Table of contents

This paper presents a novel design of MEMS logic gate that can perform Boolean algebra the same as logic devices that are composed of solid-state transistors. This MEMS logic gate design inherits all the advantages from MEMS switches and thus is expected to have more applications than MEMS switches. One unique feature of this device is that it can perform either NAND gate or NOR gate functions with the same mechanical structure but with different electrical interconnects. In a prototype design, the device is 250 µm long, 100 µm wide and has 1 µm gap. The experimental results show that this device can operate at 10/0 V and achieve the proposed logic functions. The resonant frequency of the device is measured roughly at 30 kHz. Due to no metal-to-metal contact in the current device, the logic functions of the design are verified through observations and video taping.

In this paper, we study microparticles in liquid suspension streaming around a closed rectangular track and present lateral sorting of the particles into focused streams. The track consists of a two-phase interdigitated electrode array with symmetric electrodes but asymmetric electrode spacing. We demonstrate the ability to consistently focus an initially scattered suspension of mono-size polystyrene particles into a single narrow stream traveling around the circuit. We also demonstrate the ability of the device to separate suspensions of multiple sphere sizes into distinct streams according to size. We report that focusing positions are generally consistent for a given particle size, regardless of the presence of other particles in the suspension, and that particles sort by decreasing size from the center to the edge of the track. These results are compared with finite element analysis of the steady-state electric field and analytical approximations of the electrokinetic forces. We hypothesize that the sorting is due to a balance between phase-based and gradient-based dielectrophoretic forces.

This paper describes a new method for fabricating through-wafer interconnects in atom trapping chips used in ultra-high-vacuum atom-optics cells for Bose–Einstein condensation (BEC) experiments. A fabrication process was developed which uses copper electroplating to seal the vias. The advantages of using feedthrough atom trapping chips are the simple microfabrication process and the reduction of the overall chip area bonded to the glass atom trapping cell. The results demonstrate that 11 A current can be conducted through the vias while the vacuum can be held under 4 × 10⁻¹¹ Torr at room temperature. The yield rate of fabricated via interconnects in this process after anodic bonding (requires heating to 425 °C) is 97%.

Parylene C, an emerging material in microelectromechanical systems, is of particular interest in biomedical and lab-on-a-chip applications where stable, chemically inert surfaces are desired. Practical implementation of Parylene C as a structural material requires the development of micropatterning techniques for its selective removal. Dry etching methods are currently the most suitable for batch processing of Parylene structures. A performance comparison of three different modes of Parylene C plasma etching was conducted using oxygen as the primary reactive species. Plasma, reactive ion and deep reactive ion etching techniques were explored. In addition, a new switched chemistry process with alternating cycles of fluoropolymer deposition and oxygen plasma etching was examined to produce structures with vertical sidewalls. Vertical etch rates, lateral etch rates, anisotropy and sidewall angles were characterized for each of the methods. This detailed characterization was enabled by the application of replica casting to obtain cross sections of etched structures in a non-destructive manner. Application of the developed etch recipes to the fabrication of complex Parylene C microstructures is also discussed.

We present a micromechanical device designed to be used as a non-volatile mechanical memory. The structure is composed of a suspended slender nanowire (width: 100 nm, thickness: 430 nm, length: 8 to 30 µm) clamped at both ends. Electrodes are placed on each side of the nanowire to (1) actuate the structure during the data writing and erasing mode and (2) determine its position by measuring the capacitive bridge in the reading mode. The structure is patterned by electron beam lithography on a pre-stressed thermally grown silicon dioxide layer. When later released by plasma etching, the stressed material relaxes and the beam buckles by itself to a position of lower energy. These symmetric bistable Euler beams exhibit two stable deformed. This paper presents the microfabrication process and analysis of the static buckling of nanowires. Snapping of these nanowires from one stable position to another by mechanical or electrical means will also be discussed.

For further optimization of the automotive power train of diesel engines, advanced combustion processes require a highly flexible injection system, provided e.g. by the common rail (CR) injection technique. In the past, the feasibility to implement injection nozzle volumetric flow sensors based on the thermo-resistive measurement principle has been demonstrated up to injection pressures of 135 MPa (1350 bar). To evaluate the transient behaviour of the system-integrated flow sensors as well as an injection amount indicator used as a reference method, hydraulic simulations on the system level are performed for a CR injection system. Experimentally determined injection timings were found to be in good agreement with calculated values, especially for the novel sensing element which is directly implemented into the hydraulic system. For the first time pressure oscillations occurring after termination of the injection pulse, predicted theoretically, could be verified directly in the nozzle. In addition, the injected amount of fuel is monitored with the highest resolution ever reported in the literature.

