When a rubber tube with free ends is inflated under volume control, the pressure will first reach a maximum and then decrease monotonically to approach a constant asymptote. The pressure maximum corresponds to the initiation of a localized bulge and is predicted by a bifurcation condition, whereas the asymptote is the Maxwell pressure corresponding to a ‘two-phase’ propagation state. By contrast, when the tube is first pre-stretched and then has its ends fixed during subsequent inflation, the pressure as a function of the bulge amplitude has both a maximum and a minimum, and the behaviour on the right ascending branch has previously not been fully understood. We show that for all values of the pre-stretch and tube length, the ascending branches all converge to a single curve that is dependent only on the ratio of the tube thickness to the outer radius. This curve represents the Maxwell state to be approached in each case (if Euler buckling or axisymmetric wrinkling does not occur first), but this state is pressure-dependent, in contrast to the free-ends case. We also demonstrate experimentally that localized bulging cannot occur when the pre-stretch is sufficiently large and investigate what strain-energy functions can predict this observed phenomenon. This article is part of the theme issue ‘The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity’.

Magnetically controlled capsule robots are predominantly used in the diagnosis and treatment of the human gastrointestinal tract. In this study, based on the permanent magnet method, magnetic driving and fluid measurement systems for in-pipe capsule robots were established. Using computational fluid dynamics (CFD) and particle image velocimetry (PIV), the fluid velocity and vorticity in the pipe of the capsule robot were calculated and measured. The running characteristics of the capsule robot were numerically analyzed in the curved pipe and the peristaltic flow. Furthermore, the range and variance method of orthogonal design was used to analyze the influence of four typical parameters (namely, pipe diameter, robotic translational speed, robotic rotational speed, and fluid viscosity) on the three operating performance indicators of the capsule robot (namely, the forward resistance of the robot, fluid turbulent intensity near the robot, and maximum fluid pressure to the pipe wall). In this paper, the relative magnitude and significance of the influence of each typical parameter on different performance indicators of the robot are presented. According to the different performance requirements of the robot, the different four parameter combinations are optimized. It is hoped that this work provides a reference for the selection of the appropriate mucus, translational speed, and rotational speed of the robot when it is working in pipes with different diameters.

Through discrete element method-computational fluid dynamics, the internal flow field and particle motion law of a two-stage deep-sea lifting pump at different rotational speeds were analyzed in this work. In addition, the physical phenomena, such as flow field velocity, secondary flow, and particle flow, were studied. The relationship between the rotational speed of the lifting pump and solid–liquid two-phase flow was investigated. An experiment on the hydraulic performance of the lift pump showed that the resulting lift and efficiency were consistent with the numerical simulation data. When the rotational speed was 1,450 rpm, the particles can obtain a higher kinetic energy from the flow field, the flow was more stable, and particle deposition was reduced.