range of tens of microns is superimposed on the water jet allowing the fast and accurate micromanipulation of its impingement location on the workpiece. This added tertiary motion brings more flexibility and accuracy to the process. The capability of this newly proposed method will be explored with specific focus on jet behavior control, surface pattern generation, and control of surface wetting behavior in this paper.

The rest of the paper is organized as follows: Curved water jet-guided laser micromachining and the corresponding process outcome characterizations are introduced in Sec. 2. Section 3 presents experimental results, which focus on the generation of microchannels with different geometric features. Their surface wetting behavior is then characterized on stainless steel surfaces. Conclusions are given in Sec. 4.

## 2 Process Description

In this section, the proposed curved water jet-guided laser micromachining process will be illustrated in detail, including the basics of dielectrophoresis and the corresponding experimental setup. The surface characterization techniques used are also briefly described to understand the influence of different processing conditions.

### 2.1 Dielectrophoresis.

Dielectrophoresis is a phenomenon by which a translational force, namely, the DEP force, is exerted on neutral objects in an electric field due to polarization. For ideal dielectrics, the DEP force on a neutral body in a static field can be expressed as [10,31]
$FDEP=αvE⋅∇E=12αv∇|E|2$
(1)

where v is the volume of the neutral body, E is the external electric field, and α is the dipole moment per unit volume in a unit field. In the experimental configuration to be used in this work, α and v are considered as constants. The magnitude of the DEP force depends on two major elements, i.e., the electric field strength and gradient and the volume of the neutral body and its dipole moment based on Eq. (1). The electric field strength and gradient are mainly determined by the location of the body in the electric field and the voltage applied to the electrode to generate the electric field.

### 2.2 Experimental Apparatus.

Figure 1 presents the schematics of the curved water jet-guided laser micromachining system. The developed experimental setup consists of three major components. First of all, the high-pressure water supply is provided by an air-driven pump customized by MAXPRO (Fairview, PA). Second, the laser selected for the system is a 1064 nm nanosecond pulsed fiber laser with a 70 W maximum power from SPI lasers (model redENERGY G4 70 W EP-Z, Southampton, UK). Right below the water jet nozzle exit (as shown in Fig. 1), an electrode is mounted. The location of the electrode with respect to the water jet in the traverse direction (X direction) is controlled by a manual stage. The laser source with the entire optical assembly is mounted on a XYZ manual stage. The coupling of the water jet and laser is achieved by focusing the beam directly into the jet. The focal position is controlled by the XYZ manual stage and monitored by a charge-coupled device camera to ensure that the laser beam is focused at the center of the entrance of the water jet orifice. The coupled laser power is measured by a laser power meter from Gentec-EO (model UP19K-15S-H5, Québec, Canada). The workpiece is placed 15 mm below the exit of the water jet nozzle (marked as D in Fig. 1). The main motion of the workpiece is provided by an air-bearing stage from PI (model A-311, Auburn, MA). The last component is the amplifier that provides high-voltage control signals to the electrode. Low voltage signals of the desired waveforms, generated by a data acquisition card from National Instruments (model USB6221, Austin, TX), are amplified by a factor of 1000 through a Trek amplifier (model 10/10B-HS, Lockport, NY) to create the final high voltage signals. Both laser and high-voltage signals are triggered by digital output signals from the motion stage controller. The photo of the actual physical system is given in Fig. 2.

Fig. 1
Fig. 1
Close modal
Fig. 2
Fig. 2
Close modal

### 2.3 Experimental Procedure.

In all the experiments, a high-pressure microwater jet was formed by pumping water through the nozzle with an orifice of 75 μm. The water pressure, P, was regulated around 8 MPa. The laser was configured to have a repetition rate of 70 kHz, and the beam was directly focused at the center of the orifice to allow the laser energy to reach the workpiece surface through total internal reflection at minimal losses. The final coupled laser energy into the water jet was maintained at 5.4 W. The electrode mounted below the nozzle exit has a diameter of 1 mm. Based on our previous study [29], the distance between the electrode and the workpiece was kept at 12 mm to achieve stable machining results. The distance between the water jet and electrode was maintained at 250 μm. The applied voltage signal on the electrode deflected the water jet with the coupled laser energy. The main machining power was provided by the laser while the water jet is utilized as a waveguide. All the experiments were performed on 1 mm thick 304 stainless steel (ASTM A240) with an average roughness of 207.3 nm (Ra).