An array of micro scanning grating interferometers (μSGIs) with tunable gratings is designed, fabricated and successfully tested for simultaneous static and dynamic displacement measurements. Each μSGI has capabilities of an optical scanning interferometer and in addition, miniaturization has made array operation feasible. All of the μSGIs in an array can actively tune the distances between the gratings and the corresponding samples, simultaneously and independent of the other gratings, to maintain a bias position in a fringe for high displacement measurement sensitivity. The μSGIs are fabricated on silicon-on-insulator (SOI) wafers and the gratings are moved by electrostatic actuation. The fabricated tunable gratings exhibit the first resonance mode at 50 kHz and a small damping ratio of ∼0.05. The gratings show a sufficient (∼500 nm) displacement range for tuning to a high sensitivity position, achieved with a 30 V operating voltage range. Simulation results obtained from the finite element model of the μSGI are in agreement with the experimental results. A control algorithm is implemented in real time in a field-programmable gate array (FPGA) to track the surface and to actively reduce the vibration noise. The use of the FPGA enables parallel and independent control and also operation of two μSGIs. Experimental results show that approximately 40 dB vibration noise reduction is obtained at 100 Hz with the current setup.

This paper reports a new membrane-based pneumatic micropump with new serpentine-shape (S-shape) pneumatic channels intended for achieving high-throughput pumping in a microfluidic system at a relatively low pumping rate and a board flow rate range. The key feature of this design is the ability to modulate the pumping rates by fine-tuning the fluidic resistance of injected compressed air in the designed pneumatic microchannels and the chambers of the micropump. In the study, several S-shape pneumatic micropumps with various layouts were designed and fabricated based on thick-film photoresist lithography and polydimethylsiloxane (PDMS) replication processes. To investigate designs with a suitable pumping performance, S-shape pneumatic micropumps with varied lengths (1000, 5000 and 10 000 µm), varied widths (20, 40 and 200 µm) of the pneumatic microchannel bridging two rectangular pneumatic chambers, and different numbers of pneumatic channel bends (two and four U-shape bends) were designed and evaluated experimentally by using high-speed CCD-coupled microscopic observation of the movement of PDMS membrane pulsation and pumping rate measurements. The results revealed that under the experimental conditions studied, the layout of the S-shape pneumatic micropump with three rectangular pneumatic chambers, 5000 µm long and 40 µm wide pneumatic microchannel and four U-shape bends in the pneumatic microchannel was found to be capable of providing a broader pumping rate range from 0 to 539 µl h⁻¹ compared to the other designs. As a whole, the experimental results demonstrate the use of fluidic resistance of injected air in a pneumatic micropump with S-shape layout to control its pumping performance, which largely expands the flexibility of its pumping application in a microfluidic system.

We present a simple method for fabricating and operating normally open, electrothermally actuated microvalves. These valves are fabricated by placing a gas-permeable elastomeric membrane between two etched glass plates. The reservoirs and channels on one layer are filled with a low melting point polymer (polyethylene glycol, PEG) that exhibits a large volumetric change (of up to 30%) upon phase transition (melting). This volume expansion is used to actuate the membrane and seal the microfluidic channels located in the second etched glass plate. The PEG in the reservoir is heated with integrated patterned platinum-resistive elements. The valve reliably seals the microfluidic channel against external fluid pressures of 10 psi. This valve can be readily integrated with one of the standard technologies for lab-on-a-chip (LOC) fabrication and is suitable for use with the polymerase chain reaction. The novelty of this microvalve lies in the ability to fill dead-end microchannels with a polymer, its self-sealing ability, the ability to remotely actuate the valve by transferring pressure via a microchannel and the compatibility of this microvalve with standard LOC technologies.

