JOURNAL OF MICROELECTROMECHANICAL SYSTEMS 1 …

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS 1

Rotary Liquid Droplet MicrobearingBrian E. Yoxall, Member, IEEE, Member, ASME, Mei-Lin Chan, Member, IEEE, Ryan S. Harake,

Tingrui Pan, Senior Member, IEEE, and David A. Horsley, Member, IEEE

Abstract—A rotational stage with a 10-mm-diameter single-crystal silicon rotor supported by liquid droplet ball bearingsis described. The 100–300-μm-thickness droplet bearings are re-tained on the rotor surface with a micropatterned amorphous-flouropolymer-based superhydrophobic (SHP) surface coatingthat yields a 156◦ contact angle. The droplets slide on a SHPbearing raceway that is formed from laser-roughened poly-dimethylsiloxane (PDMS) on the surface of the stator, achievinga 10◦-contact-angle hysteresis that results in very low slidingfriction. The stage is driven by a rotating external magnetic fieldthat provides up to 3 μN · m torque through a permanent magnetmounted on the rotor. The liquid bearing provides a passivewear-free interface between rotor and stator with a measureddrag coefficient of 0.94 · 10−3 μN · m/r/min, rotating up to aspeed of 2400 r/min, and a mean minimum operating torque of0.3 μN · m. The bearing design is stable in position and tip/tilt,with a tip mode stiffness of 5.4 μN · m/deg and measured nonre-peatable rotor wobble of 0.3 mrad. The experimentally measuredbearing stiffness, drag coefficient, and startup torque are shown tocompare well with values predicted from analytical models basedon surface tension forces on the droplet bearings. [2011-0268]

Index Terms—Capillary force, friction, liquid bearings, mi-croactuators, microelectromechanical systems (MEMS), rotarystage, superhydrophobic (SHP), surface tension.

I. INTRODUCTION

EXISTING microelectromechanical systems (MEMS) rota-tional platforms and micromotors suffer from friction is-

sues limiting their capability and useful lifetime; representativedevices include center-pinned electrostatic wobble motors [1],[2] and ultrasonic [3], [4] and magnetic [5] drive motors. Nu-merous attempts to alleviate wear and friction in rotary deviceshave been presented, including micro-ball bearings [6], [7],externally pressurized dynamic air bearings [8], and contact-free bearings created by electrostatic or magnetic suspension[9], [10], but these efforts either maintained wear-inducingsolid–solid contact or require externally powered actively con-trolled bearings. McCarthy et al. [11] provide a detailed dis-cussion of the advantages and shortcomings of various bearingschemes for rotary stage support.

Liquid bearings have been demonstrated as a passivelow-friction low-wear rotary stage support [12]–[14]. Our

Manuscript received September 9, 2011; revised December 15, 2011; ac-cepted January 10, 2012. This work was supported by the Defense AdvancedResearch Projects Agency under Grant W31P4Q-10-1-0002. Subject EditorR. Ghodssi.

The authors are with the University of California, Davis, CA 95616 USA(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2012.2185218

Fig. 1. Expanded schematic of the liquid bearing design demonstrated in thiswork. A Si and Cytop micropillar patterned SHP coating on the rotor definescenter and satellite liquid bearing droplets. A laser-etched nanofeatured PDMSSHP coating on the stator aligns the bearing to the stator.

previous [15] work demonstrated a self-centering wear-resistantliquid bearing technology capable of supporting both staticand dynamic loads. Magnetic drive was used in testing theperformance of the rotary stage, which is similar to [5] and[16]. Characterization of minimum torque requirements andmaximum rotation rates for three liquid bearing designs (disk,ring, and full bearings) using two fluids (water and ethyleneglycol) demonstrated good agreement between measurementand rotational viscous friction models. Previous liquid bearingshave been demonstrated [12]–[14] but were unstable in tip/tilt,or only developed stability when rotating at significant speeds.A critical requirement of successful bearing design is the abilityto support out-of-plane loads and to provide sufficient tip/tiltstiffness to accommodate forces and torques generated by theactuation system. Bearing stiffness is highly important in thecase of electrostatic actuation where the rotor is prone to snap-in instability: actuation electrodes around the perimeter of therotor act to decenter the rotor while electrodes beneath the rotoract to tip or tilt the rotor.

