|M.Sc Student||Linshits Max|
|Subject||The Effects of Internal Viscous Flow on the Deformation-|
Field, Stress-Field and Critical Buckling Load of
|Department||Department of Mechanical Engineering||Supervisor||Professor Amir Gat|
|Full Thesis text|
The interaction between low-Reynolds-number liquid flow and elastic deformation of solid-structures is relevant to various research subjects such as instabilities in micro-fabrication processes, capillary origami, flows in micro-needle arrays and fluid-induced deformation of soft robotics.
Viscous flows in contact with an elastic body apply both pressure and shear stress on the solid-liquid interface and thus create internal stress- and deformation-fields within the solid structure. In this thesis we focus on internal low-Reynolds-number flow interacting with an elastic thin-walled slender tube. We study the deformation- and stress-fields in the solid, as well as the pressure and velocity in the fluid and the effect of the viscous flow on the buckling failure mode.
The interaction between fluid and solid dynamics for the case of viscous flow through elastic cylinders was extensively studied in the context of collapsible tubes, studies of pipes conveying fluid and flows in arteries. In our work we utilize elastic shell theory and hydrodynamic lubrication to study the interaction between the viscous flow field within the cylinder and the deformation of the cylinder. We obtain a first-order solution (with regard to a small parameter characterizing the deformations) for the liquid pressure field, solid stress field and the solid deformation field.
In addition, we suggest that the stress-field created by the viscous flow can be utilized to counter stress created by external forces and thus may be applied as a tool for delaying the onset of structural failure. To illustrate this concept we study viscous flow within an elastic cylinder under compressive axial force and obtain a closed-form expression estimating the critical buckling load as a function of the viscous flow. The obtained results suggest that viscous flow can be readily utilized to gain higher effective stiffness in elastic structures and that an approximately linear relation exists between the average pressure-gradient of the liquid and the critical buckling load. Our results are validated by numerical computations and simulations.
Our results can be readily applied as a tool to temporarily increase the rigidity of micro-needles by creating flow during penetration into the skin. Future research can build on our results to design a composite solid-liquid material which combine an external elastic structure and channels containing viscous fluid. Deformation of such a structure under external force can create viscous flows which apply stress on the solid and thus significantly change the stress-field in the structure which may allow delaying structural failure.