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The effects of dilute polymer solution elasticity and viscosity on abrasive slurry jet micro-machining of glass
Wear 309 (2014) 112–119
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The effects of dilute polymer solution elasticity and viscosity on abrasive slurry jet micro-machining of glass K. Kowsari a, D.F. James a,n, M. Papini b,a,nn, J.K. Spelt a,b,nnn a b
Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, M5S 3G8, Canada Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario, M5B 2K3, Canada
art ic l e i nf o
a b s t r a c t
Article history: Received 24 July 2013 Received in revised form 7 November 2013 Accepted 9 November 2013 Available online 16 November 2013
The present study investigated the effect of dilute polymer solutions on the width, shape, and centerline roughness of micro-channels machined using a specially-designed abrasive slurry-jet micro-machining (ASJM) apparatus. A positive displacement slurry pump and a pulsation damper were connected to an open reservoir mixing tank to generate a turbulent jet containing 1 wt% 10 μm Al2O3 particles flowing through a 180 μm sapphire orifice at 4 MPa. The behavior of non-Newtonian fluids containing long-chain polymers is affected by both their viscosity and their resistance to extensional deformation (i.e. their “elasticity”). The effects of viscosity and elasticity on erosion were separated by conducting experiments using aqueous solutions of equal viscosity, but differing elasticity. It was observed that jets began to oscillate laterally if the polymer concentration became too high. The width of the machined channels decreased 21% with the addition of 50 wppm of 8 M PEO, the highest concentration possible with a stable jet. This change was accompanied by a decrease in the channel depth of 46% and an increase in the centerline roughness of 29%. These changes were due to normal stresses generated in the PEO solutions (an elasticity effect), and were not attributable to viscosity. It was also seen with this and other polymer solutions, that the channel cross-sections were more V-shaped compared with the U-shape of the reference channel machined using the glycerin solution. The same changes in shape, channel width, and centerline roughness were observed at a lower concentration of the same PEO (i.e. 25 wppm), but to a lesser degree. Similar changes were also evident with more concentrated 1-M PEO solutions (i.e. 25–400 wppm), but again to a lesser extent. However, even a very concentrated 2.5 104 wppm solution containing 0.1 M PEO had no effect, indicating the predominant role of polymer molecular weight in determining the magnitude of fluid elasticity and its influence on particle motion in the erosive slurry. The present results demonstrate that even a small amount of a high-molecular-weight polymer can significantly decrease the width of machined microchannels for a given jet diameter. & 2013 Elsevier B.V. All rights reserved.
Keywords: Micro-machining Abrasive slurry jet Polymeric additives Viscosity Fluid elasticity Erosion
1. Introduction Applications of low-pressure abrasive slurry-jet micro-machining (ASJM) have been evolving for over a decade. The suspension of a dry abrasive powder in a water jet permitted fine machining
n Corresponding author at: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, M5S 3G8, Canada. Tel.: þ1 416 978 3049; fax: þ 1 416 978 7753. nn Corresponding author at: Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario, M5B 2K3, Canada. Tel.: þ 1 416 979 5000x7655; fax: þ 1 416 979 5265. nnn Corresponding author at: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, M5S 3G8, Canada. Tel.: þ 1 416 978 5435; fax: þ1 416 978 7753. E-mail addresses: [email protected] (D.F. James), [email protected] (M. Papini), [email protected] (J.K. Spelt).
0043-1648/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.wear.2013.11.011
of virtually any material with a high-surface quality and without thermal damage. Because divergence of the jet is small, ASJM is well-suited for the milling of micro-channels, where increasing the resolution has been the focus of most research in the area. In previous research on high-pressure ASJM, slurry content has typically been 20 wt% and driving pressures have been roughly 70 MPa [1]. However, Pang et al. [2] used pressures in the 10 MPa range and evaluated dimensions and surface morphology of micro-channels in glass. By varying operating parameters, they concluded that low-pressure ASJM is a viable process in manufacturing micro-electromechanical devices. Nouraei et al. [3] compared maskless low-pressure ASJM with masked abrasive air-jet micro-machining (AJM) by using the two processes to make holes and channels in borosilicate glass. They investigated the effects of ASJM pressure, particle concentration, jet speed, and jet impact angle, and found that the side walls of channels and holes
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were steeper and the bottoms were flatter with ASJM than with AJM. Furthermore, maskless ASJM yielded smaller feature widths for a given jet diameter and produced sharper edges than could be obtained with maskless AJM. This improved performance with maskless machining represents a potentially significant financial advantage of ASJM over AJM. To explore further improvement in the smallest feature width that can be machined using a given jet diameter, the present work investigated the effects of dissolving a small amount of a highmolecular-weight polymer in the slurry. The earliest study of aqueous jets containing polymer additives appeared in the 1960s for firefighting applications [4]. Hoyt et al. [5] discovered that polymers improved jet stability by damping surface disturbances and thereby reducing or eliminating droplet formation. Another hydrodynamic effect of polymeric additives is friction reduction in pipe flows. The presence of a high-molecular-weight polymer, even at concentrations of order 10 wppm (weight parts per million), can reduce wall friction by as much as 75% in a turbulent pipe flow [6]. Both of these benefits arise from induced viscoelasticity in the fluid. In general, long-chain polymeric additives increase the resistance to elongational deformation, the effect increasing with molecular mass and concentration. When subjected to a sufficiently high strain rate, the polymer chains are stretched from their initially-coiled equilibrium state and generate normal stresses, causing the fluid to resist deformation; i.e. the liquid exhibits elasticity, a property of some non-Newtonian fluids [7]. Polymer additives have been tried in high-pressure abrasive water jet machining (AWJM), in which abrasive powder is entrained in a high-velocity water jet. Nguyen et al. [8] found that 1000–5000 wppm solutions of high molecular weight polyacrylamide enhanced the stability and increased the coherent length of the jet before breakup. Ashrafi [9] found that the addition of a large amount of cornstarch (10–22 wt%) produced a narrower cutting kerf with steeper sidewalls, but did not explain the result. As for ASJM, only a few studies have attempted to identify the role of polymer additives on the machining. Luo et al. [10] analyzed the effects of concentrated (of the order of 103 wppm) solutions of several high-molecular-weight polymers on low-pressure polishing of glass. The term ‘high’, here and elsewhere, refers to molecular weight in the millions. It was found that the additives sharpened the separation between the polished and unpolished regions by reducing the width of the transition zone between them. The authors hypothesized that the polymer chains, extended in the jet direction, minimized momentum exchange with the surrounding air and thus decreased the divergence angle of the jet. Wang et al. [11] compared ASJM holes machined in glass using relatively concentrated aqueous solutions of high-molecularweight polyacrylamide (PAM solutions of the order of 103 wppm),
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anionic polyacrylamide (HPAM), and cationic polyacrylamide (PAMA). The deepest hole with the smallest diameter was obtained using 5 M PAM; however, no comparisons were made to a hole machined with water alone. In summary, then, past studies have found that machining with concentrated, high molecular-weight polymer solutions, at pressures of 14 MPa and above, reduced channel widths and hole diameters. The objective of the present study was to examine the effect of polymer solutions in the dilute range (25–400 wppm) on machined channel width, cross-sectional shape, and centerline roughness, and to explain the observed changes in terms of the relative contributions of liquid viscosity and elasticity.
2. Experiments 2.1. ASJM apparatus An ASJM apparatus was constructed utilizing an abrasive slurry pump and pulsation damper connected to an open reservoir tank (Fig. 1). The positive displacement pump (LCA/M9/11-DC, LEWA Inc., Leonberg, Germany) had an adjustable stroke length (0–15 mm) and frequency range (0–3.5 Hz) which permitted operation over a relatively wide range of flow rates and pressures. Although the pump could deliver a flow rate of 5 mL/s at 8 MPa, in the present experiments the flow rate was maintained at 1.6770.1% mL/s at a pressure of 4 MPa, using a variable frequency drive (CFW-10, WEG, Jaraguá do Sul, Brazil). A pre-pressurized pulsation damper (FG 44969/01–9, Flowguard Ltd., Houston, TX, U.S.A.) was installed downstream of the pump to reduce pressure and flow rate pulsations to within73%. A manual valve was used to relieve the pressure before disassembling the system. To minimize the transfer of vibrations to the jet, the pump and orifice were mounted on separate supports and were connected by a flexible pipe. Aqueous slurries of 1 wt% Al2O3 abrasive particles having a nominal diameter of 10 μm (Comco Inc., CA, USA) were prepared in the 18 L reservoir tank (28 cm diameter, 33 cm deep) using an 8-cm-diameter propeller rotated at 100 rpm. The propeller was positioned 11 cm above the bottom of the tank to optimize mixing as recommended by Dutta and Pangarkar [12]. Homogeneity was confirmed visually and from jet concentration measurements, which are described below. A sapphire waterjet orifice with a diameter of 180 μm and a length/diameter ratio of 1.67 (KMT Waterjet, KS, USA, Fig. 2) was connected to stainless steel tubing (Fig. 1). The jet diameter was measured using a microscope attached to a digital camera, and the contraction coefficient (the ratio of the jet cross-sectional area to that of the orifice) was found to be 0.60 70.03 for all solutions.
