Effect of the inclined angle of micromilling tool on the fabrication of the microfluidic channel

Micromilling is a common processing method for fabricating microfluidic chips or other microproducts with high processing accuracy and low cost, which is suitable for mass production. The main concern of micromilling is the surface roughness of the work material. However, only a small range of surface roughness can be obtained in the general study of micromilling by changing the processing parameters, which is very difficult to obtain a specific roughness. In the process of micromilling with end mills, due to the structural characteristics of the tool tip, the inclination angle of the tool has a significant impact on the bottom surface of the machined channels. In this work, the influence of the tool inclination on the surface roughness was studied through the inclined micromilling tests of the poly(methyl methacrylate) (PMMA) surface, and it was proposed to realize the control of the machined surface roughness by inclined micromilling. In addition, a theoretical model considering tool inclination was established to calculate the surface roughness of the machined bottom obtained by inclined micromilling. The experimental results were consistent with the theoretical results under the low speeds. Afterwards, the polydimethylsiloxane (PDMS) was used to replicate the microchannel machined on the PMMA surface, and the microfluidic chips were prepared to control the fluid flow in the channel by adjusting the roughness of the bottom of the channel. Results indicated that the smoother channel flowed first under the same flow pressure. The study offers a new idea of surface roughness control, which can be applied to flow control in microfluidic chips.


Introduction
With the rapid development of nanotechnology, micro/ nanostructures have been widely applied in various fields [1][2][3][4][5][6][7][8]. Particularly, microfluidics is the science and technology to process or manipulate microfluidic fluids, and a variety of microfluidic devices have been designed and applied in biology, chemistry, medicine and so on [9][10][11]. Microchannels are important parts of microfluidic devices. In general, because of the low price, commercial microfluidic devices used for bioanalysis are produced with biocompatible polymers employing molding processes such as injection molding [12,13] and hot embossing [14]. However, the manufacturing cost of molds used in these processes is high and the process is complex. In most cases, especially in the prototype design stage, direct processing of polymer substrates may be more economical and suitable for preparation of microchannels. Laser ablation and micromilling are typical direct processing processes [14][15][16][17][18], which can be used for rapid prototyping of microfluidic chips. Both methods can be used to process a variety of polymer materials, such as polymethylmethacrylate (PMMA) [19], polycarbonate (PC) [20], polyethylene terephthalate (PET) [21], and cyclic olefin copolymer (COC) [22], which are generally used in microfluidic chips. However, the debris is inevitably redeposited on the sidewall and bottom of the work material during the laser ablation process. In addition, it is difficult to achieve high-dimensional accuracy due to the shape of the laser Gaussian beam [23]. On the contrary, micromilling can be used to manufacture three-dimensional structures with high-dimensional precision. Due to the progress of tool manufacturing technology, micromilling can be used to accurately manufacture microchannels and microstructure [24,25]. In addition, micromilling can achieve higher material removal efficiency compared with the traditional nano-or microscratch [26]. Therefore, considerable scholars use micromilling technique to fabricate microchannels on polymer materials for the preparation of microfluidic chips.
In the micromilling process, many machining parameters, such as tool geometry parameters, spindle speed, cutting depth, and feed per tooth, have been proved to be closely related to the machining performance [27]. The surface roughness can be influenced by these machining parameters. However, some scholars have found that the tool inclination also has an important influence on the quality of the machined surface [28]. Choosing the appropriate tool inclination can not only improve the machining quality and reduce the tool wear but also control the roughness of the machined surface more conveniently by adjusting the tool inclination in the micromilling process. More importantly, inclined micromilling can be an efficient and costeffective method to fabricate microdimples [28]. In addition, it has been found that the microdimples on the bottom of the microchannel will affect the wettability of liquid in the channel [29], thus changing the flow resistance, and then controlling the circulation of liquid. The flow condition of the reagent inside the microchannels has a distinct influence on the reaction speed and sequence in the chip, and the working efficiency and function of the microfluidic chip can be effectively improved by regulating the flow state of the reagent. Using the inclined micromilling process, the roughness of the processed channel can be simply controlled, and then, the reagent flow sequence in the microchannel can be regulated.
In this paper, the influence of inclined micromilling on the roughness of groove bottom is studied by the theoretical model and experimental tests. The effect of surface roughness on the wettability of the reagent is also studied. A microfluidic chip with microchannels of different roughness values is prepared to control the flow sequence.

