University:
Boston University
Course:
ENG ME 303 | Fluid Mechanics
Academic year:

2021
Views:

211

Pages:

23
Author:

kulawaixgi

What about wetting? Fluid Behavior Viscous Forces Coiling honey Interfacial Forces Wetting of water on a textured surface Capillary Number: viscous/interfacial Fluid Behavior Viscous Forces Capillary Number: viscous/interfacial Monodisperse droplet generation • • Droplet emulsions in immiscible fluids Injection of water into stream of oil Interfacial tension prevents the fluids from flowing alongside each other. Interfacial Forces Surface tension acts to reduce the interfacial area. Viscous stresses act to extend and drag the interface downstream. Characteristic droplet size: Capillary number: Fluid Behavior Viscous Forces Capillary Number: viscous/interfacial Large surface-to-volume ratios in microfluidic devices • • Makes surface effects increasingly important. Important when free fluid surfaces are present. Surface tensions can exert significant stress Interfacial Forces • • Result in free surface deformations. Can drive fluid motion. Capillary forces tend to draw fluid into wetting microchannels • Occurs when solid-liquid interfacial energy is lower than the solid-gas interfacial energy. Capillary Rise Classical Problem: • Noted as early as 15th by Leonardo da Vinci. • Attributed to circulation in plants in 17th century by Montanari. Balance: Surface Tension & Gravity Elastocapillarity Fluid-structure interaction: • Droplet bends and folds the sheet. • Droplet is minimizing the amount of its surface in contact with air. • Liquid-air surface area is minimized at the expense of bending the sheet. Elastocapillarity Fluid-structure interaction: Elastic energy of a plate – bending: Relation between in-plane strain to out-of-plane bending: Bending energy: Elastocapillarity Fluid-structure interaction: Bending energy: Surface energy: Elastocapillary length: Elastocapillary bending of sheet: Elastocapillarity Capillary rise between flexible fibers. Curvature of meniscus Assume gap is much smaller than width: Initial gap: Approximation of meniscus curvature: J. Bico et al (2004) Elastocapillarity Capillary rise between flexible fibers. Approximation: Scaling: J. Bico et al (2004) Balance: Bending & Surface Tension Elastocapillarity Capillary rise between flexible fibers. Potential energies: Elastic energy Gravitational potential energy Surface energy 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 Capillarity & Swelling Capillarity & Swelling 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 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 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. Swelling & Peeling Baobab Flowering

Fluids Deforming Solids - What About Wetting

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