Fig. 1. Schematic of the ASJM components (not to scale).
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This value compares well with the theoretical value of 0.64 for a sharp orifice [13]. The jet velocity, computed using Bernoulli's equation, was about 110 m/s, corresponding to a Reynolds number of 15,120; thus the jet was turbulent, being well above the critical Reynolds number of 10,000 for a water jet in air [14]. Moreover, the Mach number was about 0.07, indicating that fluid compressibility was negligible. To minimize the settling of particles in the stainless tubing upstream of the orifice, a tube diameter of 3.2 mm was selected to maintain a particle Reynolds number, Rep, of at least 300. Even so, settling occurred in the tubing and reduced the concentration from 1.00 wt% in the reservoir to 0.79 wt% in the jet, the latter measured by weighing samples collected in a beaker during 1 min periods. The collected samples were passed through a filter paper of known mass, and the wet particles and paper were dried in an oven at 150 1C to obtain the mass of the particles. Ten samples were collected this way, regularly spaced over a period of 60 min. Because the particle concentration varied less than 3%, the slurry concentration in a jet was considered to be constant over the operating periods which lasted up to one hour.
2.2. Slurry preparation Nine aqueous test fluids were prepared, the details of which are given in Table 1, and all had an abrasive concentration of 1 wt%. The first was a slurry containing only water, the second was a solution of glycerin and water, and polyethylene oxide (PEO) of
Fig. 3. Viscosity of the PEO solutions versus concentration at 21 1C.
several molecular weights and concentrations was dissolved in seven of them. The abrasive particles were taken from the supplier's 1 L bottle using the ASTM quartering technique [15] to ensure that the size distribution was uniform after shipping and handling. Samples were weighed on an electronic scale (AP110, OHAUS Corp., Pine Brooke, NJ, USA), accurate to 0.1 mg. Three widely-different molecular weights of PEO were obtained, namely 0.1 M, 1.0 M and 8.0 M (viscosity-averaged molecular weights, Sigma-Aldrich, St. Louis, MO, USA). To prepare a solution, the desired amount of a particular molecular weight was first dispersed in 20 mL of ethanol to avoid polymer aggregation, and then this mixture was added to 6 L of slurry containing 0.26 wt% of ethanol in the reservoir tank and slowly stirred to minimize polymer degradation. The addition of ethanol had a negligible effect on viscosity; e.g. the viscosity of a 0.26 wt% aqueous ethanol solution at 20 1C is only 1.3% larger than that of water [16]. The viscosity of each fluid was measured to 70.2% accuracy using a Cannon-Fenske capillary tube viscometer, following the procedure of ASTM D4889-04 [17]. As seen in Fig. 3, the viscosity increased linearly with the polymer concentration. 2.3. Machining
Fig. 2. Orifice geometry (dimensions are in μm). Table 1 Properties of the aqueous test fluids. Fluid
Additive
Viscosity–averaged molecular weight (MV) ( 106)
Concentration (wppm)
Viscosity (mPa s)
1 2 3 4 5 6 7 8 9
– Glycerin PEO PEO PEO PEO PEO PEO PEO
– N/a 8.0 8.0 8.0 1.0 1.0 1.0 0.1
– 52,000 25 50 75 25 200 400 25,000
1.00 1.10 1.05 1.10 1.14 1.02 1.18 1.36 9.00
Channels were machined in 100 50 3 mm borosilicate glass plates (Borofloat 33s, Schott Inc., NY, USA) having a Young's modulus of 63 GPa, Poisson's ratio of 0.2, fracture toughness of 0.76 MPa m1/2, and a Vickers hardness of 5.4 GPa [18]. The glass plates were mounted on a computer-controlled linear stage (Zaber Technologies Inc., Vancouver, BC, Canada), capable of vertical motion at speeds up to 7 mm/s (Fig. 1). The slurry jet was aligned to be perpendicular to a plate, which was scanned at 0.05 mm/s at a standoff distance of 20 mm (the jet centerline distance between the orifice and plate). This distance was less than the theoretical coherent length of the jet before breakup, computed to be 36 mm using the equation provided by Taylor [19]: 1=2 d0 B ρρL g xB ¼ ð1Þ f ðTÞ where d0 is the orifice diameter, B is a constant equal to 2.02, ρL and ρg represent the liquid and gas densities respectively, and T is Taylor's parameter T ¼ ρL =ρg ðReL =WeL Þ2 , in which ReL is the Reynolds number of the jet based on the jet diameter L¼ 140 μm, and WeL is the Weber number (a dimensionless ratio of the fluid inertia relative to its surface tension) calculated to be 22,430, also using the jet diameter. The function f(T)phas been numerically ffiffiffi approximated by Dan et al. [20] as f ðTÞ ¼ 3=6½1 expð 10TÞ.
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Fig. 4. (a) SEM image of the reference channel machined with the aqueous slurry without additives (fluid 1, Table 1), and (b) its cross-sectional profile, measured using an optical profilometer.
The jet diameter was measured and found to be 140 μm over the 20 mm standoff distance, regardless of the fluid. These operating parameters were selected to provide channels with depth-to-width-ratios similar to those in other ASJM studies without additives, such as those conducted by Nouraei et al. [3]. As mentioned in Section 2.1, the slurry flow rate was 1.677 0.1% mL/s for all tests, so that the dose of abrasive delivered to the surface (mass of abrasive per unit area) was constant. The cross-sectional profiles and the centerline roughness of the machined channels were measured using an optical profilometer (ST400, Nanovea Inc., CA, USA), which had a depth resolution of 0.1 μm. Depth measurements for determining the cross-sectional profiles were acquired every 5 μm across the top width of a channel, and centerline depths for roughness measurements were obtained every 0.1 μm along the channel centreline. The profilometer data were used without any filtering.
Fig. 5. Cross-sectional profiles of channels machined with the water/glycerin mixture (fluid 2) and with water-only slurry (fluid 1); the latter is the reference profile from Figure 4.
3. Results and discussion 3.1. Reference channel A reference channel was machined with fluid number 1, the slurry without additives, and the channel is shown in Fig. 4. For all test fluids, channel dimensions were found to be uniform along the length of a channel and between channels, displaying a 3% maximum variation in depth and width at the top of the channel in three scans taken 5 mm apart along a single channel, and in three additional channels. Fig. 4(b) shows that the reference channel had a U-shape with a relatively flat bottom, similar to the shapes observed in Nouraei et al. [3]. The channel was 92 μm deep and 280 μm wide. The top width was taken to be the distance between the points where the profile slope deviated 10% from the original glass surface. These slopes were estimated from linear fits to any 5 consecutive profile points.
3.2. Effects of viscosity The addition of PEO increased the viscosity and induced nonNewtonian behavior. The addition of glycerin, however, (fluid 2), increased only the viscosity because glycerin molecules are too
Fig. 6. Streamlines and expected particle trajectories and impact angles in the stagnation zone for: (a) a fluid with a lower viscosity and (b) for a fluid with a higher viscosity.
small to generate non-Newtonian behavior [7]. Fig. 5 compares the cross-sectional profiles of channels with and without glycerin; i.e. a comparison of fluids 1 and 2 under otherwise identical conditions of slurry flow rate and pressure, and hence abrasive dose. The plot shows that the 10% increase in viscosity caused by the glycerin decreased the channel depth by 19%, but had virtually no effect on the top width. It is hypothesized that the 19% reduction in depth was caused by two viscous effects. First, as a particle approached the target, its
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larger drag made it decelerate more as it approached the plate in the stagnation zone [21]; i.e. the increased viscosity reduced the particle's impact energy and hence its ability to erode. Secondly, the 10% increase in viscosity increased the momentum equilibration number, as defined by Humphrey [22], by 10%, reflecting a slightly greater tendency for particles to follow the streamlines and thereby decreasing the local impact angle at the bottom of the channel, as illustrated in Fig. 6 by trajectories (a) and (b). Since the erosion of brittle materials depends strongly on the velocity component perpendicular to the surface [23,24], the net effect was to reduce erosion and therefore the channel depth. In principle, this second effect should also have changed the channel top width, but the effect appears to be negligible for a 10% increase in viscosity.