Modeling the microstructures form on the bottom of the microchannel by inclined micromilling process
The simulation of structures formed on the groove bottom requires the establishment of the coordinate system of micromilling tool motion, as shown in Fig. 1a. The coordinate system O′-X 3 Y 3 Z 3 , denoted as {3}, is fixed on the workpiece and is known as the space coordinate system of the workpiece. which the Z 0 -axis coincides with the tool axis, and β is the inclination angle of the micromilling tool. The coordinate system O-X 2 Y 2 Z 2 , denoted as {2}, is produced by the rotation of the tool around the tool axis and is called the tool rotation coordinate system, in which the Z 2 -axis coincides with the Z 2 -axis. The structures on the bottom of the microchannel are mainly generated by the cutting motion of the micromilling tool. Figure 1c shows the cutting trajectory of the tool nose. The section of the tool nose can be regarded as a combination of two straight lines and an arc. Therefore, the tool tip equation can be expressed as follows: where α is the rake angle, β is the slant angle of the cutter, and r is the radius of the tool nose. The transformation from coordinate system {0} to coordinate system {1} is The tool rotates about the spindle during milling, and the transformation from coordinate system {2} to coordinate system {0} is Where θ is the rotation angle of the tool. The coordinates need to be transformed back to coordinate system {1}. The transformation from coordinate system {1} to coordinate system {2} is The cutter feeds along the X 1 -axis and the transformation from coordinate system {3} to coordinate system {1} is where (x 0 , y 0 , z 0 ) is the initial coordinate of coordinate system {1} with respect to frame coordinate system {3}.
Through the transformation, the coordinate of the point on the tool tip in the workpiece coordinate system can be obtained as For modeling of surface topography, the workpiece space is divided into XY grid nodes by meshing. The height coordinates of the workpiece at the discrete position swept by the tool tip are obtained and stored as the Z coordinates of the grid node through Eq. (6). Then, feed and rotation motions of the micromilling tool can be obtained by circulation, so as to construct the surface topography of the microchannel. The tool used in the model and subsequent experimental tests is a double edged flat-end micromilling tool, as shown in Fig. 2. The rake angle α is 3°, and the radius of the tool nose is about 6.026 μm measured by scanning electron microscope (SEM). Different simulated surface topographies can be obtained by changing the tool inclination angle and feed parameters, as shown in Fig. 3.
The model is obtained when the inclination angle of the tool is 5° and the feed rate of each tooth is 5 μm/tooth. From Fig. 3, it can be found that the structure on the bottom of the microchannel obtained by the inclined micromilling process is a periodic corrugated surface with a certain Radian. The corresponding contours can be extracted from the 3D topography, as shown in Fig. 3c. And the corresponding surface roughness can be calculated based on the extracted contour data. This model can be used to predict the surface morphology and surface roughness obtained by inclined micromilling for the follow-up experimental tests.

Experimental setup
As shown in Fig. 4a, a homebuilt four-axis vertical micromilling machine tool was used for performing all the micromilling experimental tests. A high-speed electric spindle (NAKANISHI, NR-3060S, Japan) is employed for this micromilling machine tool and the maximum rotation speed is 60,000 rpm. A Micro-Nano Optics high-precision rotating platform with 0.0005° resolution is used for Axis b rotating unit. High precision linear motion table is used in micromilling feed motion (Micro-Nano Optics, WN200TA150H, . The resolution is 1 μm, and the straightness is 3 μm. In addition, the micromilling machine is installed on the vibration isolation platform made of marble material to reduce the adverse effects of vibration. The polymethyl methacrylate (PMMA) has good electrochemical properties, biocompatibility, high light transmittance, easy processing, and low price and is suitable for mass production. Thus, it is often used as the material or mold for microfluidic chips. In this study, the PMMA is selected as the workpiece. The size of the PMMA is 50 mm × 50 mm × 3 mm, and the surface roughness (Ra) is less than 1 nm. The micromilling tool used for the experimental tests is a cemented carbide double-edged end milling tool (NS tools, AL2D, Japan) with a diameter of 1000 μm, as shown in Fig. 2. After the micromilling process, a white light interferometer (Zygo, NewView 9000, America) was used to observe the topography of the microchannel bottom and the surface roughness of the microchannel bottom can be obtained.