This paper presents a liquid bearing design, using wateras the working fluid, that is stable under tip/tilt loading. Thebearing design is analogous to a ball bearing in which the solidballs are replaced by liquid droplets arranged in a satellite con-figuration around a central anchor droplet, as shown in Fig. 1.The satellite droplets are fixed to the rotor using a patternedhydrophobic surface coating but slide across a hydrophobiccoating on the stator that acts as the bearing raceway. Thecenter droplet is fixed to both the rotor and stator throughhydrophobic patterning and maintains axial alignment betweenthe rotor and stator. Superhydrophobic (SHP) coatings arerequired to successfully retain the satellite droplets on the rotorand to permit sliding of the droplets across the stator raceway.

1057-7157/$31.00 © 2012 IEEE


2 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS

Fig. 2. Micropillar dimensions W , H , and P and roughness factor Rf

calculation used for Cassie–Baxter and Wenzel contact angle models.

Design and selection of the SHP coatings are discussed, andmaterial properties are characterized. Bearing friction andtip/tilt stiffness are experimentally measured and comparedwith the predictions of analytical models.

II. THEORY

A. SHP Coatings

Hydrophobic surface coatings have been used in manyMEMS applications, e.g., as an antistiction coating [17], [18],for drag reduction in microfluidics [19], [20], as critical surfacecoatings for droplet-based microfluidics [21], for biosensing ap-plications [22], and in optical displays and lenses. Hydrophobicsurfaces can be constructed using low-surface-energy coatingsthat can be spun on, chemical vapor deposited or self-assembledonto the substrate. The hydrophobicity of a surface can alsobe improved by increasing surface area through increasingsurface roughness. Microstructures on the surface form cavitiesor pockets in which air can be trapped, creating a compositesolid–air–liquid interface that increases contact angle comparedto a smooth interface with contact angle θo.

Two parameters critical to a SHP surface (contact angle150◦ < θc < 180◦) are surface roughness and surface energy.The Cassie–Baxter and Wenzel models predict the contact an-gle for square micropillars, as depicted in Fig. 2. The roughnessfactor Rf is defined as the ratio of solid–liquid area to itsprojection on a flat plane, which is expressed as

Rf = 1 +4WH

P 2(1)

where W is the width, H is the height, and P is the pitchbetween the pillars.

The Wenzel model, which assumes that the droplet is in totalcontact with the rough surface with no air pockets, predicts thecontact angle θc as [23]

cos θc = Rf cos θo. (2)

The Cassie–Baxter model modifies the Wenzel model byassuming air pockets in the rough surface and considers thecomposite interfaces involving both liquid–air and solid–air

Fig. 3. Schematic representations of (a) the patterned regions whose surfaceenergy defines the liquid bearing retention area and (b) and (c) restoringforces Fnormal and Fshear induced in a droplet between parallel plates duringloading, respectively.

interfaces by including the contribution from the fractional areaof the wetted surfaces fSL as well as the fractional area with airpockets 1 − fSL [24], i.e.,

cos θc = RffSL cos θo − 1 + fSL. (3)

The fractional area of the solid–liquid interface fSL for thesquare pillars can be described as

fSL =W 2

P 2. (4)

B. Forces for Droplets Between Parallel Plates

When transverse and normal forces are applied to the rotor,the surface tension for the fluid bearing produces restoringforces, as shown in Fig. 3. An analytical model of restoringforce Fnormal for a droplet in compression or tension betweentwo parallel plates is developed [25], [26] as a function ofsurface energy γLV, distance between plates h, droplet radiusR, and contact angle θc, i.e.,

Fnormal =2πR2γLV

hcos θo + 2πRγLV sin θc. (5)

Under shear loading, the droplet deforms, and the contactangle around the perimeter varies from θL on the left sideto θR on the right. An analytical model of shear restoringforce Fshear for a droplet in shear between two parallel platesis [27], [28]

Fshear =√

2RγLV(θR − θL). (6)

C. Magnetic Drive

Liquid bearing performance is characterized using magneticactuation to spin the rotary stage. Two orthogonal pairs ofHelmholtz coils driven 90◦ out of phase, at matched amplitudes,create a rotating magnetic field B used to spin the rotor. Thefield magnitude is in the range of 1 mT.