This paper demonstrates a novel fabrication process using electro-discharge-machining (EDM) combined with co-deposited Ni-diamond composites to build a unique micro-spherical diamond tool. A micro tool is made by a hybrid process including wire electro-discharge grinding, EDM spherical forming, electrochemical machining and co-deposition. Tungsten carbide material is used as the tool substrate. The influence of EDM spherical forming and co-deposition parameters on the tool geometry is presented. The experimental result shows a unique micro-spherical diamond tool can be successfully built with suitable spherical forming parameters that are a peak current of 3 A, pulse duration of 40 µs and spindle rotational speed of 0 rpm in the air, and in Ni-diamond co-deposition are a current density of 7 A dm⁻², diamond particle size of 3 µm, diamond particle concentration of 10 g l⁻¹ and rotational speed of 15 rpm. When using this method, the micro tool has a better geometric shape, uniform particle distribution and suitable particle adhesion quantity. The tool is tested to machine a mold provided with a micro-spherical cavity in a high nickel alloy.

Piezoelectric polymers have been known to exist for more than 40 years, but in recent years they have been recognized as smart materials for the fabrication of microsensors, microactuators and other micro-electro-mechanical systems (MEMS). In this work, femtosecond laser micromachining of a polyvinylidene fluoride (PVDF) film, coated with NiCu on both sides, has been studied to understand selective patterning mechanisms of NiCu layers and ablation characteristics of PVDF films. A detailed characterization of morphological changes of the laser-irradiated areas has been investigated using scanning electron microscopy. Through morphological analysis, the multiple shot damage thresholds of a 28 µm thick PVDF film and 40 nm thick NiCu layer have been determined. Surface morphology examination indicates that NiCu layers are removed from the PVDF film through a sequence of cracking–peeling off-curling. In addition, the NiCu layer on the rear side was also removed by the partially transmitted laser energy. The PVDF film was removed in forms of bundles of filaments and solid fragments by a combination of pure ablation and explosive removal of material by bursting of bubbles; the role of the explosive removal becomes more dominant with the increase of laser fluence. Optimal process conditions for cutting of the PVDF film and patterning of the NiCu coating without damaging the PVDF polymer have been established and applied to fabricate a vibration microsensor prototype that shows significant potential in using PVDF-based functional microdevices for telecommunications, transportation and biomedical applications.

This paper analyzes in detail the effect of nanoscale non-uniform deflections, caused by the residual stress phenomenon and/or applied actuation dc voltages, on the capacitance in RF MEMS parallel-plate variable capacitors in an effort to determine the severity of this effect on the ideal parallel-plate capacitance expression normally used. Closed-form capacitance expressions and integrals are given for second order, fourth order, elliptic paraboloidal and hyperbolic paraboloidal models of the bending behavior of the top plate caused by the residual stress and/or actuation. The theoretical analysis is then verified using the finite-element modeling method and results from both analyses exhibit excellent agreement. The equations obtained are then applied to a fabricated chip and other fabricated capacitors in the literature. It was found that anticipating the capacitance using the ideal parallel-plate formula can deviate from the capacitance incorporating the deflections by as much as 80%. The presented equations better anticipate the real capacitance of actual fabricated chips and can take into account deflections in the top plate even if they were in the order of a few nanometers.

In this work, we detail a method whereby a polymeric hydrogel layer is grafted to negative tone photoresist SU-8 in order to improve its wettability. A photoinitiator is first immobilized on freshly prepared SU-8 samples, acting as the starting point for various surface modification strategies. Grafting of a 2-hydroxyethylmethacrylate-based hydrogel from the SU-8 surface resulted in the reduction of the static contact angle of a water droplet from 79 ± 1° to 36 ± 1°, while addition of a poly(ethylene glycol)-rich hydrogel layer resulted in further improvement (8 ± 1°). Wettability is greatly enhanced after 30 min of polymerization, with a continued but more gradual decrease in contact angle up to approximately 50 min. Hydrogel formation is triggered by exposure to UV irradiation, allowing for the formation of photopatterned structures using existing photolithographic techniques.

This paper presents scalar and vector analyses of sawtooth gratings with a period of 2.0 µm in terms of Fourier transformation and rigorous coupled wave analysis (RCWA) and its fabrication on a slanted silicon substrate by a newly proposed fast atom beam (FAB) etching method. First, the optical and geometrical properties of sawtooth gratings were investigated and optimized under the phase-matching requirement, and the 1st diffraction efficiency for TM polarization and the scalar approximation, 73.0% and 100%, were estimated, respectively. Second, sawtooth gratings optimized by two diffraction analysis methods were successfully fabricated by the FAB etching method. Last, by a hot-embossing process suitable for mass production, 100 µm thick poly-methyl methacrylate (PMMA) material was replicated from a sawtooth-patterned silicon substrate, and its 1st diffraction efficiency for TM polarization, 63.0%, was measured from optical testing.