Effects of micromilling parameters on the surface roughness of the microchannels
In order to study the effects of the micromilling parameters on the machining outcomes, the orthogonal tests were carried out by different combinations of the spindle speed, feed rate and cutting depth, while the tool inclination angle was set as 5°. Detailed cutting parameters were given in Table 1.
The typical surface morphology of the microchannel bottom was measured by the white light interferometer, as shown in Fig. 4. The surface roughness was measured at random positions for each cutting condition, and the measurement results were given in Table 2. The morphology of the microchannel bottom shown in Fig. 4c was a ripple surface with a certain period, which was mainly consistent with predicted surface shown in Fig. 3. However, there was a difference between the machined and predicted surfaces due to the influence of the runout of the micromilling tool. The experimental results were analyzed   using the simple and practical analysis of extreme variance (ANOVA) to determine the order of influence factors and optimal level of each factor in orthogonal tests, and the results of ANOVA were shown in Table 3.
According to the results of the extreme variance analysis, it can be found that the spindle speed has the greatest influence on the surface roughness among the cutting parameters, the feed is the second, and the cutting depth has the least influence. The average surface roughness value decreases with the increase of spindle speed, increases with the increase of feed, and decreases with the increase of cutting depth. According to the above experimental results, the spindle speed is the parameter that has the greatest influence on the surface roughness. In order to study the influence of spindle speed and tool inclination on the surface roughness of the bottom of the groove and then to control the desired surface roughness by adjusting the machining parameters, four typical tool inclination angles and eight spindle speeds are selected in the subsequent micromilling experimental tests, the feed rate and depth of cut are kept constant. The detailed cutting parameters are shown in Table 4.
From the above experimental tests, the surface roughness of the bottom of the microchannel is obtained when the spindle speed changes from 4000 r/min to 11,000 r/min under different inclination angles. The prediction value of the surface roughness can be obtained by extracting the height value of the surface structure through the model established in the Section 2. The surface roughness prediction curve shown in Fig. 5a is obtained by substituting the machining parameters used in the experimental tests shown in Table 4 into the surface prediction model. According to the prediction curve, under the ideal condition, the surface roughness obtained from the model decreases with the increase of the spindle speed, that is, with the increase of the feed per tooth, while the surface roughness increases with the increase of the tilt angle of the spindle, and the change of the surface roughness decreases with the increase of the feed per tooth. The results are obtained from the ideal surface prediction model without considering the influence of spindle runout, machine tool vibration and workpiece material. However, the actual machining situation will be different, and according to the machining conditions, when the spindle speed exceeds 8000 r/min, the spindle vibration intensifies, the influence of vibration begins to increase, and the stability of micromilling becomes worse; thus, the results obtained from the experimental tests at a high speed should have a large difference compared with the theoretical results. As shown in Fig. 5b, the variation of surface roughness with the spindle speed obtained from the experimental tests is given.
From Fig. 5b, it can be found that the overall trend of surface roughness at the bottom of the microchannel with the spindle speed for four different tool inclination angles is decreasing first and then increasing, and the surface roughness basically reaches the minimum value at 7000-9000 r/ min. Comparing with Fig. 5a, it can be seen that the change trend before 8000 r/min is basically in line with the results obtained by the prediction model; however, the surface roughness gradually increases after the speed is greater than 8000 r/min, which is consistent with the previous discussion. The possible reason is with the increase of the spindle speed,   5000  6000  7000  8000  9000  10000  11000  10  4000  5000  6000  7000  8000  9000  10000  11000  15  4000  5000  6000  7000  8000  9000  10000  11000  20  4000  5000  6000  7000  8000  9000  10000  11000 the spindle runout and the overall vibration of the machine intensifies, and the cutting becomes more and more unstable. Moreover, there is no cutting fluid and coolant during the micromilling process, as the spindle speed increases, the friction and heat between the tool and the workpiece increases, which also leads to a certain impact on the morphology of the machined surface. At the same time, when the spindle speed is too high, the feed per tooth is too small, which may lead to the cutting layer thickness less than the minimum cutting thickness of the sample material, and the PMMA is extruded and scraped but not removed with the movement of the cutting tool and the material accumulation. When the material accumulation exceeds the minimum cutting thickness, the workpiece material could be removed by the cutting tool. In addition, this instable material removal state will also lead to poor quality of the bottom of the microchannel and increase of surface roughness. The variation of the surface roughness with the tool inclination is consistent with the results obtained by the prediction model that the surface roughness increases with the increase of the inclination angle. The difference between the prediction values and that experimental results for the four different inclination angles at low speed are relatively small, and the deviation of the prediction model at 6000 r/ min is from 1 to 12.5%, which shows that the effect of spindle runout and vibration at lower speed is not significant. However, as the spindle speed increases, especially when the speed exceeds 8000 r/min, the effect of tool runout and vibration increases sharply, due to the insufficient rigidity of the machine tool system. Furthermore, as the spindle speed continues to increase, due to lack of cutting fluid lubrication and coolant, and the melting point of PMMA is relatively low, only 130-140 ℃, the cutting heat will also become one of the important factors affecting the quality of the machined surface, the tool nose cutting the workpiece surface at the extreme speed, and the rapid rise in local temperature may cause the bottom structure of the groove to partially melt, which will also affect the value of surface roughness. When the feed per tooth is too small, the plowing material removal state is also a possible factor of the quality of the machined surface. Based on the experimental results, it is found that the desired surface of the microchannel bottom with different roughness values of the bottom surface can be obtained within a certain range of the cutting parameters.