For applied magnetic field B and rotor magnetic momentm, the torque on the rotor is described by (7). Because boththe field amplitude |B| and the moment |m| are directly mea-sureable, it is possible to apply a well-controlled magnetictorque to the rotor. Maximum torque is achieved when the


YOXALL et al.: ROTARY LIQUID DROPLET MICROBEARING 3

Fig. 4. (a) Satellite bearing retention locations defined by SHP micropatterns.(b) Cross section A–A showing relationship of rotor, liquid bearings, and stator.(c) Mechanism for tip/tilt restoring torque given induced rotor tilt.

angle φ between B and m is 90◦ and is simply the productmax(τapplied) = |B||m|, i.e.,

τapplied = m⇀ × B

⇀

= |m||B| sin φ. (7)

D. Satellite Bearing Tip/Tilt Restoring Torque Model

The use of satellite droplet bearings improves rotary stagestability by producing a restoring torque to correct tip and tiltof the rotor relative to the stator. The satellite droplet designutilizes eight small droplets near the rotor edge to produce therestoring torque and a single central droplet that maintains axialalignment between rotor and stator, as shown in Fig. 4(a).

Fig. 4(c) illustrates the tip/tilt restoring torque. When anexternal torque induces tilt on the rotor, the right-hand satellitedroplet’s contact angle increases, while the left-hand droplet’scontact angle decreases. Based on (5), the normal restoringforce increases with contact angle. The tip/tilt restoring torqueτtip is the sum of the normal force Fi,normal multiplied bythe distance to the axis of rotation Li,SB for each of the eightsatellite droplets, i.e.,

τtip =8∑

i=1

Fi,normalLi,SB. (8)

E. Satellite Bearing Startup Torque Model

Minimum startup torque for the satellite droplet bearingsupported rotor is a function of the shear restoring force from(6). The satellite droplets are pinned to the rotor by the pat-terned surface. When the shear force generated by the externaltorque exceeds the maximum shear that the satellite dropletscan withstand, the satellite droplets slide across the surface ofthe stator SHP coating.

The contact angles θR and θL correspond to the advanc-ing and receding contact angles (θadv and θrec, respectively)specific to the stator surface treatment and liquid used in the

bearing. The startup torque τstartup is the sum of the shearrestoring force Fi,shear multiplied by the distance to the axisof rotation Li,SB for each satellite droplet, i.e.,

τstartup =8∑

i=1

Fi,shearLi,SB. (9)

F. Rotational Drag Coefficient

Measuring the maximum rotation rate as a function of inputtorque allows direct identification of the drag coefficient for theliquid bearing. Equation (10) is a second-order model of therotary stage, where I is the moment of inertia for the rotor,bdrag is the rotational drag coefficient, and k is the rotationalstiffness of the liquid bearing. θ, ω, and α correspond to angularposition, velocity, and acceleration, respectively, and τinput

is the input torque. Based on a previous study of the liquidbearing drag coefficient [15], (10) assumes that the drag termdepends linearly on rotation rate. When the rotor is spinning,the liquid bearing provides no restoring force, and therefore,k = 0. At steady-state rotation, angular acceleration α = 0, and(10) simplifies to (11), i.e.,

τinput = Iα + bdragω + kθ (10)

τSS = bdragω. (11)

III. FABRICATION

In this paper, two different SHP surfaces are created onthe silicon (Si) rotor and glass stator. For the Si rotor, mi-crostructures are etched onto the Si wafer to create a texturedsurface, and a spin-on fluoropolymer is then applied to givethe microstructure a low surface energy. The stator surface is aspin-on polydimethylsiloxane (PDMS) photoresist coating thatis roughened using a laser beam.