An unsteady microfluidic T-form mixer driven by pressure disturbances was designed and investigated. The performance of the mixer was examined both through numerical simulation and experimentation. Linear Stokes equations were used for these low Reynolds number flows. Unsteady mixing in a micro-channel of two aqueous solutions differing in concentrations of chemical species was described using a convection-dominated diffusion equation. The task was greatly simplified by employing linear superimposition of a velocity field for solving a scalar species concentration equation. Low-order-based numerical codes were found not to be suitable for simulation of a convection-dominated mixing process due to erroneous computational dissipation. The convection-dominated diffusion problem was addressed by designing a numerical algorithm with high numerical accuracy and computational-cost effectiveness. This numerical scheme was validated by examining a test case prior to being applied to the mixing simulation. Parametric analysis was performed using this newly developed numerical algorithm to determine the best mixing conditions. Numerical simulation identified the best mixing condition to have a Strouhal number (St) of 0.42. For a T-junction mixer (with channel width = 196 µm), about 75% mixing can be finished within a mixing distance of less than 3 mm (i.e. 15 channel width) at St = 0.42 for flow with a Reynolds number less than 0.24. Numerical results were validated experimentally by mixing two aqueous solutions containing yellow and blue dyes. Visualization of the flow field under the microscope revealed a high level of agreement between numerical simulation and experimental results.

This paper reports on the design, fabrication and evaluation of solid immersion blazed-phase diffractive optics for near-infrared radiation of wavelength 1064 nm. The practical application of enhancing the analysis of integrated circuits using scanning laser microscopy through the silicon substrate is demonstrated. A general design technique using computer generated holography (CGH) is developed to create a numerical program that calculates the structure required for spherical wavefront reconstruction through a silicon substrate into any user-defined pattern. Fabrication of the blazed-phase structure with a diffraction efficiency of 87.9% is achieved in a single-process step by using a combination of the focused ion beam to implant gallium atoms according to the phase pattern, followed by reactive-ion etching using CHF₃ chemistry. The implant conditions and etch times are experimentally adjusted to achieve a continuous blazed-phase profile with the required height of 440 nm with a minimum implant spacing of 140 nm. The imaging capability of the solid immersion blazed-phase lens is compared to a binary-phase lens with a diffraction efficiency of 38.8%, where the more efficient blazed design results in a corresponding improvement with image contrast. The complete technique is then extended to the reconstruction of multiple focal points and ring patterns, to produce analysis techniques that use phase contrast to produce differential images between each focal point from the same diffractive optic. Analysis results are presented that demonstrate lateral resolutions up to 3.5 times better than without the diffraction optic and the capability of selectively removing of specific spatial frequencies from repetitive integrated circuits.

Corrections were made to equation 2.9 in this article on 11 March 2008. The corrected electronic version is identical to the print version.

An automatic ultramicro-volume DNA ligation process using a coplanar electrode type of electrowetting-on-dielectric (EWOD) microfluidic system was designed for economy of reagent. The droplets, containing DNA, a ligation enzyme and a multi-salt reaction buffer, served to complete the ligation using a developed EWOD system. Droplets of ultramicro volume (0.3 µL) were successfully generated from reservoirs between one plate with coplanar electrodes and another plate with a hydrophobic surface free of electrodes. In one successful cloning, the total usage of reagents in an ultramicro-volume EWOD chip was 2.1 µL; no volume was wasted, in comparison with 85% waste with the standard protocol and 80% waste with a free-cover coplanar EWOD chip. The results also show that the entire process was accomplished without damage to the chip surface and without biomaterial annulment. With a design consisting of electrode pathways in a flexible pattern and multiplex reservoirs, an EWOD digital microfluidic system with coplanar electrodes would be improved as an efficient parallel DNA-cloning system in the construction of an artificial library or expression library.