3.3. Effects of PEO In a dilute polymer solution at rest, the long chains are loosely and randomly coiled because of Brownian motion. At a sufficiently high deformation rate, in either shear or extension, hydrodynamic forces cause the polymer chains to be stretched out and oriented in the flow direction. The extended chains are under tension and thus increase the normal stress in the flow direction. Because of this additional stress, the polymer solution behaves as a viscoelastic material, resisting extension like a solid as well as resisting shear like a fluid [25]. Larson [7] explained how this viscoelastic behavior increases with molecular weight and concentration. To investigate the effects of this elasticity or additional stress, channels were machined using the seven different PEO solutions of Table 1. 3.3.1. PEO and agglomeration Türkman [26] describes the use of polymeric additives in industrial wastewater treatment to coagulate particles and promote their settling. Hence it was necessary to determine whether agglomeration affected the present experiment. Laser shadowgraphy was used to measure the size distribution and settling velocities of the aluminum oxide particles, in water and in the 50 wppm solution of 8 M PEO (fluid 4). The latter fluid, as Table 1 shows, was 10% more viscous than water. The velocities and size distributions were measured in a 50 100 3 mm glass vessel using a double-pulsed Nd:YAG laser (neodymium: yttrium aluminum garnet), which produced up to 0.3 J/pulse at a repetition rate of 1 kHz and which passed through a diffuser (1108417, Lavision GMbH, Goettingen, Germany). The laser was placed opposite a high-speed CCD camera (Imager Pro PlusX, Lavision GmbH, Goettingen, Germany) with a zoom lens. More details of this system and the shadowgraphic technique can be found in Dehnadfar et al. [27]. Based on 1500 measurements made in each liquid, it was found that the particle size distributions were the same, indicating that the polymer did not cause agglomeration. The settling velocity did decrease, though, but the value was consistent with the 10% increase in the drag force predicted by Stokes' law. Fig. 7(a) presents the channel cross-sectional profiles for the 25 and 50 wppm 8 M PEO solutions (fluids 3 and 4), along with the profile of the reference channel (fluid 1) under identical experimental conditions of pressure and slurry flow rate. The 25 and 50 wppm solutions decreased the channel top width by 10% and 21%, respectively, and the depth by 20% and 46%. Fig. 7(a) and (b) also show that the profiles of the channels made with the PEO solutions had more of a V-shape than the U-shape for the wateronly slurry shown in Fig. 4. Fig. 7(c) shows that the channel top width decreased linearly with polymer concentration in this range. The decreased top width for the two PEO solutions in Fig. 7 was attributed to normal stresses (i.e. stresses due to fluid elasticity),
Fig. 7. (a) Cross-sectional profiles of channels machined with slurries of water, 25 and 50 wppm solutions of 8-M PEO (fluids 1, 3, 4) with identical slurry flow rate and pressure. (b) SEM image of the channel machined with the slurry containing 50 wppm of 8-M PEO (fluid 4). (c) The decrease of channel widthtop width with 8-M PEO concentration.
Fig. 8. Stagnation point regions where normal stresses create an extra drag on a particle approaching the target.
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because Section 3.2 showed that a 10% increase in viscosity did not change the top width. The depth decrease of 46% relative to the water-only case, was the sum of the effects of viscosity and normal stresses. A 19% reduction was caused by the increased viscosity, as shown by Fig. 5 for the glycerin/water mixture. Because the 50 wppm solution had the same shear viscosity as the glycerin solution (Table 1), the additional 27% decrease in depth with this fluid must have been caused by normal stresses. Such stresses can reduce the energy of a particle close to the target as the fluid velocity approaches zero. Fig. 8 shows stagnation-point regions where normal stresses are generated, at the front of a particle and at the impact point on the target. The induced stresses create an additional resistance to motion, thereby further decelerating the particle. The decreased channel top width produced with the polymer solutions could have been the result of changes in the jet velocity distribution. However, this possibility is unlikely, because Goren and Norbury [28] and Barker [29] found that the velocity profile in turbulent jets of aqueous PEO solutions did not change significantly. It is therefore more likely that fluid elasticity reduced the jet footprint in the stagnation region by focussing the streamlines and decreasing the spread of the flow. The stagnation region of a Newtonian jet impinging on a flat surface has hyperbolic-like streamlines (Fig. 6) and a uniform extensional strain rate throughout [30]. In this flow field, the stretch of a polymer chain depends on its residence time, which increases with proximity to the stagnation point. Consequently, elastic effects increase in streamlines that are progressively nearer to the stagnation point. This behavior has been confirmed by Muller et al. [31] who used optical birefringence to show that the degree of chain extension in a dilute high-molecular-weight polymer solution was maximum near the stagnation point. Given that polymer chains resist flow extension in proportion to the amount by which they are stretched, streamlines leaving the stagnation point spread less, causing the impacting particles to strike closer to the centreline. That is, the jet is more focussed (Fig. 9), decreasing the channel top width and causing cross-sectional profiles with more curvature at the bottom of the channel. When the slurry had a concentration of 75 wppm of the same PEO (solution 5), the channel top width increased by 5%, contrary to the trend of Fig. 7(c) where the top width decreased as the concentration increased. The increase was caused by a jet instability that resulted in a 40 μm amplitude oscillation, producing an effective jet diameter of 220 μm. This was measured by capturing microscope images having a field of view of 3 2 mm for 10 s at a frequency of 29 Hz, and then extracting the position of the jet from each frame. The amplitude of the oscillation decreased with decreasing 8 M PEO concentration, becoming 20 μm for the 50 wppm fluid. Without the PEO, the jet had the same diameter (140 μm), and did not oscillate. Furthermore, the jet containing glycerin did not oscillate. Rothstein and McKinley [32] found that instabilities in non-Newtonian jets can result from randomly fluctuating vortices formed upstream of a sharp orifice. In the
Fig. 9. Comparison of particle impact angle in a polymeric solution (θ) and water (ϕ).
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Fig. 10. Cross-sectional profiles of a single-pass channel machined with the wateronly slurry (fluid 1) and with three passes with the 50 wppm 8 M PEO solution (fluid 4).
present work, avoiding this instability limited the concentration range for each polymer molecular weight. The experiments were extended to include additional scanning passes. Fig. 10 shows that a second and a third pass with the same 50 wppm of 8 M PEO solution (fluid 4) had no effect on the top width, but increased the channel depth by 35% and 106%, respectively, resulting in a total depth 10% larger than that of the reference channel. Therefore, the reduction in depth brought about with PEO solutions can be compensated for by additional machining passes without affecting the decreased top width. This, of course, increases the machining time. Another machining characteristic of interest was centerline surface roughness. In the present experiments, channel roughness was measured along the centreline for 5 mm using an optical profilometer, and the data were analyzed with a cut-off length of 800 μm according to the ISO 4288 [33] standard. The average centerline roughness, Ra, was relatively constant for a given set of machining conditions, varying by less than 7% along a single channel, and between three separately machined channels. The Ra values using water and the glycerin/water mixture (fluids 1 and 2) were both approximately 0.5 μm, while the centerline roughness from a single pass with the 50 wppm 8 M PEO solution was 0.7 μm. A t-test analysis showed that the difference between these values was statistically significant with a confidence interval of 95%. Micrographs of the two surfaces are presented in Fig. 11, which shows that the surface of the channel machined with the PEO solution (Fig. 11c) was significantly coarser than that of the channel machined with water alone (Fig. 11b). Since roughness increases with the normal impact velocity component as discussed, for example, by Slikkerveer et al. [23], the difference is believed to be caused by the focusing effect discussed earlier and shown in Fig. 9. Since glycerin had a negligible focusing effect, it did not increase the roughness.
3.3.2. Tests with the 1 M PEO Fluid elasticity increases with molecular weight, because longer chains generate more tension and thus produce larger normal stresses, as described by Bird et al. [25]. With shorter chains, lower effects are expected, and these effects were assessed in the present work by using 1 M PEO. Concentrations with this polymer were varied up to 400 wppm, at which point the jet became unstable. As shown by Fig. 12, (i) a 25 wppm solution (fluid 6) had no significant effect on the channel top width, but decreased the channel depth, relative to the reference channel, by 32%; (ii) a 200 wppm solution (fluid 7) reduced the top width by 13% and the depth by 39%; and (iii) when the concentration was 400 wppm (fluid 8), the jet was unstable and its larger effective diameter due to the lateral jet oscillation caused the top width to increase by 7%.
