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Abstract. When a capillary bridge of a constant volume is formed between two surfaces, the shape of the liquid bridge will change as the separation between those surfaces is varied. To investigate the variable forces and Laplace pressure of the capillary bridge, as the shape the bridge evolves, a pseudo-three-dimensional force model of the capillary bridge is developed. Based on the characteristics of the slender structured surface, an efficient method is employed to directly solve the differential equations defining the shape of the capillary bridge. The spacing between the plates satisfying the liquid confined within the hydrophobic region of the structured surface is calculated. The method described in this paper can prevent meshing liquid surfaces such that, compared with Surface Evolver simulations, the computing speed is greatly improved. Finally, by comparing the results of the finite element simulations performed with Surface Evolver with those of the method employed in this paper, the practicality of the method is demonstrated.

In industries such as electronics, automobiles, and luxury goods, we have observed numerous cases of intentional undersupply when a new product is introduced. Previous research has shown that introductory scarcity has a positive effect on consumers' willingness to pay, but this effect has yet to be quantified. This paper investigates how scarcity strategies affect product pricing and a firm's profits. We consider two types of scarcity strategies, a real and a fake scarcity strategy, and propose a two-period model in both markdown and markup scenarios. We find that an introductory scarcity strategy is profitable in a markup scenario only if the discount factor is greater than a critical value and payoffs are compartmentalized. Moreover, an introductory scarcity strategy could result in profits in a markdown scenario if consumers are sensitive to scarcity. However, a scarcity strategy is always detrimental to a firm with low-quality products in both scenarios. If there are uninformed consumers in the market, a fake scarcity strategy is beneficial for firms in the short term but not in the long term.

To investigate the fretting wear of involute spline couplings in aerospace, rack-plane spline couplings rather than the conventional involute spline couplings in aerospace were used to conduct tribological experiments, and it was assumed that the rack-plane spline couplings exhibit consistent contact stress with the real involute spline couplings in aerospace. The relationships among the static friction coefficient, dynamic friction coefficient, and fretting friction coefficient were established via tribological experiments, as well as the fretting-wear mechanism of the rack-plane spline couplings was examined. A fretting-wear estimation model based on the fretting-wear mechanism was developed. By applying the modified Archard equation and Arbitrary Lagrangian–Eulerian adaptive, mesh smoothing algorithm of Abacus was used. According to our experimental results, the fretting wear of the rack-plane spline couplings consisted primarily of abrasive wear, oxidative wear, and adhesive wear. For both, lubrication and non-lubrication settings, the fretting friction coefficient of 18CrNi4A steel (0.27) fluctuated between 0.12 (dynamic friction coefficient) and 0.35 (static friction coefficient). The fretting-wear results estimated via numerical prediction were consistent with the experimental results. When sm (vibration amplitude) was 20, 35, and 50 µm, the most difference in the fretting wear between the experimental results and numerical estimation was 0.001, 0.0007, and 0.001 mm, respectively. Therefore, the proposed model provides a method for accurate estimation of the fretting-wear. Additionally, the model contributes to the precise design of involute spline couplings in aerospace.

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