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We present an unsteady blade element theory (BET) model to estimate the aerodynamic forces produced by a freely flying beetle and a beetle-mimicking flapping wing system. Added mass and rotational forces are included to accommodate the unsteady force. In addition to the aerodynamic forces needed to accurately estimate the time history of the forces, the inertial forces of the wings are also calculated. All of the force components are considered based on the full three-dimensional (3D) motion of the wing. The result obtained by the present BET model is validated with the data which were presented in a reference paper. The difference between the averages of the estimated forces (lift and drag) and the measured forces in the reference is about 5.7%. The BET model is also used to estimate the force produced by a freely flying beetle and a beetle-mimicking flapping wing system. The wing kinematics used in the BET calculation of a real beetle and the flapping wing system are captured using high-speed cameras. The results show that the average estimated vertical force of the beetle is reasonably close to the weight of the beetle, and the average estimated thrust of the beetle-mimicking flapping wing system is in good agreement with the measured value. Our results show that the unsteady lift and drag coefficients measured by Dickinson et al are still useful for relatively higher Reynolds number cases, and the proposed BET can be a good way to estimate the force produced by a flapping wing system.

Equivalent beam and equivalent bimorph beam models for IPMC (ionic polymer-metal composite) actuators are described in the ensuing paper. Important physical properties of IPMCs including Young's modulus and electro-mechanical coupling coefficient were determined using the rule of mixture, bimorph beam equations, and measured force-displacement data of a cantilevered IPMC actuator. By using a beam equation with estimated physical properties, the actuation displacements of a cantilevered IPMC actuator were calculated to show an excellent agreement between the computed tip displacements and the measured data. Finite element analysis (FEA), along with the predetermined physical properties, was used to predict the force-displacement relationship of an IPMC actuator, which is key data to effectively design many engineering devices of interest. Indicated by the results from the FEA agreeing with the measured data, the proposed models can be adopted for modeling of IPMC actuators with advanced shapes and other boundary conditions.

Slippage effects in microchannels that depend on the surface characteristics are investigated, taking into account hydrophilic, hydrophobic, and superhydrophobic wettabilities. Microscale grooves are fabricated along the vertical walls to form superhydrophobic surfaces, which enable both the visualization of the flow field near the walls and the direct measurement of the slip length. Velocity profiles are measured using microparticle image velocimetry and those in hydrophilic glass, hydrophobic polydimethylsiloxane (PDMS), and superhydrophobic PDMS microchannels are compared. For the hydrophilic glass surface, the velocity near the wall smoothly decreases to zero, which is consistent with the well-known, no-slip boundary condition. On the other hand, for the flow in the hydrophobic PDMS microchannel, the velocity profile approaches some finite value at the wall, showing a slip length of approximately 2μm. In addition, to directly measure the velocity in the superhydrophobic microchannel, transverse groove structures are fabricated along the vertical walls in the microchannel. For this surface, the velocity profile approaches a value that is larger than that for the PDMS case. Incidentally, instabilities in the velocity profile are observed at the interface with the air gap. Furthermore, the velocity profile near the wall shows a larger slip length than for any of the other experimental setups. For groove structures that are high and wide, the liquid meniscus forms curves in the cavity so that a wavy flow is created beyond the grooves. Moreover, if the pitch-to-width ratio of the groove structure increases, meniscus penetration into the cavity is observed.