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Fig. 11. SEM images of surfaces in the central regions of channels, indicated by the rectangle in (a), machined using: (b) water-only slurry (fluid 1) and (c) water with 50 wppm of 8-M PEO (fluid 4).
Fig. 12. Cross-sectional profiles of channels machined with the water-only slurry and with three concentrations of 1-M PEO (fluids 1, 6, 7, and 8, Table 1), all with identical slurry flow rate and pressure.
Fig. 14. Cross-sectional profiles of channels machined with the water-only slurry (fluid 1) and a 2.5 wt% solution of 0.1-M PEO (fluid 9) under identical pressure and slurry flow rate.
suggests that normal stresses were larger with the 8 M PEO slurries even though polymer concentrations were much lower. Therefore, the polymer focussing effect depends more strongly on molecular weight than concentration, a finding consistent with other flows containing polymer additives [34].
Fig. 13. Percentage change decrease in channel widthtop width relative to the water-only slurry, for the 8-M and 1-M PEO solutions. The dashed lines are only to help guide the eye.
These data with 1 M PEO solutions confirm that, with a stable jet, the polymer caused both the channel depth and top width to decrease, as was found with the 8 M solutions. Fig. 13 compares the change in the channel top width obtained with the two highest molecular-weight polymers, over their range of concentrations. The maximum for each curve corresponds to the onset of jet instability and the transverse oscillation it produced. This instability began at a substantially higher concentration for the 1 M PEO solution than for the 8 M PEO solution, and below these concentrations the channels made with the 1 M PEO were significantly wider than those machined with the 8 M PEO. This result
3.3.3. Test with 0.1 M PEO To further probe the effect of molecular weight, channels were machined with a slurry containing the lowest-molecular-weight PEO, the 0.1 M sample (fluid 9). This short-chain polymer increased the shear viscosity significantly, as Table 1 indicates, and thus the channel depth was reduced considerably, as Fig. 14 shows. But, even at a concentration of 2.5 wt% (25,000 wppm), the channel top width was unchanged and elasticity-induced jet oscillations were absent, re-confirming that polymeric effects depend more strongly on molecular weight than concentration. Because the top width was not affected, the shallow depth appears to have been caused solely by this fluid's higher viscosity; i.e. 9 mPa s versus 1.1 mPa s for the other PEO solutions (Table 1). Similar to the findings of Ashrafi [9], the present “elastic” solutions resulted in decreased channnel top widths. However, the present data showed that significant top width reductions for a given jet diameter can be obtained with merely trace amounts of a high-molecular-weight polymer, compared with the much more concentrated solutions used by Ashrafi [9]. Moreover, our experiments showed that higher concentrations caused jet lateral instabilities, which made the channels wider. 4. Summary and conclusions An abrasive slurry jet micro-machining (ASJM) system was used to investigate the effects of polyethylene oxide (PEO), of varying
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molecular weight and concentration, on the shape, top width, and centerline roughness of micro-channels machined in borosilicate glass. The flow of these non-Newtonian fluids containing long-chain polymers is known to be affected by both their viscosity and their resistance to extensional deformation (i.e. their “elasticity”). For the first time, the effects of viscosity and elasticity on the erosion produced by such a non-Newtonian abrasive slurry were separated by comparing the erosion results to those obtained with an aqueous solution of glycerin, which had a viscosity equal to that of the PEO solutions. A reference channel was machined with water and particles only. Under otherwise identical conditions, machining with a 50 wppm solution of the 8-million (8 M) molecular weight PEO decreased the channel top width by 21%, decreased its depth by 46%, and increased its centerline roughness by 29%. The channel machined with the PEO solution also had more of a V-shape than the U-shape obtained with the water-only slurry. These changes were attributable to the effect of both viscosity and elasticity. For channels machined with the glycerin/water slurry that had the same viscosity as the 8 M PEO solution, but which had no elasticity, the top width remained unchanged relative to the water-only slurry, and only a 19% decrease in depth was observed. Therefore, increasing only the viscosity of the slurry decreased the channel depth, but left the top width unchanged. The decrease in channel top width with increasing PEO concentration, and hence elasticity, was attributed to a reduction in the spread of the jet in the stagnation region. The elasticity also decreased the channel depth by reducing the impact velocity of the abrasive particles. About 40% of the depth decrease relative to the water-only channel for the 50 wppm 8 M PEO solution could be attributed to increased viscosity, while the remaining 60% was evidently due to elasticity. An additional pass of the 8 M PEO was found to increase the channel depth without changing the top width or the roughness. Similar changes in channel shape, top width, and depth were seen in channels machined with 1 M PEO in larger concentrations, but the changes were smaller. With the lowest molecular weight PEO, 0.1 M, a concentration of 2.5 wt% did not change the channel top width, but decreased the depth by 83%. This is consistent with the literature which indicates that short-chain polymers increase the viscosity, but generate little fluid elasticity. When PEO was added, the jet was stable until an upper limit in concentration was reached. Above this limit, the jet oscillated laterally at a high frequency, and thus its effective diameter increased. This polymer concentration limit decreased with increasing molecular weight. Further decreases in channel top width for a given jet diameter may be possible using orifice designs that preserve the stability of a jet at higher polymer concentrations. Acknowledgments The authors acknowledge the Natural Sciences and Engineering Research Council of Canada, Micralyne Inc. and BIC Fuel Cells Inc. The authors thank Hooman Nouraei for assisting with the design and construction of the apparatus. References [1] D.S. Miller, Micromachining with abrasive waterjets, J. Mater. Process. Technol. 149 (2004) 37–42. [2] K.L. Pang, T. Nguyen, J.M. Fan, J. Wang, Machining of micro-channels on brittle glass using an abrasive slurry jet, Key Eng. Mater. 443 (2010) 639–644.
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[3] H. Nouraei, A. Wodoslawsky, M. Papini, J.K. Spelt, Characteristics of abrasive slurry jet micro-machining: a comparison with abrasive air jet micromachining, J. Mater. Process. Technol. 213 (2012) 1711–1724. [4] D.A. Summers, Waterjetting Technology, Taylor & Francis, New York (1995) 472. [5] J. Hoyt, J. Taylor, C.D. Runge, The structure of jets of water and polymer solution in air, J. Fluid Mech. 63 (1974) 635–640. [6] B.R. Elbing, M.J. Solomon, M. Perlin, D.R. Dowling, S.L. Ceccio, Flow-induced degradation of drag-reducing polymer solutions within a high-Reynoldsnumber turbulent boundary layer, J. Fluid Mech. 670 (2011) 337–364. [7] R.G. Larson, The Structure and Rheology of Complex Fluids, Oxford University Press, New York (1999) 107–132. [8] T. Nguyen, D.K. Shanmugam, J. Wang, Effect of liquid properties on the stability of an abrasive waterjet, Int. J. Mach. Tools Manuf. 48 (2008) 1138–1147. [9] N. Ashrafi, Viscoelastic abrasive waterjet, ASME 2011 International Mechanical Engineering Congress and Exposition, 3, 677–681. [10] W.S. Luo, C.Y. Wang, Y.X. Song, Y.P. Liao, Characteristics and polishing effect of abrasive jet beam with polymer abrasive suspension additives, Adv. Mater. Res. 126 (2010) 9–13. [11] C.Y. Wang, P. Yang, J.M. Fan, Y.X. Song, Effect of slurry and nozzle on hole machining of glass by micro abrasive suspension jets, Key Eng. Mater. 404 (2009) 177–183. [12] N. Dutta, V. Pangarkar, Critical impeller speed for solid suspension in multi‐ impeller three phase agitated contactors, Can. J. Chem. Eng. 73 (1995) 273–283. [13] G. Falkovich, Fluid Mechanics – A Short Course for Physicists, Cambridge University Press, Cambridge, England, 2011. [14] P.E. Dimotakis, The mixing transition in turbulent flows, J. Fluid Mech. 409 (2000) 69–98. [15] American Society for Testing and Materials (ASTM), ASTM C702-98 Standard Practice for Reducing Samples of Aggregate to Testing Size, American Society for Testing and Materials, West Conshohocken, PA, 2003. [16] C. Simmonds, Alcohol, Its Production, Properties, Chemistry, And Industrial Applications, Macmillan and Co., Limited, London (1919) 154. [17] American Society for Testing and Materials (ASTM), ASTM D4889-04 Standard Test Methods for Polyurethane Raw Materials: Determination of Viscosity of Crude or Modified isocyanates, American Society for Testing and Materials, West Conshohocken, PA, 2011. [18] T.E. Wilantewicz, J.R. Varner, Vickers indentation behavior of several commercial glasses at high temperatures, J. Mater. Sci. 43 (2008) 281–298. [19] G.I. Taylor, Generation of Ripples by Wind Blowing Over Viscous Fluids, Cambridge Univ. Press, Cambridge (1962) 244–254. [20] T. Dan, T. Yamamoto, J. Senda, H. Fujimoto, Effect of nozzle configurations for characteristics of non-reacting diesel fuel sprays, Society of Automotive Engineers Technical Paper 970355, 1997. [21] H.M.I. Clark, The influence of the flow field in slurry erosion, Wear 152 (1992) 223–240. [22] J. Humphrey, Fundamentals of fluid motion in erosion by solid particle impact, Int. J. Heat Fluid Flow 11 (1990) 170–195. [23] P. Slikkerveer, P. Bouten, H. Scholten, Erosion and damage by sharp particles, Wear 217 (1998) 237–250. [24] Y. Ballout, J. Mathis, J. Talia, Solid particle erosion mechanism in glass, Wear 196 (1996) 263–269. [25] R.B. Bird, R.C. Amstrong, O. Hassager, 2nd edition, Dynamics of Polymeric Liquids, vol. 1, John Wiley & Sons, New York, 1987. [26] A. Türkman, Polymer application examples in industrial wastewater treatment, New Dev. Ind. Wastewater Treat. 191 (1991) 93–109. [27] D. Dehnadfar, J. Friedman, M. Papini, Laser shadowgraphy measurements of abrasive particle spatial, size and velocity distributions through micro-masks used in abrasive jet micro-machining, J. Mater. Process. Technol. 212 (2011) 137–149. [28] Y. Goren, J. Norbury, Turbulent flow of dilute aqueous polymer solutions, J. Basic Eng. 89 (1967) 814–822. [29] S.J. Barker, Laser-Doppler measurements on a round turbulent jet in dilute polymer solutions, J. Fluid Mech. 60 (1973) 721–731. [30] H. Schlichting, K. Gersten, Boundary-Layer Theory, Springer, New York (2004) 110. [31] A. Müller, J. Odell, J. Tatham, Stagnation-point extensional flow behavior of M1, J. Non Newton. Fluid Mech. 35 (1990) 231–250. [32] J.P. Rothstein, G.H. McKinley, Extensional flow of a polystyrene Boger fluid through a 1:4 axisymmetric contraction/expansion, J. Non-Newton. Fluid Mech. 86 (1999) 61–88. [33] International Organization for Standardization (ISO), ISO 4288 Geometrical Product Specifications (GPS)—Surface Texture: Profile Method—Rules and Procedures for the Assessment of Surface Texture, British Standards Institute, London, 1996. [34] D.F. James, D.R. Mclaren, The laminar flow of dilute polymer solutions through porous media, J. Fluid Mech. 70 (1975) 733–752.