A. Si Rotors With SHP Cytop Coating

Many studies demonstrate fabrication techniques to produceroughness on Si substrates [29]–[31]. In this paper, the focus isto create microstructure arrays compatible with the standard mi-crofabrication process steps for the liquid bearing rotary stage,where a more resilient SHP coating is required to withstand thesubsequent processing steps. The rotor is fabricated from singlecrystal Si. In Fig. 5 (numbers 1, 2, and 3), the rotor topside isdefined with a photoresist layer and etched using a deep reactiveion etcher (DRIE, Alcatel 601E). In Fig. 5 (numbers 4, 5, and 6and inset A), the microstructures on the rotor bearing surfaceare defined with photoresist and DRIE etched to a depth of∼10 μm. An acetone rinse and oxygen plasma cleaning step iscarried out to remove remaining photoresist. In Fig. 5 (numbers7, 8, and 9), the Cytop (Asahi Glass) layer is deposited by spincoating (∼1000 r/min) over the Si microstructures. Finally, inFig. 5 (numbers 10, 11, and 12), the rotor is released from thewafer by through wafer DRIE. After removing photoresist inFig. 5 (number 12), the rotor bearing surface has hydrophobic



Fig. 5. Fabrication process flow for SHP rotor.

Fig. 6. PDMS SHP coating fabrication. (a) Spin- or cast-coated PDMSprepolymer on glass. (b) Laser etch to create nanostructured SHP coating.(c) Laser ablation of PDMS to define hydrophilic droplet retention regions.

regions of Cytop on Si microstructures (shown in inset B) andflat Si elsewhere.

The rotor is a 10-mm-diameter disk etched from a 300-μm-thick Si wafer. Photoresist and DRIE etch form frontsidefeatures for permanent magnet alignment, as well as backsidefeatures. As described above, the backside microstructurescovered with Cytop create the rotor SHP droplet confinementregions. Finally, the disks are patterned and released by DRIEthrough-wafer etch.

B. Stators With Laser-Etched PDMS SHP Coating

Two stator designs were tested based on the fabricationmethod described in [32]. The stators consist of a glass slidespin or cast coated with a 50-μm-thick PDMS prepolymerlayer (10:1 mix of PDMS precursor with curing agent, Sylgard184) that is laser etched (at 11 mm/s scan speed and 1.1 Wpower, Universal Laser) to create a nanofeatured SHP surface,as shown in Fig. 6. Laser ablation of the PDMS surface createshydrophilic regions for droplet retention. The contact angleof the surface depends on the parameters of the laser etchingprocess. To demonstrate the effect of contact angle on bearingperformance, two surfaces were tested: one formed with opti-mized etch parameters, shown in Fig. 7(a), with surface featureson the order of 100 nm in width, and a second formed using anunderpowered etch, shown in Fig. 7(b), with minimum featuresof ∼1 μm width.

Fig. 7. SEM image of (a) optimally etched stator SHP surface and(b) underetched surface. The scale bar for (a) is 10 μm and for (b) is 5 μm.The field of each SEM image is approximately 30 μm wide.

Fig. 8. Image of the rotor, stator, and liquid bearings during assembly process.Clearly visible are the eight satellite bearings and single central bearing, thestator SHP coating with patterned anchor location for central bearing, and thevacuum pick-and-place tool head.

C. Assembly

Deposition of the liquid H2O droplets onto the rotor is donemanually by a micropipette. The rotor is then aligned andplaced onto the stator by a vacuum pick-and-place tool attachedto a six-axis stage with micrometer positioning capability. Therotor, with eight satellite droplets and a single central anchordroplet, is suspended over the stator surface by a vacuumtool head, shown in Fig. 8. The high surface tension of waterprovides stiffer restoring forces. Initial rotor tilt varies due toinconsistency in manual micropipette deposition of satellitedroplet volumes; eight satellite droplets balance assembly ro-bustness with performance loss.