A piezoresistive stress sensor is developed using silicon-on-insulator (SOI) wafers and calibrated for stress measurement for high-temperature applications. The stress sensor consists of 'silicon-island-like' piezoresistor rosettes that are etched on the SOI layer. This eliminates leakage current and enables excellent electrical insulation at high temperature. To compensate for the measurement errors caused by the misalignment of the piezoresistor rosettes with respect to the crystallographic axes, an anisotropic micromachining technique, tetramethylammonium hydroxide etching, is employed to alleviate the misalignment issue. To realize temperature-compensated stress measurement, a planar diode is fabricated as a temperature sensor to decouple the temperature information from the piezoresistors, which are sensitive to both stress and temperature. Design, fabrication and calibration of the piezoresistors are given. SOI-related characteristics such as piezoresistive coefficients and temperature coefficients as well as the influence of the buried oxide layer are discussed in detail.

Electrochemical discharge machining (ECDM) is an effective spark-based machining method for nonconductive materials such as glass. The spark generation in ECDM processes is closely related to the electrode effects phenomenon, which has been explained as an immediate breakdown of electrolysis due to the gas film formation at the electrode surface. The initiation of the electrode effects is mainly influenced by the critical current density, which is dependent on several parameters such as the wettability of the gas bubble, surface conditions of the electrode and hydrodynamic characteristics of the bubbles. In ECDM processes, precise control of the spark generation is difficult due to the random formation of the dielectric gas film. In this study, a partially side-insulated electrode that maintained a constant contact surface area with the electrolyte was used for the ECDM process to ensure that a uniform gas film was formed. Visual inspections indicated that the side-insulated tool provides new possibilities for describing the exact geometry of a gas film by inducing single bubble formations. Experiment results demonstrated that ECDM with a side-insulated electrode immersed in the electrolyte generated more stable spark discharges compared to non-insulated electrodes. Microchannels were fabricated to investigate the effects of the side insulation on the geometric accuracy and the surface integrity of the machined part.

This paper explores the technological capabilities as well as theoretical limitations of electroplating bonding technology (EBT). EBT is of particular interest for the fabrication of complex three-dimensional electrical components (e.g. inductors, high frequency antennae, etc) as well as high aspect ratio mechanical structures with exotic geometrical features. Two separate substrates, each containing identical arrays of 150 µm tall copper microstructures, are aligned and then joined together using electrodeposition of copper under forced convection conditions to form 300 µm long structures that mechanically and electrically link the two substrates. Theoretical and experimental approaches are used to develop this bonding system. Mass transfer calculations of diffusion and convection are performed to predict optimal fabrication conditions. To demonstrate the ability to predict optimal plating conditions, a test coupon mimicking a chip-scaled interconnect system with 256 chip interconnects is designed, fabricated and characterized. The mechanical and electrical connectivity are verified by formation of daisy-chained test beds. The electrical testing of the bonded system shows an excellent conductivity of 0.097 Ohm/test row. Thermal-cycling-accelerated aging tests are performed over a temperature range from −55 to +125 °C. Electroplating bonded structures show excellent mechanical stability as well as electrical performance.

A relatively low-cost fabrication method using soft lithography and molding for large-area, high-aspect-ratio microfluidic devices, which have traditionally been difficult to fabricate, has been developed and is presented in this work. The fabrication process includes novel but simple modifications of conventional microfabrication steps and can be performed in any standard microfabrication facility. Specifically, the fabrication and testing of a microfluidic device for continuous flow deposition of bio-molecules in an array format are presented. The array layout requires high-aspect-ratio elastomeric channels that are 350 µm tall, extend more than 10 cm across the substrate and are separated by as little as 20 µm. The mold from which these channels were fabricated consisted of high-quality, 335 µm tall SU-8 structures with a high-negative aspect ratio of 17 on a 150 mm silicon wafer and was produced using spin coating and UV-lithography. Several unique processing steps are introduced into the lithographic patterning to eliminate many of the problems experienced when fabricating tall, high-aspect-ratio SU-8 structures. In particular, techniques are used to ensure uniform molds, both in height and quality, that are fully developed even in the deep negative-aspect-ratio areas, have no leftover films at the top of the structures caused by overexposure and no bowing or angled sidewalls from diffraction of the applied UV light. Successful microfluidic device creation was demonstrated using these molds by casting, curing and bonding a polydimethylsiloxane (PDMS) elastomer. A unique microfluidic device, requiring these stringent geometries, for continuous flow printing of a linear array of 16 protein and antibody spots has been demonstrated and validated by using surface plasmon resonance imaging of printed arrays.