Modulation of roughness and wettability of the machined surface
When preparing microfluidic channels, the surface characteristics of microfluidic channels, such as wettability and chemical properties [30], should be taken into account. Wettability is usually evaluated by the contact angle of droplets on its surface [31]. When the contact angle is less than 90°, it is hydrophilic and more than 90° is hydrophobic. The contact angle on the same material will be affected by the surface characteristics [32][33][34]. And the surface wettability can be influenced by surface roughness, which will affect the flow of liquid in the microfluidic channel [35,36]. Therefore, the liquid flow state in the microfluidic channel can be controlled by the surface roughness. Based the prediction model and experimental tests, surfaces with different roughness values are processed and the contact angles of water droplets are measured using a contact angle measuring instrument (KRUSS, DSA100S, Germany). The machining parameters are shown in Table 5. The experimental tests measured the contact angle change of another material commonly used for microfluidics, polydimethylsiloxane (PDMS), in addition to the original workpiece material, PMMA, which was used as a mold to replicate the machined surface for measurement. Since PDMS microfluidic chips require oxygen plasma treatment to achieve bonding, the treated PDMS was also tested. The measurement results of the contact angle are shown in Fig. 6a.
According to the experimental results, PDMS changed from hydrophobic to hydrophilic after oxygen plasma treatment, and the variation of water contact angle on the surfaces with different roughness values of PDMS before and after the treatment showed an overall increase with the increase of roughness. The effect of the surfaces with different roughness values, including PMMA, PDMS, and PDMS after oxygen plasma treatment, on the water contact angle is the same, and the contact angle mainly increases with the increase of the surface roughness. For the explanation of contact angle on the rough surfaces, Wenzel model and Cassie-Baxter model are the most representative wetting models. According to the Wenzel model, an increase in surface roughness leads to an increase in the contact angle of hydrophobic surfaces and a decrease in the contact angle of hydrophilic surfaces. On the contrary, according to the Cassie-Baxter model, an increase in air pocket caused by the increase in surface roughness below the droplet leads to an increase in contact angle, regardless of whether the surface is hydrophobic or hydrophilic. According to the measured results, the variation of the contact angle is consistent with the prediction of the Cassie-Baxter model, where air pockets may form within the regularly undulating structure of the bottom surface due to the bottom structure formed by the inclined micromilling process. In addition, according to the  equations of the model, the depth and period of the bottom structure increase as the roughness increases, which results in the decrease of the contact area fraction between the liquid and the solid. Therefore, the contact angle increases as the as the roughness increases. With the increase of the contact angle, the flow of the liquid in the microchannel will also be affected. From the general rule of the capillary phenomenon, it can be found that it is more difficult for the liquid to enter the capillary when the contact angle is larger. Thus, it can be presumed that the liquid flow in the microchannel will also be impeded with the increase of contact angle. The above experimental tests indicate that the wettability of these three surfaces can be changed by different roughness values; therefore, the microfluidic chips with different roughness values of the microchannel can be processed to realize the flow control of the microfluidic channel.