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The effects of dilute polymer solution elasticity and viscosity on abrasive slurry jet micro-machining of glass K. Kowsari a, D.F. James a,n, M. Papini b,a,nn, J.K. Spelt a,b,nnn a b
Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, M5S 3G8, Canada Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario, M5B 2K3, Canada
art ic l e i nf o
a b s t r a c t
Article history: Received 24 July 2013 Received in revised form 7 November 2013 Accepted 9 November 2013 Available online 16 November 2013
The present study investigated the effect of dilute polymer solutions on the width, shape, and centerline roughness of micro-channels machined using a specially-designed abrasive slurry-jet micro-machining (ASJM) apparatus. A positive displacement slurry pump and a pulsation damper were connected to an open reservoir mixing tank to generate a turbulent jet containing 1 wt% 10 μm Al2O3 particles flowing through a 180 μm sapphire orifice at 4 MPa. The behavior of non-Newtonian fluids containing long-chain polymers is affected by both their viscosity and their resistance to extensional deformation (i.e. their “elasticity”). The effects of viscosity and elasticity on erosion were separated by conducting experiments using aqueous solutions of equal viscosity, but differing elasticity. It was observed that jets began to oscillate laterally if the polymer concentration became too high. The width of the machined channels decreased 21% with the addition of 50 wppm of 8 M PEO, the highest concentration possible with a stable jet. This change was accompanied by a decrease in the channel depth of 46% and an increase in the centerline roughness of 29%. These changes were due to normal stresses generated in the PEO solutions (an elasticity effect), and were not attributable to viscosity. It was also seen with this and other polymer solutions, that the channel cross-sections were more V-shaped compared with the U-shape of the reference channel machined using the glycerin solution. The same changes in shape, channel width, and centerline roughness were observed at a lower concentration of the same PEO (i.e. 25 wppm), but to a lesser degree. Similar changes were also evident with more concentrated 1-M PEO solutions (i.e. 25–400 wppm), but again to a lesser extent. However, even a very concentrated 2.5 104 wppm solution containing 0.1 M PEO had no effect, indicating the predominant role of polymer molecular weight in determining the magnitude of fluid elasticity and its influence on particle motion in the erosive slurry. The present results demonstrate that even a small amount of a high-molecular-weight polymer can significantly decrease the width of machined microchannels for a given jet diameter. & 2013 Elsevier B.V. All rights reserved.
Keywords: Micro-machining Abrasive slurry jet Polymeric additives Viscosity Fluid elasticity Erosion
1. Introduction Applications of low-pressure abrasive slurry-jet micro-machining (ASJM) have been evolving for over a decade. The suspension of a dry abrasive powder in a water jet permitted fine machining
n Corresponding author at: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, M5S 3G8, Canada. Tel.: þ1 416 978 3049; fax: þ 1 416 978 7753. nn Corresponding author at: Department of Mechanical and Industrial Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario, M5B 2K3, Canada. Tel.: þ 1 416 979 5000x7655; fax: þ 1 416 979 5265. nnn Corresponding author at: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, M5S 3G8, Canada. Tel.: þ 1 416 978 5435; fax: þ1 416 978 7753. E-mail addresses: [email protected] (D.F. James), [email protected] (M. Papini), [email protected] (J.K. Spelt).
0043-1648/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.wear.2013.11.011
of virtually any material with a high-surface quality and without thermal damage. Because divergence of the jet is small, ASJM is well-suited for the milling of micro-channels, where increasing the resolution has been the focus of most research in the area. In previous research on high-pressure ASJM, slurry content has typically been 20 wt% and driving pressures have been roughly 70 MPa [1]. However, Pang et al. [2] used pressures in the 10 MPa range and evaluated dimensions and surface morphology of micro-channels in glass. By varying operating parameters, they concluded that low-pressure ASJM is a viable process in manufacturing micro-electromechanical devices. Nouraei et al. [3] compared maskless low-pressure ASJM with masked abrasive air-jet micro-machining (AJM) by using the two processes to make holes and channels in borosilicate glass. They investigated the effects of ASJM pressure, particle concentration, jet speed, and jet impact angle, and found that the side walls of channels and holes
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were steeper and the bottoms were flatter with ASJM than with AJM. Furthermore, maskless ASJM yielded smaller feature widths for a given jet diameter and produced sharper edges than could be obtained with maskless AJM. This improved performance with maskless machining represents a potentially significant financial advantage of ASJM over AJM. To explore further improvement in the smallest feature width that can be machined using a given jet diameter, the present work investigated the effects of dissolving a small amount of a highmolecular-weight polymer in the slurry. The earliest study of aqueous jets containing polymer additives appeared in the 1960s for firefighting applications [4]. Hoyt et al. [5] discovered that polymers improved jet stability by damping surface disturbances and thereby reducing or eliminating droplet formation. Another hydrodynamic effect of polymeric additives is friction reduction in pipe flows. The presence of a high-molecular-weight polymer, even at concentrations of order 10 wppm (weight parts per million), can reduce wall friction by as much as 75% in a turbulent pipe flow [6]. Both of these benefits arise from induced viscoelasticity in the fluid. In general, long-chain polymeric additives increase the resistance to elongational deformation, the effect increasing with molecular mass and concentration. When subjected to a sufficiently high strain rate, the polymer chains are stretched from their initially-coiled equilibrium state and generate normal stresses, causing the fluid to resist deformation; i.e. the liquid exhibits elasticity, a property of some non-Newtonian fluids [7]. Polymer additives have been tried in high-pressure abrasive water jet machining (AWJM), in which abrasive powder is entrained in a high-velocity water jet. Nguyen et al. [8] found that 1000–5000 wppm solutions of high molecular weight polyacrylamide enhanced the stability and increased the coherent length of the jet before breakup. Ashrafi [9] found that the addition of a large amount of cornstarch (10–22 wt%) produced a narrower cutting kerf with steeper sidewalls, but did not explain the result. As for ASJM, only a few studies have attempted to identify the role of polymer additives on the machining. Luo et al. [10] analyzed the effects of concentrated (of the order of 103 wppm) solutions of several high-molecular-weight polymers on low-pressure polishing of glass. The term ‘high’, here and elsewhere, refers to molecular weight in the millions. It was found that the additives sharpened the separation between the polished and unpolished regions by reducing the width of the transition zone between them. The authors hypothesized that the polymer chains, extended in the jet direction, minimized momentum exchange with the surrounding air and thus decreased the divergence angle of the jet. Wang et al. [11] compared ASJM holes machined in glass using relatively concentrated aqueous solutions of high-molecularweight polyacrylamide (PAM solutions of the order of 103 wppm),
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anionic polyacrylamide (HPAM), and cationic polyacrylamide (PAMA). The deepest hole with the smallest diameter was obtained using 5 M PAM; however, no comparisons were made to a hole machined with water alone. In summary, then, past studies have found that machining with concentrated, high molecular-weight polymer solutions, at pressures of 14 MPa and above, reduced channel widths and hole diameters. The objective of the present study was to examine the effect of polymer solutions in the dilute range (25–400 wppm) on machined channel width, cross-sectional shape, and centerline roughness, and to explain the observed changes in terms of the relative contributions of liquid viscosity and elasticity.
