Ph.D Student | Elbaz Shai |
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Subject | Viscous Flows in Elastic Channels |

Department | Department of Mechanical Engineering |

Supervisor | Dr. Gat Amir |

Full Thesis text |

Viscous flows in contact with elastic structures apply both pressure and shear stress at the solid-liquid interface and thus create internal stress and deformation fields within the solid structure. The corresponding motion of elastic boundaries induces the flow-field. The onset of these viscous-elastic dynamics is characterized by a transient process governed by nonlinear diffusion laws. This thesis is largely dedicated to studying this transient process.

We study the propagation of viscous liquids and gases into elastic channels of cylindrical and planar (two-dimensional) geometries. In addition, we develop practical working methods for spatial and temporal actuation of the examined fluid-solid structures. We investigate three principal configurations. The first, described in chapter 2, is a closed cylindrical shell containing a viscous liquid and subject to external forcing, it is examined as a canonical form of a soft robot. The functionality of the viscous-elastic diffusion process is explored within the context of soft-robotic and peristaltic pumping applications. Shell material compressibility is shown to have a unique effect in inducing different flow and deformation regimes.

The second examined configuration, presented in chapter 3, is that of axial flow in the annular gap between a rigid cylinder and a concentric elastic tube. In this chapter we focus on the viscous peeling limit in which there is initially a negligible prewetting fluid layer in the annulus. In this case the governing equations describe the motion of a distinct propagation front with finite speed. The solution of the fluid film profile near the front requires higher order corrections of the thin shell approximation as well as the regularization of singularities associated with the edges of the lubrication approximation, in similar fashion to free-surface flows. A constructive example is shown in which isolated moving deformation patterns are created and superimposed to form a travelling wave displacement field. The interaction between viscosity and elasticity in the annular configuration may be leveraged to achieve time-dependent control of an axisymmetric compliant boundary.

The third examined configuration, presented in chapter 4, is that of gaseous viscous flow in a two-dimensional compliant walled microchannel. In this chapter we assume low-Mach number compressiblity for the flow and take into account weak rarefaction effects characteristic of gaseous microflows. As in chapter 3 we focus on large fluidic displacements relative to initial channel height and derive a governing nonlinear diffusion equation describing the evolution of channel height. Several physical limits

allow simplification of the governing equation and solution by self-similarity. These limits, representing different physical regimes, include compressibility-elasticity-viscosity, compressibility-viscosity and elasticity-viscosity dominant balances. Transition of the flow field between these regimes and corresponding exact solutions is illustrated for the case of an impulsive mass insertion in which the order of magnitude of the deflection evolves in time.