To characterize the machined surfaces after processing by the curved water jet-guided laser micromachining process, an Alicona Infinite Focus microscope was employed to obtain the three-dimensional (3D) profile of the surfaces. A scanning electron microscope (SEM) from FEI (model FEI Quanta 650 ESEM, Hillsboro, OR) was utilized to capture the 2D surface morphology. To understand the wetting conditions of the textured surfaces, the contact angle of a ∼3 μL water droplet was measured by a KRÜSS contact angle measurement system (model FM40Mk2, Hamburg, Germany) on different textured surfaces.

## 3 Results and Discussion

To verify the concept shown in Fig. 1, an experimental study was conducted and is discussed in this section. All the experiments were performed on 304 stainless steel surfaces. The research starts with the strategy of producing different surface patterns by various process parameters in Sec. 3.1. After fully understanding the way of controlling the surface patterns, several specific surface patterns are generated on larger areas to form a textured surface in Sec. 3.2. Surface wettability is then studied in terms of its contact angles.

### 3.1 Surface Pattern Generation.

The idea behind curved water jet-guided laser texturing process is to deflect the water jet while machining by dielectrophoresis as introduced Sec. 2.1. During machining, the XY motion stage (PI air-bearing stage in this case) is utilized to provide the general motion (in tens or hundreds of microns or millimeter range), which can be characterized with X and Y positions as functions of time, t, as presented in Fig. 3. On the other hand, the water jet deflection by dielectrophoresis is typically less than 50 μm but can take place at hundreds of Hertz. In the author's previous work, it was revealed that the magnitude of the water jet deflection is mainly dependent on water jet pressure, distance between the electrode and the water jet, and the voltage applied to the electrode [16]. When a changing voltage signal is applied to the electrode, a dynamic electric field is generated. Since only one electrode is used in this study, the water jet is deflected only in the X direction. The water jet position in the changing electric field can also be considered as a function of time, i.e., XDEP(t). The combined motion of the XY motion stage and of the DEP deflection can then be described as a superimposed motion between the two, i.e., as (Xst(t) + XDEP(t), Yst(t)).

Fig. 3
Fig. 3
Close modal
In this study, the XY motion is assumed to be a simple motion with uniform velocity, Vst, in the Y direction. Therefore, the XY motion can be represented as
$Xst(t)=0Yst(t)=Vstt$
(2)
For the case with only one electrode, the water jet deflection, DWJ, can be expressed by the empirical function of three major parameters, namely, the water jet pressure, P, applied voltage, U, and the distance between the water jet and electrode, d, as [16]
$DWJ=CU2Pd$
(3)
where C is a constant that depends on the actual experimental conditions and configuration and is determined experimentally. If a changing voltage signal is given, the applied voltage, U, is a function of time. As a result, the water jet deflection, DWJ, also changes with time. If the delay of the water jet deflection in dynamic electric fields is not considered at frequencies below 100 Hz, the DEP deflection induced on the water jet in the Y direction can be expressed based on Eq. (3) as
$XDEP(t)=CU(t)2Pd$
(4)
In conclusion, by combining Eqs. (2) and (4), the coordinates of the water jet on the workpiece can be expressed as
${x=Xst(t)+XDEP(t)=CU(t)2Pdy=Yst(t)=Vstt$
(5)
For example, if a sinusoidal voltage signal is applied to the electrode, U(t) can be expressed as U(t) = Vppsin(2πft)). Since both x and y coordinates are functions of time, by eliminating time, t, from Eq. (5), the final path (relationship between the x and y coordinates) on the workpiece can be obtained as
$x=CU(t)2Pd=CVpp sin (2πfVsty)2Pd$
(6)

where Vpp is the peak-to-peak voltage of the sinusoidal signal and f is its frequency. In other cases where different waveforms are applied, the motion path on the workpiece surface can be easily obtained by changing the expression for U(t). The typical frequency, f, and travel range of this motion can reach up to 500 Hz and 50 μm without having a significant motion delay and instability of the water jet [16].