2. Experiments 2.1. ASJM apparatus An ASJM apparatus was constructed utilizing an abrasive slurry pump and pulsation damper connected to an open reservoir tank (Fig. 1). The positive displacement pump (LCA/M9/11-DC, LEWA Inc., Leonberg, Germany) had an adjustable stroke length (0–15 mm) and frequency range (0–3.5 Hz) which permitted operation over a relatively wide range of flow rates and pressures. Although the pump could deliver a flow rate of 5 mL/s at 8 MPa, in the present experiments the flow rate was maintained at 1.6770.1% mL/s at a pressure of 4 MPa, using a variable frequency drive (CFW-10, WEG, Jaraguá do Sul, Brazil). A pre-pressurized pulsation damper (FG 44969/01–9, Flowguard Ltd., Houston, TX, U.S.A.) was installed downstream of the pump to reduce pressure and flow rate pulsations to within73%. A manual valve was used to relieve the pressure before disassembling the system. To minimize the transfer of vibrations to the jet, the pump and orifice were mounted on separate supports and were connected by a flexible pipe. Aqueous slurries of 1 wt% Al2O3 abrasive particles having a nominal diameter of 10 μm (Comco Inc., CA, USA) were prepared in the 18 L reservoir tank (28 cm diameter, 33 cm deep) using an 8-cm-diameter propeller rotated at 100 rpm. The propeller was positioned 11 cm above the bottom of the tank to optimize mixing as recommended by Dutta and Pangarkar [12]. Homogeneity was confirmed visually and from jet concentration measurements, which are described below. A sapphire waterjet orifice with a diameter of 180 μm and a length/diameter ratio of 1.67 (KMT Waterjet, KS, USA, Fig. 2) was connected to stainless steel tubing (Fig. 1). The jet diameter was measured using a microscope attached to a digital camera, and the contraction coefficient (the ratio of the jet cross-sectional area to that of the orifice) was found to be 0.60 70.03 for all solutions.
Fig. 1. Schematic of the ASJM components (not to scale).
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This value compares well with the theoretical value of 0.64 for a sharp orifice [13]. The jet velocity, computed using Bernoulli's equation, was about 110 m/s, corresponding to a Reynolds number of 15,120; thus the jet was turbulent, being well above the critical Reynolds number of 10,000 for a water jet in air [14]. Moreover, the Mach number was about 0.07, indicating that fluid compressibility was negligible. To minimize the settling of particles in the stainless tubing upstream of the orifice, a tube diameter of 3.2 mm was selected to maintain a particle Reynolds number, Rep, of at least 300. Even so, settling occurred in the tubing and reduced the concentration from 1.00 wt% in the reservoir to 0.79 wt% in the jet, the latter measured by weighing samples collected in a beaker during 1 min periods. The collected samples were passed through a filter paper of known mass, and the wet particles and paper were dried in an oven at 150 1C to obtain the mass of the particles. Ten samples were collected this way, regularly spaced over a period of 60 min. Because the particle concentration varied less than 3%, the slurry concentration in a jet was considered to be constant over the operating periods which lasted up to one hour.
2.2. Slurry preparation Nine aqueous test fluids were prepared, the details of which are given in Table 1, and all had an abrasive concentration of 1 wt%. The first was a slurry containing only water, the second was a solution of glycerin and water, and polyethylene oxide (PEO) of
Fig. 3. Viscosity of the PEO solutions versus concentration at 21 1C.
several molecular weights and concentrations was dissolved in seven of them. The abrasive particles were taken from the supplier's 1 L bottle using the ASTM quartering technique [15] to ensure that the size distribution was uniform after shipping and handling. Samples were weighed on an electronic scale (AP110, OHAUS Corp., Pine Brooke, NJ, USA), accurate to 0.1 mg. Three widely-different molecular weights of PEO were obtained, namely 0.1 M, 1.0 M and 8.0 M (viscosity-averaged molecular weights, Sigma-Aldrich, St. Louis, MO, USA). To prepare a solution, the desired amount of a particular molecular weight was first dispersed in 20 mL of ethanol to avoid polymer aggregation, and then this mixture was added to 6 L of slurry containing 0.26 wt% of ethanol in the reservoir tank and slowly stirred to minimize polymer degradation. The addition of ethanol had a negligible effect on viscosity; e.g. the viscosity of a 0.26 wt% aqueous ethanol solution at 20 1C is only 1.3% larger than that of water [16]. The viscosity of each fluid was measured to 70.2% accuracy using a Cannon-Fenske capillary tube viscometer, following the procedure of ASTM D4889-04 [17]. As seen in Fig. 3, the viscosity increased linearly with the polymer concentration. 2.3. Machining
Fig. 2. Orifice geometry (dimensions are in μm). Table 1 Properties of the aqueous test fluids. Fluid
Additive
Viscosity–averaged molecular weight (MV) ( 106)
Concentration (wppm)
Viscosity (mPa s)
1 2 3 4 5 6 7 8 9
– Glycerin PEO PEO PEO PEO PEO PEO PEO
– N/a 8.0 8.0 8.0 1.0 1.0 1.0 0.1
– 52,000 25 50 75 25 200 400 25,000
1.00 1.10 1.05 1.10 1.14 1.02 1.18 1.36 9.00
Channels were machined in 100 50 3 mm borosilicate glass plates (Borofloat 33s, Schott Inc., NY, USA) having a Young's modulus of 63 GPa, Poisson's ratio of 0.2, fracture toughness of 0.76 MPa m1/2, and a Vickers hardness of 5.4 GPa [18]. The glass plates were mounted on a computer-controlled linear stage (Zaber Technologies Inc., Vancouver, BC, Canada), capable of vertical motion at speeds up to 7 mm/s (Fig. 1). The slurry jet was aligned to be perpendicular to a plate, which was scanned at 0.05 mm/s at a standoff distance of 20 mm (the jet centerline distance between the orifice and plate). This distance was less than the theoretical coherent length of the jet before breakup, computed to be 36 mm using the equation provided by Taylor [19]: 1=2 d0 B ρρL g xB ¼ ð1Þ f ðTÞ where d0 is the orifice diameter, B is a constant equal to 2.02, ρL and ρg represent the liquid and gas densities respectively, and T is Taylor's parameter T ¼ ρL =ρg ðReL =WeL Þ2 , in which ReL is the Reynolds number of the jet based on the jet diameter L¼ 140 μm, and WeL is the Weber number (a dimensionless ratio of the fluid inertia relative to its surface tension) calculated to be 22,430, also using the jet diameter. The function f(T)phas been numerically ffiffiffi approximated by Dan et al. [20] as f ðTÞ ¼ 3=6½1 expð 10TÞ.
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Fig. 4. (a) SEM image of the reference channel machined with the aqueous slurry without additives (fluid 1, Table 1), and (b) its cross-sectional profile, measured using an optical profilometer.