The PDMS SHP coating is visible on the stator surface withthe smooth hydrophilic region to anchor the center droplet.

IV. TEST AND CHARACTERIZATION DATA

A. SHP Coatings

An experimental study of patterned Si surfaces with variousheights H , widths W , and pitches P , as shown in Table I, wasconducted to investigate the dependence of the contact angle θc

on the geometrical parameters. The results show that smallerstructures with higher aspect ratio result in an increased su-perhydrophobicity. All of the microstructured geometries showbetter performance than Cytop coated Si with no microfeatureswhich has a static contact angle θo of ∼98◦.

Scanning electron microscopy (SEM) was used to image thecross-sectional profile of the structures in Table I to determinetheir dimensions. The experimental data are plotted against theWenzel and Cassie–Baxter models in Fig. 9. The measuredcontact angle increases with the roughness factor, following thetrend of both models, but lies between the predicted contact



TABLE ISUMMARY OF THE VARIOUS GEOMETRIES USED IN Si AND CYTOP SHPSURFACE TESTING. COLUMN 1 SHOWS OPTICAL MICROGRAPHS OF THE

ETCHED Si MICROSTRUCTURE GEOMETRIES, AND THE WHITE SCALE

BAR IN EACH FIGURE INDICATES 25 μm. COLUMN 2 LISTS THE

GEOMETRICAL PARAMETERS. COLUMN 3 IS THE AVERAGE OF THREE

MEASURED CONTACT ANGLES TAKEN AT DIFFERENT LOCATIONS ON

THE DIE

angles from the two models. The deviation from the predictedCassie–Baxter model for a composite interface can be attributedto the surface defects resulting from the spin coating of theCytop layer.

An SEM image of the micropillars after Cytop coating,shown in Fig. 10(b), has prominent bumps and grooves at thesidewalls of the pillars. These bumps/grooves have been shownto create stable/unstable equilibrium points at the liquid-airinterface, causing variations in the resulting contact angles [33].

Much higher contact angles have been reported by generatingnanoscale roughness on Si substrates [34] or using a two-tier roughness profile [35]. These techniques pose tremendouschallenges when incorporated with other steps in our fabrica-tion process to develop a functional device with high yield.Therefore, the rotor SHP surface for our devices is confinedto a minimum feature size of 2–3 μm and an aspect ratio ∼4.

Fig. 9. Plot of the predicted and measured contact angle of water on Si waferpatterned with micropillars. The experimental results ( ) follow the trend ofboth the Cassie–Baxter ( ) model and Wenzel ( ) model, where increasingroughness factor results in an increase in contact angle. (Inset) Illustration of thecross-sectional and top view of the micropillar and the geometrical parametersused for roughness factor calculation.

Fig. 10. Micropillars etched in Si (a) before and (b) after coating with a Cytopflouropolymer to create SHP surface.

Fig. 11. Water droplets on the SHP cytop on Si pillar coating used on the rotor(a) in the static condition and (b) immediately prior to sliding to the right. Thedifference between advancing and receding contact angles in (b) is 3.5◦.

The SHP surface from the study that performed best, shown inthe last row of Table I, was selected for fabrication on the rotor.

Static contact angle for a water droplet on the micropat-terned Si rotor is shown in Fig. 11(a); advancing and recedingcontact angles induced by tilting the rotor relative to gravityand measuring immediately prior to droplet sliding are shownin Fig. 11(b). Fig. 12 shows advancing and receding contactangle on the laser-etched PDMS-coated glass stator for the (a)optimized and (b) underpowered etch coatings. The optimizedetch parameter stator SHP coating has a difference betweenθadv and θrec of 10◦, while the underpowered etch parameterSHP coating had a contact angle difference of 44◦.



Fig. 12. Advancing and receding contact angle measurements immediatelybefore droplet sliding for (a) optimally etched PMDS are 10◦ and 20◦,respectively, and for (b) underpowered etch PDMS coatings are 10◦ and 54◦,respectively.