For demonstration purposes in this study, all other process parameters are fixed except for the voltage. Consequently, the only parameter that controls the deflection magnitude will be the voltage signal U(t).

Figure 4 presents an experimental result of a sinusoidal signal with a Vpp of 4000 V and a frequency f of 50 Hz. The motion stage velocity, Vst, is set to be 5 mm/s. The measured 3D profile and one cross section profile at the location marked by the solid line are shown in Fig. 4. Instead of a straight channel, a curved channel is successfully generated due to the applied voltage signal. The average depth of the channel is 40 μm and its width is 45 μm.

Fig. 4
Fig. 4
Close modal

To further demonstrate the flexibility of the process, four classic waveforms are implemented. Figure 5 compares the channels machined by a sinusoidal, sawtooth, triangular and a square waveform with a 50% duty cycle. All the signals have the same peak-to-peak voltage, Vpp, and frequency, f, as the one used in Fig. 4. The motion stage velocity is again kept at 5 mm/s. All four channels basically follow the voltage signal waveforms that agree with the prediction results on water jet behavior in dynamic electric fields in Ref. [16]. However, the final channel quality varies depending on the applied waveforms. Sinusoidal and sawtooth signals generate better channels with sharper edges than the triangular and square signals. Square signals have suddenly rising edges which can deteriorate jet quality and cause delays in the jet's deflection as shown in our previous study [16] that will lead to lower quality channel edges as shown in Fig. 5.

Fig. 5
Fig. 5
Close modal

Changing waveforms is not the only way to modify the final shape of the feature on the workpiece. Form Eq. (5), the frequency, f, and motion stage velocity, Vst, are other ways to modify the feature spacing (distance between peaks on the workpiece). One of the major advantages of using DEP deflections rather than the motion stage to generate microlevel features is the speed. The frequency of the voltage can be easily regulated to hundreds of Hertz, which cannot be achieved by conventional stages. Figure 6 shows channels machined by different frequencies and motion stage velocities. The combination of frequency and motion stage velocity directly determines the spacing of the features. In the actual experiments, frequency and motion stage velocity affect different aspects of the channels generated. Signals with higher frequency tend to deteriorate the integrity of the water jet. When the water jet is deflected at a higher frequency, disturbances can be generated on the jet's surface, which cause the coupling efficiency to decrease. Consequently, the channel quality in terms of edges decreases as shown in Figs. 6(a) and 6(b). On the other hand, motion stage velocity influences the depth of the channel. Higher motion stage velocities yield shallower features (Fig. 6(c)) than the ones machined at lower motion stage velocities (Fig. 6(b)). To obtain high quality curved channels with deep profile, low signal frequency and motion stage velocity are preferred.

Fig. 6
Fig. 6
Close modal

### 3.2 Modification of Surface Wettability Through Texturing.

As pointed out in Sec. 1, simple grid patterns (Fig. 7(a)) exhibit isotropic wetting behavior [30], while, on the contrary, channel patterns exhibit anisotropic behavior (Fig. 7(b)) [28]. The aim of the current section will be to explore the possibility of using channel patterns to impart isotropic wetting behavior. Compared to the grid pattern, channel patterns can save half of the processing time over the same texturing area with the same spacing. Curved water jet-guided laser micromachining developed in Sec. 3.1 has the capability to add tiny features to the channels to create different types of texturing patterns. Therefore, in this section, an experimental study will be conducted to understand the influence of curved water jet-guided laser texturing on surface wettability by using the toolpath shown in Fig. 7(c). The only parameter that dominates the pattern is its spacing, Δl.

