Fluid Mechanics of Pneumatic Soft Robots

Pressurization of gas within embedded channels and cavities is a popular method for actuating soft robots. Various previous works examined the effects of internal fluid mechanics on this actuation approach, as well as on leveraging viscous effects to extend the capabilities of soft robots. However, no existing works studied the combined effects of fluid viscosity and compressibility, relevant to miniaturized configurations, which is the aim of the current work. We derive a general model for compressible viscous flow in an elastic media representing a simplified miniaturized soft robot. We illustrate applying this model to periodic configurations, simplifying it via a long-wave approximation. Steady, and time-dependent solutions are obtained, allowing to model the flow and to provide insight into the actuation dynamics of miniaturized pneumatic soft robots.

Growth of continental plateaus by channel injection: models designed to address constraints and thermomechanical consistency

Weak, possibly partially molten, middle crust may exist and deform by channel flow beneath continental plateaus, thereby significantly influencing their dynamics. The role of channel flows in the transition zone between the plateau and the foreland is, however, unclear. We develop successively more complete approximate models for the channel injection (CI) mode in which differential pressure pumps channel material from beneath the plateau into the transitional crust, which thickens it and widens the plateau. The motivation is to improve our understanding of the controls on the growth of continental plateaus and the interactions in the transition zone, and to gain more insight into the results of more complex numerical models. In model CI-1, a channel with constant viscosity and thickness exists in the transitional crust and the pumped material accretes/freezes above and below the channel. Although results compare favourably with the geometry of some natural examples, this model is incomplete because the connection between the transition zone and the plateau is not considered. Model CI-2 includes a decrease in channel viscosity when the channel depth exceeds a critical value, D*, a proxy for onset of melt weakening or low viscosities at high temperatures. The model completes the connection to the plateau, but relies on the arbitrary choice of D*. Model CI-3 is more physically based, and considers the channel viscosity and thickness to depend on temperature, calculated by an associated thermal model that includes radioactive self-heating, and advection of heat by channel material. This model demonstrates self-consistent plateau widening if the channel viscosity decreases at the critical temperature, T*. Acceptable comparisons with the topography of Tibet are achieved with transition zone viscosities that decrease from 1019−1022 Pa s to subplateau values of 1018–1019 Pa s, with T* of 700−750°C. Additional analyses and tests are used to determine the range of parameter values for which CI models are both internally consistent and compatible with observations. Additional modes of deformation in the transition zone, viscous thickening (VT) and plastic translation (PT), may also be important.