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For plane channel flow, thermal stratification resulting from a wall-normal temperature gradient together with an opposing gravitational field can lead to buoyancy-driven instability of three-dimensional waves. Moreover, viscosity-driven instability can lead to the amplification of two-dimensional Tollmien-Schlichting waves. Temporal stability simulations considering different combinations of Reynolds number and Rayleigh number were performed to investigate both the buoyancy and viscosity-driven instability of Rayleigh-Benard-Poiseuille flow. The investigated cases are either (1) stable, (2) unstable with respect to three-dimensional waves (buoyancy-driven instability), or (3) unstable with respect to two-dimensional waves (viscosity-driven instability). Two new and highly accurate computational fluid dynamics codes have been developed for solving the full and linearized unsteady compressible Navier-Stokes equations in Cartesian coordinates. The codes employ fifth-order-accurate upwind-biased compact finite differences for the convective terms and fourth-order-accurate compact finite differences for the viscous terms. For the case with buoyancy-driven instability, strong linear growth is observed for a broad range of spanwise wavenumbers and the wavelength of the spanwise mode with the strongest non-linear growth is gradually decreasing in time. For the case with viscosity-driven instability, the linear growth rates are lower and the first mode to experience non-linear growth is a higher harmonic with half the wavelength of the primary wave. The present results are consistent with the neutral curves from the linear stability theory analysis by Gage and Reid.
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This content will become publicly available on July 10, 2025
A theory of hydrogel mechanics that couples swelling and external flow
Two aspects of hydrogel mechanics have been studied separately in the past. The first is the swelling and deswelling of gels in a quiescent solvent bath triggered by an environmental stimulus such as a change in temperature or pH, and the second is the solvent flow around and into a gel domain, driven by an external pressure gradient or moving boundary. The former neglects convection due to external flow, whereas the latter neglects solvent diffusion driven by a gradient in chemical potential. Motivated by engineering and biomedical applications where both aspects coexist and potentially interact with each other, this work presents a poroelasticity model that integrates these two aspects into a single framework, and demonstrates how the coupling between the two gives rise to novel physics in relatively simple one-dimensional and two-dimensional flows.
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- PAR ID:
- 10528329
- Publisher / Repository:
- The Royal Society of Chemistry
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 20
- Issue:
- 27
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 5389 to 5406
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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