Fig. 7
Fig. 7
Close modal

In all experiments in this study, the motion stage speed, Vst, is fixed at 5 mm/s. The spacing, Δl, for the toolpath is first set to 50 μm. The overall size of the textured area is 5 by 5 mm. The processing time for the grid pattern (Fig. 7(a)) is close to 5 min. However, to texture the same area, only 2.5 min are needed for the channel pattern (Fig. 7(b)). As an example, a stainless surface is textured by curved water jet-guided laser micromachining with an applied sinusoidal voltage signal with a peak-to-peak voltage of Vpp = 4000 V and a frequency f =50 Hz. The voltage signal persists during the entire texturing process. The toolpath is a channel pattern (Fig. 7(b)) in the Y direction only. Figure 8 illustrates the SEM image, actual photo of the textured surface, and the measured 3D profile. It can be clearly observed that the curvy channel pattern shown in Fig. 5 has been successfully applied over a larger area. It can be noticed in Fig. 8 that the textured patterns show variations in terms of both depth and geometric fidelity of the wavy patterns generated. This is mainly due to the variations in water jet pressure with the air-driven pump used in the experiments that is particularly pronounced at low pressures, i.e., at 8 MPa in this case. Fluctuations of water jet pressure cause variations in both coupled laser energy and DEP deflection. The measured surface roughness (Ra) is 6.0 μm, which is slightly smaller than the surface roughness (i.e., 6.4 μm) of the textured grid pattern (at the same Δl =50 μm) by the water jet-guided laser process without DEP deflection in our previous study [29].

Fig. 8
Fig. 8
Close modal

In the author's earlier work, it was revealed that the wettability of water jet-guided laser textured surfaces changes when the textured surface is exposed to ambient conditions [29]. The surface wetting will change from the Wenzel state [32] to the Cassie Baxter [33] state due to surface chemical changes [29]. To ensure that surface wetting conditions are fully stabilized, all the contact angle measurements in this paper were conducted after 30 days. To demonstrate that surface wettability can be altered by additionally added curvy features on the channels, a comparison study was performed. In this study, two textures were generated. The reference texture is a set of parallel channels (like the ones shown in Fig. 7(b)) made by water jet-guided laser texturing without DEP deflection. The second texture is the same pattern but with DEP deflection added. As shown in Fig. 7, pure channel features will yield anisotropic wetting behavior. In the present case, the optical image of the droplet on the reference textured surface indeed indicates that anisotropic wetting behavior is realized, as shown in Fig. 9, on the textured surface with straight channels. The droplet is obviously elongated (anisotropic wetting) instead of being circular (isotropic wetting). For the surface textured with curvy channels, the wetting behavior is closer to isotopic wetting. To further quantify the results, contact angles in two different directions, parallel to the channel direction, $θ∥$, and perpendicular to the channel direction, $θ⊥$, were measured. All the contact angles measured are averaged values from four individual measurements. For texturing without DEP deflection, a huge difference, Δθ = 60.7 deg can be found between the two contact angles. However, for the surface textured with DEP deflection, the difference between the contact angles in two direction, Δθ, is only 8.8 deg. In conclusion, the added curvy feature can potentially change the wetting behavior from anisotropic to isotropic without any additional processing time. The curvy channel pattern can be used as an alternative to the conventional grid pattern to achieve isotropic wetting in only half of the processing time as compared to customary water jet-guided laser texturing discussed in the author's previous work [29] and other laser texturing works [34,35]. Furthermore, fine-tuning of the applied electric signal such as synchronization of the phase between channels and the use of complex waveforms may lead to droplets with controlled geometry or higher contact angles.

Fig. 9
Fig. 9
Close modal

### 3.3 Influence of Process Parameters on Surface Wettability.

For curved water jet-guided laser texturing, there are several important parameters that can influence the surface pattern so that different wetting behaviors can be achieved. Three process parameters will be studied in this section.

The first parameter is the waveform of the applied voltage signals. The same four waveforms as shown in Fig. 5 will be employed. All other parameters remain fixed. The frequency and the peak-to-peak voltage of the voltage signal are set to 150 Hz and 4000 V, respectively. Table 1 lists all the corresponding measured contact angles in two directions. As it can be seen, all four waveforms result in a Δθ of around 10 deg so that the wetting behavior can be considered nearly isotropic. Sinusoidal and triangular signals yield higher contact angles, ∼132 deg, than the square and sawtooth signals. Overall, the influence of the waveforms on wetting behavior is not significant. The largest difference is less than 10 deg.

