University:
Boston University
Course:
ENG ME 302 | Engineering Mechanics II
Academic year:

2022
Views:

255

Pages:

20
Author:

Randall Kane

Elastocapillarity Capillary rise between flexible fibers. Characteristic length scales: Elastocapillary length Capillary gravity length Elastogravity length Elastocapillarity Capillary rise between flexible fibers. Dimensionless parameters Bond number: Elastocapillary number Elastogravity number Elastocapillarity Elastocapillarity Elastocapillarity Elastocapillarity Capillarity & Swelling Capillarity & Swelling Capillarity & Swelling 1. Elastocapillary rise between flexible fibers. Capillarity & Swelling 1. Elastocapillary rise between flexible fibers. Stationary meniscus height rises linearly with elastocapillary length. Polymers & Swelling Bad Solvent Good Solvent Swelling Capillarity & Swelling 2. Swelling-induced bending. Dynamics of bending ~ Diffusion of temperature Capillarity & Swelling 2. Swelling-induced bending. • Thermal diffusion through the beam thickness. • Shape obtained by minimizing the bending moment in the beam. • Beam curvature as temperature diffuses. • Poroelastic time scale μ = Solvent viscosity h = Thickness k = Permeability (k ≈ 10-18 m2/s) E = Elastic modulus (E = 106 Pa) Capillarity & Swelling 2. Swelling-induced bending. Capillarity & Swelling 3. Bending dominates surface tension. Bending energy Peeling occurs if the curvature exceeds the bending capillary length. Surface energy Capillarity & Swelling 1. Elastocapillary rise between flexible fibers. At short times, elastocapillary rise dominates the deformation. 2. Swelling-induced bending. Bending is constrained by surface tension, as the beam bends with a lower curvature than a free swelling beam. 3. Bending dominates surface tension. Separation occurs as the “natural” curvature of the beam exceeds the fluids ability to confine it. Capillarity & Swelling Stretching energy Bending energy Surface energy Capillarity & Swelling Baobab Flowering Summary Confined Fluid Flow: Microfluidics and Capillarity Reynolds Number: Inertia vs. Viscous effects • Review of characteristic flows… Péclet Number: Transport phenomena in a continuum • Diffusion, separation, and mixing… Geometric confinement: Controlling and manipulating fluid flow • Microfluidic fabrication, valving, pumping… Capillary Number: Viscosity vs. Surface tension • Droplet formation, capillary rise, elasticity…