Fig. 13. Side view of the rotor supported on liquid droplets. Droplets inimage are much thicker (∼1 mm) than those used in testing (∼100−300 μm).A neodymium magnet is epoxied to the top rotor surface and used for bothspinning torque tests and tip/tilt tests.

Fig. 14. Plot of test data, analytical model, and linear data fit for satellitebearing tip/tilt stiffness measurement.

B. Satellite Bearing Tip/Tilt Tests

The test bearing setup used for testing tip/tilt stiffness andsubsequent rotational torque tests is shown in Fig. 13. Thedroplets in the image are much thicker than those used for thepresented data to aid in visibility.

The satellite bearings stiffness determines stability for therotary stage in response to external forces created by the rotorpayload or the actuation system. To measure the stiffness, atip/tilt torque was applied to the rotor using a sinusoidallyvarying magnetic field and the rotor tilt angle was calculatedfrom optical measurement of satellite bearing thickness. Themaximum tilt angle versus maximum torque for the test isplotted in Fig. 14 for satellite bearings with uncompressedthickness of ∼250 μm and 75 μm radius at the rotor surfacedefined by the SHP coating pattern. The inverse slope of the

Fig. 15. Startup torque versus bearing thickness for an optimized statorcoating and underpowered etched coating.

linear fit of the measured data gives the tip/tilt stiffness to be5.4 μN · m/deg.

The analytical model described in (5) and (8), for the geom-etry of the bearing described in the test data, is plotted againstthe test data and shows good agreement. Deviation between testdata and model is due to nonideal initial bearing volumes andexcessive bearing deformation at high tilt angles.

C. Satellite Bearing Minimum Startup Torque

Minimum startup torque was measured for the two statorcoatings at a range of bearing thicknesses, as shown in Fig. 15.Variation in the startup torque derives from small differencesin the initial droplet position on the rough surface of thestator SHP coating. Measured mean startup torque values are0.315 μN · m for the optimized coating and 1.4 μN · m forthe underpowered etch coating. The mean values match withmodel predictions from (9) based on the measured contact angledifference of 10◦ and 44◦, respectively, and test parameters R =0.75 mm, n = 8, γLV = 72.8 · 10−3 N/m, and LSB = 2.75 mm.

D. Maximum Rotation Rate and Drag Coefficient

Determination of the drag coefficient is based on the modeldescribed in (11). Steady-state drag torque τSS is a functionof the bearing drag coefficient bdrag and the rotation rate ω.The magnetic drive system torque is described in (7), with amaximum drive torque achieved when the phase angle betweenthe rotor and magnetic field is 90◦. For this test, the steady-state rotation rate is incrementally increased, until τSS exceedsτapplied, at which time the rotor ceases to rotate. The maximumrotation rate is plotted as a function of input torque in Fig. 16for a 300-μm-thick bearing. The slope of the linear data fit givesa measurement of 1/bdrag. For the device measured, bdrag =0.94 · 10−3 μN · m/r/min, which is an improvement of 21%over [14] and within a factor of 5 of the 0.2 · 10−3 μN · m/r/minfriction torque constant reported for thrust-balanced micro-ballbearing rotors [7].



Fig. 16. Maximum rotation rate versus input torque for a 300-μm-thickbearing. Slope of the test data linear fit is equal to 1/bdrag and gives a dragcoefficient of 0.94 · 10−3 μN · m/r/min.

Fig. 17. Wobble measurement for the satellite bearing supported rotor. Non-repeatable wobble is 0.3 and 0.2 mrad for the x- and y-axis, respectively.

E. Wobble

Wobble is a measurement of the out-of-plane rotation of therotor normal relative to the stator normal. The measurementis performed by reflecting a laser off the surface of the rotorat approximately 45◦ to the stator normal and collecting thereflected beam in a position sensing diode and then calculatingthe rotor motion using the beam path length.