Preparation of microfluidic chips
The above method of inclined micromilling to control the roughness at the bottom of the groove can be applied to prepare microfluidic channels to achieve the control of fluid flow in microfluidic channels. Wu et al. reported that the flow friction in silicon microchannels increases with increasing the surface roughness [29]. The lower the value of surface roughness, the lower the flow friction. Based on this, a better control method of the channel bottom roughness by inclined micromilling is proposed, and a larger flow pressure is required to pass through the microchannel with a larger flow friction. Therefore, the flow path can be controlled by changing the surface roughness at the bottom of the microchannel. Three channels with different roughness values of the bottom were processed to achieve selective fluid flow. The bottom surface roughness of the smooth channel was 0.0384 μm, the bottom surface roughness of the rougher channel was 0.156 μm, and the bottom surface roughness of the roughest channel was 0.351 μm, and fluid flow experiments were conducted to control the pressure by changing the flow rate. The experimental results are shown in Fig. 7.
When the liquid speed is 5 μL/min, the liquid circulation can only be found in the middle smooth channel. When the flow rate increases to 20 μL/min, the liquid circulation can also be observed in the upper rougher channel. When the flow rate is more than 50 μL/min, the three channels are circulating. The experimental results show that the order of the circulation of three channels is related to the surface roughness. The smoother the bottom, the smaller the water contact angle, the easier it is for red ink to go through the channel. The rougher the surface, the greater the through-liquid pressure required for circulation. According to the experimental results, microchannels machined by inclined micromilling can be used to prepare the microfluidic chips with controllable circulation order of the microchannels.

Conclusions
In this paper, the effects of tool inclination and cutting amount on the surface roughness of the microchannel bottom machined by inclined micromilling process were investigated. A structural model of the microchannel bottom was established and roughness prediction was performed. The relationship between the surface roughness and droplet contact angle was investigated, and a microfluidic chip with controlled flow was prepared based on the experimental results. The conclusions were drawn as follows: • The structure model of the microchannel bottom for inclined micromilling process can reflect the actual surface shape and predicted roughness within a certain range, which can be used to guide the actual machining with a small error at a low spindle speed. When the milling speed is high, the error between the experimental and predicted results becomes larger and larger due to the influence of the tool runout and machine tool vibration. It can be seen that the prediction accuracy is limited by the accuracy of the machine tool. • Among the machining parameters, the spindle speed has the greatest influence on the surface roughness of the microchannel bottom. The roughness decreases and then increases with the increase of the spindle speed and increases with the increase of the tool inclination angle. The inclination angle of the tool can significantly affect the machined surface roughness. Therefore, according to the theoretical and experimental results, the surface roughness can be easily controlled by controlling the inclination angle of the tool to obtain a specific surface roughness. • According to the study of droplet contact angle on the surface with different roughness values and liquid flow experiments of microfluidic chips, different roughness values of the bottom surface affect the wettability of liquid droplets, which in turn affects the liquid flow in the microchannel. In the smooth microchannel, the liquid will flow first, and the rougher microchannel will flow by increasing the pump pressure. Therefore, the flow can be controlled directly by machining the microfluidic channel with different roughness values.

Declarations
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Consent to publish
We would like to submit the manuscript entitled "Effect of the inclined angle of micromilling tool on the fabrication of the microfluidic channel," for your consideration for publication in International Journal of Advanced Manufacturing Technology. No conflict of interest exits in the submission of this manuscript, and the manuscript is approved by all authors for publication.

Competing interests
The authors declare no competing interests.