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The laminar boundary layer of a viscous incompressible fluid subject to a two-dimensional wall curvature is evaluated. It is well known that a curved surface induces streamwise pressure gradient as well as wall curvature driven pressure gradient. Under certain assumptions, a family of similarity solutions can be obtained under the influence of flow acceleration/deceleration, which is known as the Falkner-Skan similarity solutions. In this study, the effect of the wall normal pressure gradient is taken into consideration, and the freestream flow parameters are adjusted for flow over a curved surface. Present results are obtained by numerical solution of a generalized Falkner-Skan equation governing similar solutions for flows over curved surfaces. The Falkner-Skan equations are solved by an RK4 shooting algorithm. Additionally, the transport of a passive scalar is incorporated in the present analysis at different Prandtl numbers. The objective of this paper is to use the curvilinear or axisymmetric boundary layer and energy equations to assess the effect of Favorable, Adverse and Zero pressure gradient on the laminar momentum and thermal boundary layer development. Major conclusions are summarized as follows: (i) as the pressure gradient β increases from negative values (APG) towards positive (FPG) values, the displacement (Δ∗) and momentum (θ∗) thickness tend to decrease no matter the curvature type, and, (ii) the normalized wall shear stress (i.e., f′′) exhibits a linear decreasing behavior as the wall curvature switches from concave (negative) to convex (positive) at a constant pressure gradient.
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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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