Different photocurable acrylates, including two hyperbranched monomers, are compared with an epoxy negative-tone photoresist (SU-8) with respect to their suitability for the fabrication of ultra-thick polymer microstructures in a photolithographic process. To this end, a resolution pattern was used and key parameters, such as the maximum attainable thickness and aspect ratio, the minimum resolution and the processing time were determined. Compared to SU-8, all acrylate materials allowed the fabrication of thicker layers with a fast single layer fabrication procedure. Microstructures with thicknesses of up to 850 µm, an aspect ratio of up to 7.7, a 5.5-fold reduction in internal stress and a 6-fold reduction in processing time compared to SU-8 were demonstrated using an acrylated hyperbranched polyether. The specific development process of the hyperbranched polymer combined with channel design moreover enabled us to produce a high-performance valve for micro-battery devices.

Hot embossing an open-die process with a flat mold has limited capabilities in embossing thick films with high-aspect-ratio microstructures. The process suffers from a small process window due to a coupled control scheme for both embossing pressure and embossing thickness. To enlarge the process window, the standard flat mold was modified to include a circumferential landing area, with which the embossing pressure can be separately controlled. Theoretical analyses were carried out to understand the cause of the small process window in hot embossing and the benefits from the new tool design. A case study involving a disk with a centered high-aspect-ratio feature was performed. The analysis showed that, in the new process, the filling aspect ratio is not limited and uniform embossing pressure can be attained on the entire embossing disk. Experiments were conducted to partly verify the analytical findings. With the simple and yet useful tool modification, thick and discrete parts with high-aspect-ratio surface features were successfully embossed in a single-step operation.

In this paper, we show how surface-micromachined buckled cantilevers can be used to construct out-of-plane structures. We include the relevant theory necessary to predict the height and angle of plates attached to buckled cantilevers, as well as the mechanical stresses involved in assembly. These platforms can be assembled to any angle between 0° and 90° with respect to the substrate by changing the attachment point and the amount of deflection. Example devices were fabricated using PolyMUMPs™ and assembled. Using these devices, the deflection of the buckled cantilevers was verified, as well as the placement for raised platforms.

In this study, we have explored the hot-embossing of polyimide films through dynamic mechanical thermal analysis (DMTA), forming and mold fabrication studies. First, the relationship between the formability and the temperature for the polyimide film was investigated by DMTA and hot-embossing tests. The DMA results represented that, as a polyimide goes through its glass transition, it exhibited dramatic decreases in storage elastic modulus, storage shear modulus and viscosity as well as the peak of tangent delta, and continued to show strong dependence on frequency and temperature. The filling characteristics of the polyimide film investigated by hot-embossing tests showed a sharp increase in the replicated depth near the glass transition temperature. Second, silicon microfluidic platforms and molds were prepared by electron beam lithography (EBL) combined with inductively coupled plasma (ICP). An ICP etching condition to prevent reverse taper of a microstructure was investigated, and Si microfluidic channels and high aspect-ratio microstructures with nearly vertical sidewall were structured. Finally, the channel structures could be successfully replicated on the polyimide surface by hot-embossing with the Si mold prepared by using EBL combined with ICP plasma etching.

This work investigates the use of polydimethylglutarimide, or PMGI, as a structural material for surface micromachining. PMGI is a commercially available, positive-toned deep-UV resist designed for use in bi-layer lift-off techniques. This paper presents a technique for the microfabrication of free-standing PMGI structures, and uses those structures to extract the coefficient of thermal expansion and Young's modulus for PMGI. Our study found PMGI's coefficient of thermal expansion to be 56 ± 6 ppm °C⁻¹ and Young's modulus to be 5.0 ± 0.5 GPa. Active structures were also fabricated by including a patterned metal layer. This allows the fabrication of active devices, such as bent-beam actuators. PMGI is a commercially available polymer being used in micromachining, and this paper provides the first report of its thermo-mechanical properties.

Thermocapillary manipulation of a droplet in a planar microchannel with periodic actuations has been demonstrated by both theoretical simulation and experimental characterization. The driving temperature gradients are provided by four micro heaters embedded in the boundaries of the planar channel. The temperature distributions corresponding to the periodic actuations are calculated, and are coupled to the droplet through the surface tensions which drive the droplet. The results show that the droplet will be driven to move along closed loops whose patterns can be designed and controlled by the periodic heating schemes and actuation frequencies. Qualitative agreement between the simulation and experimental observation, in terms of the temperature distributions and droplet moving tracks, has been obtained.