The jet diameter was measured and found to be 140 μm over the 20 mm standoff distance, regardless of the fluid. These operating parameters were selected to provide channels with depth-to-width-ratios similar to those in other ASJM studies without additives, such as those conducted by Nouraei et al. [3]. As mentioned in Section 2.1, the slurry flow rate was 1.677 0.1% mL/s for all tests, so that the dose of abrasive delivered to the surface (mass of abrasive per unit area) was constant. The cross-sectional profiles and the centerline roughness of the machined channels were measured using an optical profilometer (ST400, Nanovea Inc., CA, USA), which had a depth resolution of 0.1 μm. Depth measurements for determining the cross-sectional profiles were acquired every 5 μm across the top width of a channel, and centerline depths for roughness measurements were obtained every 0.1 μm along the channel centreline. The profilometer data were used without any filtering.
Fig. 5. Cross-sectional profiles of channels machined with the water/glycerin mixture (fluid 2) and with water-only slurry (fluid 1); the latter is the reference profile from Figure 4.
3. Results and discussion 3.1. Reference channel A reference channel was machined with fluid number 1, the slurry without additives, and the channel is shown in Fig. 4. For all test fluids, channel dimensions were found to be uniform along the length of a channel and between channels, displaying a 3% maximum variation in depth and width at the top of the channel in three scans taken 5 mm apart along a single channel, and in three additional channels. Fig. 4(b) shows that the reference channel had a U-shape with a relatively flat bottom, similar to the shapes observed in Nouraei et al. [3]. The channel was 92 μm deep and 280 μm wide. The top width was taken to be the distance between the points where the profile slope deviated 10% from the original glass surface. These slopes were estimated from linear fits to any 5 consecutive profile points.
3.2. Effects of viscosity The addition of PEO increased the viscosity and induced nonNewtonian behavior. The addition of glycerin, however, (fluid 2), increased only the viscosity because glycerin molecules are too
Fig. 6. Streamlines and expected particle trajectories and impact angles in the stagnation zone for: (a) a fluid with a lower viscosity and (b) for a fluid with a higher viscosity.
small to generate non-Newtonian behavior [7]. Fig. 5 compares the cross-sectional profiles of channels with and without glycerin; i.e. a comparison of fluids 1 and 2 under otherwise identical conditions of slurry flow rate and pressure, and hence abrasive dose. The plot shows that the 10% increase in viscosity caused by the glycerin decreased the channel depth by 19%, but had virtually no effect on the top width. It is hypothesized that the 19% reduction in depth was caused by two viscous effects. First, as a particle approached the target, its
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larger drag made it decelerate more as it approached the plate in the stagnation zone [21]; i.e. the increased viscosity reduced the particle's impact energy and hence its ability to erode. Secondly, the 10% increase in viscosity increased the momentum equilibration number, as defined by Humphrey [22], by 10%, reflecting a slightly greater tendency for particles to follow the streamlines and thereby decreasing the local impact angle at the bottom of the channel, as illustrated in Fig. 6 by trajectories (a) and (b). Since the erosion of brittle materials depends strongly on the velocity component perpendicular to the surface [23,24], the net effect was to reduce erosion and therefore the channel depth. In principle, this second effect should also have changed the channel top width, but the effect appears to be negligible for a 10% increase in viscosity.
3.3. Effects of PEO In a dilute polymer solution at rest, the long chains are loosely and randomly coiled because of Brownian motion. At a sufficiently high deformation rate, in either shear or extension, hydrodynamic forces cause the polymer chains to be stretched out and oriented in the flow direction. The extended chains are under tension and thus increase the normal stress in the flow direction. Because of this additional stress, the polymer solution behaves as a viscoelastic material, resisting extension like a solid as well as resisting shear like a fluid [25]. Larson [7] explained how this viscoelastic behavior increases with molecular weight and concentration. To investigate the effects of this elasticity or additional stress, channels were machined using the seven different PEO solutions of Table 1. 3.3.1. PEO and agglomeration Türkman [26] describes the use of polymeric additives in industrial wastewater treatment to coagulate particles and promote their settling. Hence it was necessary to determine whether agglomeration affected the present experiment. Laser shadowgraphy was used to measure the size distribution and settling velocities of the aluminum oxide particles, in water and in the 50 wppm solution of 8 M PEO (fluid 4). The latter fluid, as Table 1 shows, was 10% more viscous than water. The velocities and size distributions were measured in a 50 100 3 mm glass vessel using a double-pulsed Nd:YAG laser (neodymium: yttrium aluminum garnet), which produced up to 0.3 J/pulse at a repetition rate of 1 kHz and which passed through a diffuser (1108417, Lavision GMbH, Goettingen, Germany). The laser was placed opposite a high-speed CCD camera (Imager Pro PlusX, Lavision GmbH, Goettingen, Germany) with a zoom lens. More details of this system and the shadowgraphic technique can be found in Dehnadfar et al. [27]. Based on 1500 measurements made in each liquid, it was found that the particle size distributions were the same, indicating that the polymer did not cause agglomeration. The settling velocity did decrease, though, but the value was consistent with the 10% increase in the drag force predicted by Stokes' law. Fig. 7(a) presents the channel cross-sectional profiles for the 25 and 50 wppm 8 M PEO solutions (fluids 3 and 4), along with the profile of the reference channel (fluid 1) under identical experimental conditions of pressure and slurry flow rate. The 25 and 50 wppm solutions decreased the channel top width by 10% and 21%, respectively, and the depth by 20% and 46%. Fig. 7(a) and (b) also show that the profiles of the channels made with the PEO solutions had more of a V-shape than the U-shape for the wateronly slurry shown in Fig. 4. Fig. 7(c) shows that the channel top width decreased linearly with polymer concentration in this range. The decreased top width for the two PEO solutions in Fig. 7 was attributed to normal stresses (i.e. stresses due to fluid elasticity),
Fig. 7. (a) Cross-sectional profiles of channels machined with slurries of water, 25 and 50 wppm solutions of 8-M PEO (fluids 1, 3, 4) with identical slurry flow rate and pressure. (b) SEM image of the channel machined with the slurry containing 50 wppm of 8-M PEO (fluid 4). (c) The decrease of channel widthtop width with 8-M PEO concentration.
Fig. 8. Stagnation point regions where normal stresses create an extra drag on a particle approaching the target.
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because Section 3.2 showed that a 10% increase in viscosity did not change the top width. The depth decrease of 46% relative to the water-only case, was the sum of the effects of viscosity and normal stresses. A 19% reduction was caused by the increased viscosity, as shown by Fig. 5 for the glycerin/water mixture. Because the 50 wppm solution had the same shear viscosity as the glycerin solution (Table 1), the additional 27% decrease in depth with this fluid must have been caused by normal stresses. Such stresses can reduce the energy of a particle close to the target as the fluid velocity approaches zero. Fig. 8 shows stagnation-point regions where normal stresses are generated, at the front of a particle and at the impact point on the target. The induced stresses create an additional resistance to motion, thereby further decelerating the particle. The decreased channel top width produced with the polymer solutions could have been the result of changes in the jet velocity distribution. However, this possibility is unlikely, because Goren and Norbury [28] and Barker [29] found that the velocity profile in turbulent jets of aqueous PEO solutions did not change significantly. It is therefore more likely that fluid elasticity reduced the jet footprint in the stagnation region by focussing the streamlines and decreasing the spread of the flow. The stagnation region of a Newtonian jet impinging on a flat surface has hyperbolic-like streamlines (Fig. 6) and a uniform extensional strain rate throughout [30]. In this flow field, the stretch of a polymer chain depends on its residence time, which increases with proximity to the stagnation point. Consequently, elastic effects increase in streamlines that are progressively nearer to the stagnation point. This behavior has been confirmed by Muller et al. [31] who used optical birefringence to show that the degree of chain extension in a dilute high-molecular-weight polymer solution was maximum near the stagnation point. Given that polymer chains resist flow extension in proportion to the amount by which they are stretched, streamlines leaving the stagnation point spread less, causing the impacting particles to strike closer to the centreline. That is, the jet is more focussed (Fig. 9), decreasing the channel top width and causing cross-sectional profiles with more curvature at the bottom of the channel. When the slurry had a concentration of 75 wppm of the same PEO (solution 5), the channel top width increased by 5%, contrary to the trend of Fig. 7(c) where the top width decreased as the concentration increased. The increase was caused by a jet instability that resulted in a 40 μm amplitude oscillation, producing an effective jet diameter of 220 μm. This was measured by capturing microscope images having a field of view of 3 2 mm for 10 s at a frequency of 29 Hz, and then extracting the position of the jet from each frame. The amplitude of the oscillation decreased with decreasing 8 M PEO concentration, becoming 20 μm for the 50 wppm fluid. Without the PEO, the jet had the same diameter (140 μm), and did not oscillate. Furthermore, the jet containing glycerin did not oscillate. Rothstein and McKinley [32] found that instabilities in non-Newtonian jets can result from randomly fluctuating vortices formed upstream of a sharp orifice. In the
Fig. 9. Comparison of particle impact angle in a polymeric solution (θ) and water (ϕ).