Table 1

Averaged contact angles in two directions for four different waveforms after 30 days (VPP = 4000 V, f =150 Hz, and Δl =50 mm)

SinusoidSquareTriangleSawtooth
$θ∥$ (deg)132.2123.6132.1128.9
$θ⊥$ (deg)124.1113.5120.4116.3
Δθ (deg)8.110.111.712.6
SinusoidSquareTriangleSawtooth
$θ∥$ (deg)132.2123.6132.1128.9
$θ⊥$ (deg)124.1113.5120.4116.3
Δθ (deg)8.110.111.712.6

The second parameter is the frequency of the voltage signals. Sinusoidal signals with three frequencies, 50 Hz, 100 Hz, and 150 Hz, were implemented. The peak-to-peak voltage is again kept at 4000 V. With a motion stage speed, Vst, of 5 mm/s, the corresponding peak-to-peak distances (pitch) for the resulting curvy channels are 100 μm, 50 μm, 33.3 μm, respectively. Figure 10(a) plots the contact angles in two different directions with respect to different frequencies. The low frequency, 50 Hz, yields almost perfect isotropic wetting (Δθ close to 0 deg). However, the contact angles in both directions are smaller than for the surfaces textured with 100 and 150 Hz signals. For surfaces with higher contact angles, Δθ increases to 10 deg, which still can be considered as nearly isotropic. The highest contact angle occurs on the surfaces textured by the 150 Hz sinusoidal signal.

Fig. 10
Fig. 10
Close modal

The last parameter studied in this paper is the spacing, Δl, between the channels (as shown in Fig. 7(c)). Spacing varies from 25 to 100 μm. The voltage signal used for all different spacings is the sinusoidal signal with Upp = 4000 V and f =150 Hz. Contact angles in both directions are shown in Fig. 10(b). It can be observed that the difference between the contact angles in the two directions, Δθ, increases as the spacing increases. Large spacing (> 75 μm) tends to generate anisotropic wetting. The trend for the magnitude of the contact angle is different. The highest contact angle is obtained on the surfaces textured with a 50 μm spacing. Compared to surfaces textured with a spacing larger than 50 μm, contact angles around 30 deg are observed in both directions on surfaces textured with a 25 μm spacing. The low contact angles indicate that surfaces textured with a 25 μm spacing are in the Wenzel rather than the Cassie–Baxter state like the surfaces textured with a spacing larger than 50 μm. This response is the result of both surface chemistry and morphology [29].

## 4 Conclusion

This paper provides an experimental study of introducing a new manufacturing process, curved water jet-guided laser micromachining, for surface feature generation. Fast microlevel motions were induced on water jets by dielectrophoresis for texturing for the very first time. The added controllable motion of the water jet greatly improves the flexibility of the process in terms of its ability to control texture geometry and increase processing speed. Stainless steel surfaces were textured with curved water jet-guided laser micromachining to achieve both isotropic and anisotropic wetting behaviors. The key findings are:

• Curvy channels (∼50 μm deflection) can be successfully generated by curved water jet-guided laser micromachining instead of straight channels for the very first time.

• Surface patterns can be easily modified by controlling the magnitude of the DEP-induced jet deflection using different voltage signals, which makes the process very flexible.

• Textured surfaces with large spacing (≥75 μm) exhibit anisotropic wetting behavior.

• Isotropic wetting can be achieved with channel patterns instead of grid patterns with spacings ≤50 μm. The corresponding processing time is cut into half.

## Acknowledgment

The authors would like to thank Professor Q. Jane Wang's tribology lab for providing the contact angle measurement system. This work made use of the EPIC facility of Northwestern University's NUANCE Center, which has received support from the Soft and Hybrid Nanotechnology Experimental (SHyNE) Resource (No. NSF ECCS-1542205); the MRSEC Program (No. NSF DMR-1720139) at the Materials Research Center; the International Institute for Nanotechnology (IIN); the Keck Foundation; and the State of Illinois, through the IIN.

## Funding Data

• National Science Foundation (Award No. CMMI #1234491).

## Nomenclature

d =

distance between electrode and water jet

D =

stand-off distance

DWJ =

water jet deflection

E =

electric field

f =

frequency of electric signal

P =

water jet pressure

U =

voltage signal

v =

volume of neutral body

Vpp =

peak-to-peak voltage of electric signal

Vst =

motion stage speed

α =

dipole moment per unit volume in a unit field

Δl =

Δθ =

difference between $θ∥$ and $θ⊥$

$θ∥$ =

contact angles parallel to channel

$θ⊥$ =

contact angles perpendicular to channel

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