Wobble measurement data are plotted in Fig. 17. Repeatablewobble due to volume mismatch between the satellite bearingsis 5 mrad in the x-axis and 2 mrad in the y-axis. Nonrepeatablewobble, which is due to stator roughness and vibration of therotor on the bearings, is 0.3 and 0.2 mrad in the x- and y-axis, respectively, corresponding to a vertical displacement atthe rotor edge of 1.5 and 1.0 μm. This wobble is attributable tothe micrometer-scale surface roughness of the laser-roughenedstator SHP coating on the stator surface.

TABLE IIOPERATING SPACE FOR CONTACT-FREE ROTARY STAGE BEARING

DESIGNS BASED ON THE METHOD USED TO PROVIDE CENTERING

OF THE ROTOR RELATIVE TO THE STATOR

V. DISCUSSION

Previously reported rotary rotary stages that operated withoutany solid–solid contact between rotor and stator have beenlimited in their operating range or through their use of activelycontrolled centering mechanisms. Table II shows the relation-ship between bearing centering forces and the operating spacefor each of them.

The surface tension based liquid bearing technology is theonly passive noncontrolled method that provides static cen-tering capability. Both surface-tension- and minimum-energy-based designs [14] provide centering at low rotation rates.Externally pressurized gas bearings [8] operate in a range fromtens of revolutions per minute to very high rotation rates.

Magnetic and electrostatic [9], [10] supported air bearingrotary motors operate at a range of rotation speeds, but activelycontrolled fields are required for stability introduce complexityin implementation.

An ideal rotary stage bearing design will cover the operat-ing space, providing passive positioning capability free fromsolid–solid friction and wear that allows operation from zero to106 r/min and higher rotation rates. To date, no device is able toachieve all the desired characteristics.

The satellite-droplet-based liquid bearing design character-ized here operates in the static to low-speed range with lowfriction and a stable bearing geometry. Development of pat-terned SHP coatings maintains the geometry of droplets andprovides the low drag interface. The highest rotation rate isa function of liquid drag, bearing geometry, and input torque.Future development should involve reducing the rotary stagesize and bearing thickness, developing onboard drive methods(either electrostatic or magnetic) and optimizing the bearinggeometry for lateral and tip/tilt stiffness.

VI. CONCLUSION

Liquid bearing technology extends the operating space ofrotary stages by providing low-friction, wear-free, passive, sta-ble translational, piston, and tilt mode reference between rotor



and stator, all in a design with no solid–solid interfaces. Byeliminating sliding and rolling friction forces, the performanceof the technology is improved compared with other frictionreduction methods in the static to medium revolutions perminute operating range. Characterization of the liquid bearingdemonstrated minimum startup torque at 0.3 μN · m, rotationaldrag coefficient at 0.94 · 10−3 μN · m/r/min, and maximumrotation rate at 14 400◦/s for an input torque of 2.3 μN · m.The measured drag and startup torque agree well with thepredictions of a model based on surface tension forces on theliquid droplets.

Tilt stability and stiffness are particularly important factorsthat must be considered during drive mechanism selection anddesign. The tilt stiffness of the satellite bearing design wasmeasured at 5.4 μN · m/deg. Tilt stiffness measurement andanalytical models provide the design tools needed for predictingpull-in instability threshold gaps and voltages.

Two SHP coatings are demonstrated and characterized inthis paper. The rotor SHP coating consists of micropatternedSi pillars coated with the amorphous fluoropolymer Cytop thatis compatible with subsequent wafer processing and achieves astatic contact angle of 156◦ and advancing and receding contactangles of 166.0◦ and 162.5◦, respectively. The stator uses alaser-roughened PDMS coating to achieve a static contact angleof 162◦ and advancing and receding angles of 10◦ and 20◦,respectively. The SHP coatings are critical to the ability of liq-uid bearings to provide alignment in five axes (x/y translation,piston, tip, and tilt) while allowing low operating friction in therotational axis of the motor.

