Simulation and theoretical study of swimming and resistive forces within granular media

One way to investigate the physics of a medium is to study the forces on intruders moving through the media. A special case of intruders moving in media is the locomotion of organisms. Locomotion within fluids (flying in air and swimming in water) has been extensively studied and the complexity of interaction between intruders and fluids is well recognized. Locomotion within yielding substrates like sand, soil and debris that display both solid and fluid-like behavior has been less studied and is therefore less understood than to locomotion within fluids or on solid ground. In such materials, validated theories for describing the flow and resistive forces on intruders have not reached the levels of those for fluids.;As a representative case of subsurface locomotion in granular media, we study on the undulatory sand-swimming of the sandfish lizard ( Scincus scincus), a small (∼10 cm) desert-dwelling lizard. We use numerical simulations and theoretical models of the interactions between granular media and simple objects, biological and robotic systems to reveal principles of undulatory locomotion in granular media. We also use the models to investigate the resistive forces on intruders with different orientations and shapes, which is essential for the understanding of locomotion ability and performance of locomotors. Previous experimental work using high speed x-ray imaging showed that the sandfish lizard swims within dry granular media without limb use by propagating a single period traveling sinusoidal wave along its body. The wave efficiency eta, the ratio of the forward speed to the traveling wave speed, was approximately 0.5, independent of the packing state of the media (close and loose). To explain these results, we develop a resistive force model with empirical force laws to explain the swimming speed observed in the animal experiment. We show that the higher wave efficiency reached by the sandfish compared to the low Re swimmers (∼ 0.2) was because of the different functional form of the resistive forces on a rod dragged in granular media. We vary the ratio of undulation amplitude (A) to wavelength (lambda) and demonstrate that an optimal waveform A/lambda ≈ 0.2 for sand-swimming exists, which results from the competition between eta and lambda. To test assumptions in RFT and to study more detailed mechanics of sand-swimming, we developed a numerical model of the sandfish coupled to a discrete element method simulation of the granular medium. The numerical model confirmed that inertial forces are negligible and that the forces on the animal can be approximated by the forces on rods dragged at constant speed in granular media. The wave efficiency predicted by simulation qualitatively matched both the RFT model and the prediction of the optimal A/lambda; However, the simulation revealed that the RFT over predicted the swimming speed because the reduction in magnitude of the resistive forces during velocity reversal was not considered. The RFT model and simulation helped the development of a sand-swimming robot, and the robot verified predictions from the RFT model and the simulation, such as the value of the wave efficiency, the actuator torque, and the effect of varying kinematic parameters including A/lambda and number of periods. Inspired by the shovel-shaped head of the sandfish lizard, we studied the drag induced lift in granular media. We found that when a submerged intruder moves at a constant speed within a granular medium it experiences a lift force whose sign and magnitude depend on the intruder shape. We demonstrated that the lift forces and hence vertical position of the sand-swimming robot as it moves forward within granular media can be controlled by varying its head shape. The models together with robots explained biological observations of the kinematics of the animal and provide a hypothesis for the morphological adaptation (head shape) of the animal as well as guidance for building biophysically inspired robot that could explore challenging environments. The principles learned about the resistive forces can also help the design of the other machines that interact with granular media. My studies have given new insights into localized intrusion of simple and complex/composite shapes in granular media.