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Fig. 10. Cross-sectional profiles of a single-pass channel machined with the wateronly slurry (fluid 1) and with three passes with the 50 wppm 8 M PEO solution (fluid 4).
present work, avoiding this instability limited the concentration range for each polymer molecular weight. The experiments were extended to include additional scanning passes. Fig. 10 shows that a second and a third pass with the same 50 wppm of 8 M PEO solution (fluid 4) had no effect on the top width, but increased the channel depth by 35% and 106%, respectively, resulting in a total depth 10% larger than that of the reference channel. Therefore, the reduction in depth brought about with PEO solutions can be compensated for by additional machining passes without affecting the decreased top width. This, of course, increases the machining time. Another machining characteristic of interest was centerline surface roughness. In the present experiments, channel roughness was measured along the centreline for 5 mm using an optical profilometer, and the data were analyzed with a cut-off length of 800 μm according to the ISO 4288 [33] standard. The average centerline roughness, Ra, was relatively constant for a given set of machining conditions, varying by less than 7% along a single channel, and between three separately machined channels. The Ra values using water and the glycerin/water mixture (fluids 1 and 2) were both approximately 0.5 μm, while the centerline roughness from a single pass with the 50 wppm 8 M PEO solution was 0.7 μm. A t-test analysis showed that the difference between these values was statistically significant with a confidence interval of 95%. Micrographs of the two surfaces are presented in Fig. 11, which shows that the surface of the channel machined with the PEO solution (Fig. 11c) was significantly coarser than that of the channel machined with water alone (Fig. 11b). Since roughness increases with the normal impact velocity component as discussed, for example, by Slikkerveer et al. [23], the difference is believed to be caused by the focusing effect discussed earlier and shown in Fig. 9. Since glycerin had a negligible focusing effect, it did not increase the roughness.
3.3.2. Tests with the 1 M PEO Fluid elasticity increases with molecular weight, because longer chains generate more tension and thus produce larger normal stresses, as described by Bird et al. [25]. With shorter chains, lower effects are expected, and these effects were assessed in the present work by using 1 M PEO. Concentrations with this polymer were varied up to 400 wppm, at which point the jet became unstable. As shown by Fig. 12, (i) a 25 wppm solution (fluid 6) had no significant effect on the channel top width, but decreased the channel depth, relative to the reference channel, by 32%; (ii) a 200 wppm solution (fluid 7) reduced the top width by 13% and the depth by 39%; and (iii) when the concentration was 400 wppm (fluid 8), the jet was unstable and its larger effective diameter due to the lateral jet oscillation caused the top width to increase by 7%.
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Fig. 11. SEM images of surfaces in the central regions of channels, indicated by the rectangle in (a), machined using: (b) water-only slurry (fluid 1) and (c) water with 50 wppm of 8-M PEO (fluid 4).
Fig. 12. Cross-sectional profiles of channels machined with the water-only slurry and with three concentrations of 1-M PEO (fluids 1, 6, 7, and 8, Table 1), all with identical slurry flow rate and pressure.
Fig. 14. Cross-sectional profiles of channels machined with the water-only slurry (fluid 1) and a 2.5 wt% solution of 0.1-M PEO (fluid 9) under identical pressure and slurry flow rate.
suggests that normal stresses were larger with the 8 M PEO slurries even though polymer concentrations were much lower. Therefore, the polymer focussing effect depends more strongly on molecular weight than concentration, a finding consistent with other flows containing polymer additives [34].
Fig. 13. Percentage change decrease in channel widthtop width relative to the water-only slurry, for the 8-M and 1-M PEO solutions. The dashed lines are only to help guide the eye.
These data with 1 M PEO solutions confirm that, with a stable jet, the polymer caused both the channel depth and top width to decrease, as was found with the 8 M solutions. Fig. 13 compares the change in the channel top width obtained with the two highest molecular-weight polymers, over their range of concentrations. The maximum for each curve corresponds to the onset of jet instability and the transverse oscillation it produced. This instability began at a substantially higher concentration for the 1 M PEO solution than for the 8 M PEO solution, and below these concentrations the channels made with the 1 M PEO were significantly wider than those machined with the 8 M PEO. This result
3.3.3. Test with 0.1 M PEO To further probe the effect of molecular weight, channels were machined with a slurry containing the lowest-molecular-weight PEO, the 0.1 M sample (fluid 9). This short-chain polymer increased the shear viscosity significantly, as Table 1 indicates, and thus the channel depth was reduced considerably, as Fig. 14 shows. But, even at a concentration of 2.5 wt% (25,000 wppm), the channel top width was unchanged and elasticity-induced jet oscillations were absent, re-confirming that polymeric effects depend more strongly on molecular weight than concentration. Because the top width was not affected, the shallow depth appears to have been caused solely by this fluid's higher viscosity; i.e. 9 mPa s versus 1.1 mPa s for the other PEO solutions (Table 1). Similar to the findings of Ashrafi [9], the present “elastic” solutions resulted in decreased channnel top widths. However, the present data showed that significant top width reductions for a given jet diameter can be obtained with merely trace amounts of a high-molecular-weight polymer, compared with the much more concentrated solutions used by Ashrafi [9]. Moreover, our experiments showed that higher concentrations caused jet lateral instabilities, which made the channels wider. 4. Summary and conclusions An abrasive slurry jet micro-machining (ASJM) system was used to investigate the effects of polyethylene oxide (PEO), of varying
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molecular weight and concentration, on the shape, top width, and centerline roughness of micro-channels machined in borosilicate glass. The flow of these non-Newtonian fluids containing long-chain polymers is known to be affected by both their viscosity and their resistance to extensional deformation (i.e. their “elasticity”). For the first time, the effects of viscosity and elasticity on the erosion produced by such a non-Newtonian abrasive slurry were separated by comparing the erosion results to those obtained with an aqueous solution of glycerin, which had a viscosity equal to that of the PEO solutions. A reference channel was machined with water and particles only. Under otherwise identical conditions, machining with a 50 wppm solution of the 8-million (8 M) molecular weight PEO decreased the channel top width by 21%, decreased its depth by 46%, and increased its centerline roughness by 29%. The channel machined with the PEO solution also had more of a V-shape than the U-shape obtained with the water-only slurry. These changes were attributable to the effect of both viscosity and elasticity. For channels machined with the glycerin/water slurry that had the same viscosity as the 8 M PEO solution, but which had no elasticity, the top width remained unchanged relative to the water-only slurry, and only a 19% decrease in depth was observed. Therefore, increasing only the viscosity of the slurry decreased the channel depth, but left the top width unchanged. The decrease in channel top width with increasing PEO concentration, and hence elasticity, was attributed to a reduction in the spread of the jet in the stagnation region. The elasticity also decreased the channel depth by reducing the impact velocity of the abrasive particles. About 40% of the depth decrease relative to the water-only channel for the 50 wppm 8 M PEO solution could be attributed to increased viscosity, while the remaining 60% was evidently due to elasticity. An additional pass of the 8 M PEO was found to increase the channel depth without changing the top width or the roughness. Similar changes in channel shape, top width, and depth were seen in channels machined with 1 M PEO in larger concentrations, but the changes were smaller. With the lowest molecular weight PEO, 0.1 M, a concentration of 2.5 wt% did not change the channel top width, but decreased the depth by 83%. This is consistent with the literature which indicates that short-chain polymers increase the viscosity, but generate little fluid elasticity. When PEO was added, the jet was stable until an upper limit in concentration was reached. Above this limit, the jet oscillated laterally at a high frequency, and thus its effective diameter increased. This polymer concentration limit decreased with increasing molecular weight. Further decreases in channel top width for a given jet diameter may be possible using orifice designs that preserve the stability of a jet at higher polymer concentrations. Acknowledgments The authors acknowledge the Natural Sciences and Engineering Research Council of Canada, Micralyne Inc. and BIC Fuel Cells Inc. The authors thank Hooman Nouraei for assisting with the design and construction of the apparatus. References [1] D.S. Miller, Micromachining with abrasive waterjets, J. Mater. Process. Technol. 149 (2004) 37–42. [2] K.L. Pang, T. Nguyen, J.M. Fan, J. Wang, Machining of micro-channels on brittle glass using an abrasive slurry jet, Key Eng. Mater. 443 (2010) 639–644.
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