Fluid pumping in a horizontal slot using the pattern interaction effect has been analysed. This pumping is of interest as it operates without external energy sources beyond those required to create the necessary heating patterns. Activation of this effect involves a combination of fixed surface topography and adjustable heating patterns. The flow rate, including its direction, can be controlled by moving the heating pattern relative to the groove pattern. This analysis extends that of Abtahi & Floryan (2017 J. Fluid Mech . vol. 826, pp. 553–582), who considered only small-amplitude grooves in which the achieved flow rate is proportional to the groove amplitude. Grooves with arbitrary amplitudes spanning the slot were considered in the current analysis, and their most effective heights and distributions have been identified. A detailed analysis was conducted of groove and heating patterns described by a single Fourier mode applied to one or both plates bounding the slot. In all cases, the flow rate increased proportionally to the groove amplitude until an excessively large amplitude caused flow choking, and to the heating intensity until saturation was reached. The groove wavenumber of approximately 0.8 was found to be the most effective in the case of one groove plate, and 0.5–0.7 in the case of two groove plates. The flow rate decreases rapidly at both smaller and larger wavenumbers. The largest flow rate was achieved by placing grooves on both plates to form a wavy slot, with hot spots positioned halfway between the groove peaks and troughs.
Wang et al. (Tue,) studied this question.