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Brian E. Yoxall (M’10) received the B.S. degreein engineering and the M.Eng. degree from HarveyMudd College, Claremont, CA, in 2002 and 2003,respectively, and the Ph.D. degree in mechanicaland aeronautical engineering from the University ofCalifornia, Davis, in 2011.

He was with Lockheed Martin Space Systemsfrom 2003 to 2007 as a Systems Engineer doingvibration control, system integration, and systemtesting before returning to graduate studies. He was agraduate student researcher in the MEMS laboratory

at the University of California, Davis, from 2007 to 2011. He currently is anEngineer working at Lawrence Livermore National Laboratory.

Mei-Lin Chan (M’09) received the B.Eng. andM.Eng. degrees in mechanical engineering from theNational University of Singapore, Singapore, in 2000and 2002, respectively, and the Ph.D. degree inmechanical and aeronautical engineering from theUniversity of California, Davis, in 2010.

She is currently doing postdoctoral research inthe MEMSLab, Department of Mechanical andAeronautical Engineering, University of California,Davis. She was previously a Research Engineer withthe Institute of Materials Research and Engineering,

Singapore. Her research interests include the design, modeling, fabrication, andexperimental characterization of MEMS/NEMS devices for varied applications.

Ryan S. Harake received the B.S. degree in biomed-ical engineering from the University of California,Davis, in 2011, while also completing a minor intechnology management. He is currently workingtoward the M.S. degree in biomedical engineering atthe University of California, Davis.

He is a member of the research team in the Micro-Nano Innovations (MiNI) Laboratory, Department ofBiomedical Engineering, where he has been since2008. As a graduate student, he continues his re-search centered on the design and fabrication of

microfluidic devices for a variety of biological and medical applications.

Tingrui Pan (M’03–SM’06) received the B.Eng.degree in thermal engineering from TsinghuaUniversity, Beijing, China, and the M.S. degree inbiomedical engineering and the Ph.D. degree in elec-trical engineering from the University of Minnesota,Minneapolis.

From 2005 to 2006, he was a Research Scientistin the Department of Ophthalmology, University ofMinnesota. He joined the Department of BiomedicalEngineering, University of California (UC), Davis,in 2006, where he is currently an Assistant Pro-

fessor. He is currently an Editorial Board Member of the Annals of Bio-medical Engineering. His research is focused on interfacial microfluidics,lab-on-a-chip integration, out-of-cleanroom micro-nanofabrication, and multi-functional nanomaterials. Leading an active research laboratory—Micro-NanoInnovations (MiNI) Laboratory (http://mini.ucdavis.edu)—with built-in micro-nanofabrication facility, he has been extending the principles and utilities ofmicro-nanoengineering to a variety of biomedical applications, including diag-nostics and therapeutics of ocular diseases, ultrahigh-throughput biomoleculescreening, tissue and cell engineering, point-of-care diagnostics, biosensing andbiomanipulation, and regenerative medicine.

Dr. Pan was a recipient of a National Science Foundation (NSF) CAREERAward and Xerox Foundation Award and is a corecipient of the NSF EmergingFrontiers in Research and Innovation Award. He founded the UC Davis GlobalResearch and Education in Advanced Technologies (GREAT) Program. He cur-rently cochairs the U.S. Contest of Applications in Nano/Micro Technologies(uCAN).

David A. Horsley (M’97) received the B.S., M.S.,and Ph.D. degrees in mechanical engineering fromthe University of California, Berkeley, in 1992, 1994,and 1998, respectively.

He is an Associate Professor in the Departmentof Mechanical and Aerospace Engineering, Univer-sity of California (UC), Davis, and has been a Co-director of the Berkeley Sensor and Actuator Center(BSAC) since 2005. Prior to joining the faculty atUC Davis, he held research and development posi-tions at Dicon Fiberoptics, Hewlett Packard Labora-

tories, and Onix Microsystems. His research interests include microfabricatedsensors and actuators with applications in optical MEMS, communication,displays, and biological sensors.

Dr. Horsley was a recipient of a National Science Foundation CAREERAward and the UC Davis College of Engineering’s Outstanding Junior FacultyAward.

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