In this paper, a broadband, low insertion loss, and compact folded substrate integrated waveguide (FSIW) phase shifter is proposed for the first time. By loading the complementary split-ring resonators (CSRRs) on the middle metal layer of the FSIW, a closed-type slow-wave transmission line (TL) is obtained, which can provide a wideband phase shift (39%) compared with the equal-length fast-wave one. The enclosed structure of the CSRR-loaded FSIW prevents the CSRRs from radiation as suffered in the previous reported CSRR-loaded TLs, resulting in a low insertion loss. This feature greatly reduces the amplitude imbalance between the main line and the reference line of the phase shifter. In addition, no transition structure is required between the FSIWs with and without CSRRs for broadband impedance matching, which makes the phase shifter more compact and easier to integrate with other FSIW devices. To validate the performance of the proposed phase shifter and to illustrate its ease integration, a novel FSIW 180° directional coupler that consists of an FSIW 90° coupler and an FSIW 90° phase shifter is designed, fabricated, and measured. The measured results agree well with the simulated data.

This paper theoretically studies the effect of eccentricity on the conditions of capillary emptying (determined by critical Bond number) in a horizontal annular tube in a downward gravity field. Experiments are conducted to compare with theoretical results. We find that non-horizontal eccentricity can lead to the occurrence of a re-entrant liquid-state transition (from liquid non-occlusion to liquid plug to liquid non-occlusion) with increasing Bond number, when the eccentricity (e) or inner-to-outer radius ratio (χ) is large enough, and the two liquid non-occlusion states correspond to different emptying mechanisms dominated by the gravity effect and the ‘wedge’ effect, respectively. Existence of the re-entrant transition is accompanied by occurrence of unconditional liquid non-occlusion at large enough or small enough contact angles regardless of Bond numbers. The critical Bond numbers at a contact angle γ for vertical upward eccentricity are equal to those at a contact angle 180° − γ for vertical downward eccentricity. In a parameter space (γ, e/(1 − χ)), the region with the re-entrant transition becomes larger with the eccentric angle varying from 0° (horizontal) to 90° (vertical). Optimization of geometrical parameters and inner and outer contact angles can lead to better effect of capillary emptying. This paper provides a very effective scheme for removing a liquid blockage from a capillary in optofluidics/microfluidics.

Metal additive manufacturing has enabled geometrically complex internal cooling channels for turbine and heat exchanger applications, but the process gives rise to large-scale roughness whose size is comparable to the channel height (which is 500 $\mathrm {\mu }$m). These super-rough channels pose previously unseen challenges for experimental measurements, data interpretation and roughness modelling. First, it is not clear if measurements at a particular streamwise and spanwise location still provide accurate representation of the mean (time- and plane-averaged) flow. Second, we do not know if the logarithmic layer survives. Third, it is unknown how well previously developed rough-wall models work for these large-scale roughnesses. To answer the above practical questions, we conduct direct numerical simulations of flow in additively manufactured super-rough channels. Three rough surfaces are considered, all of which are obtained from computed tomography scans of additively manufactured surfaces. The roughness’ trough to peak sizes are 0.1$h$, 0.3$h$ and 0.8$h$, respectively, where $h$ is the intended half-channel height. Each rough surface is placed opposite a smooth wall and the other two rough surfaces, leading to six rough-wall channel configurations. Two Reynolds numbers are considered, namely $Re_\tau =180$ and $Re_\tau =395$. We show first that measurements at one streamwise and spanwise location are insufficient due to strong mean flow inhomogeneity across the entire channel, second that the logarithmic law of the wall survives despite the mean flow inhomogeneity and third that the established roughness sheltering model remains accurate.