scholarly journals The equilibria of vesicles adhered to substrates by short-ranged potentials

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120729 ◽  
Author(s):  
Maurice J. Blount ◽  
Michael J. Miksis ◽  
Stephen H. Davis
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Layer Structure ◽  
Two Dimensional ◽  
Adhesive Interaction ◽  
Contact Potential ◽  
Layer Structures ◽  
Bending Stresses ◽  
Dimensional Boundary ◽  
Horizontal Substrate

In equilibrium, a vesicle that is adhered to a horizontal substrate by a long-range attractive, short-range repulsive force traps a thin layer of fluid beneath it. In the asymptotic limit that this layer is very thin, there are quasi-two-dimensional boundary-layer structures near the edges of the vesicle, where the membrane's shape is governed by a balance between bending and adhesive stresses. These boundary layers are analysed to obtain corrections to simpler models that instead represent the adhesive interaction by a contact potential, thereby resolving apparent discontinuities that arise when such models are used. Composite expansions of the shapes of two-dimensional vesicles are derived. When, in addition, the adhesive interaction is very strong, there is a nested boundary-layer structure for which the adhesive boundary layers match towards sharp corners where bending stresses remain important but adhesive stresses are negligible. Outside these corners, bending stresses are negligible and the vesicle's shape is given approximately by the arc of a circle. Simple composite expansions of the vesicle's shape are derived that account for the shape of the membrane inside these corners.

The Interaction of Thermal Radiation in Optically Thick Boundary Layers

1967 ◽  
Vol 89 (4) ◽  
pp. 309-312 ◽  
Author(s):  
J. L. Novotny ◽  
Kwang-Tzu Yang
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Boundary Layers ◽  
Optical Thickness ◽  
Asymptotic Expansions ◽  
Energy Equation ◽  
Two Dimensional ◽  
Small Temperature ◽  
Dimensional Boundary

An analysis is presented to examine the role of the Rosseland or optically thick approximation in convection-radiation interaction situations. The analysis is formulated for the flow of a gray gas in a laminar two-dimensional boundary layer under the restriction of small temperature differences within the flow field. The boundary-layer energy equation is treated using the method of matched asymptotic expansions based on a parameter which characterizes the optical thickness of the gas. Two illustrative examples of the resulting equations are presented.

The spanwise perturbation of two-dimensional boundary layers

1966 ◽  
Vol 24 (1) ◽  
pp. 153-164 ◽  
Author(s):  
S. C. Crow
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Plate Boundary ◽  
Wind Tunnels ◽  
Two Dimensional ◽  
Surface Shear ◽  
Flow Reynolds Number ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Small Periodic

Large spanwise variations of boundary-layer thickness and surface shear have been found recently in wind tunnels designed to maintain two-dimensional flow. Bradshaw (1965) argues that these variations are caused by minute deflexions in the free-stream flow rather than by any intrinsic instability of the boundary layers. This paper is a study of the effect of a small, periodic transverse flow on a flat-plate boundary layer. The perturbation flow Reynolds number is assumed to be O(1) as it is in the experiments.

Equilibrium turbulent boundary layers with lateral streamline convergence or divergence

2009 ◽  
Vol 623 ◽  
pp. 273-282 ◽  
Author(s):  
T. B. NICKELS
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Equilibrium Solutions ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
Convergence And Divergence ◽  
Necessary Constraints

The constraints necessary for equilibrium solutions of the boundary layer equations are explored for turbulent boundary layers subject to lateral convergence and divergence and with longitudinal pressure gradients. It is shown that in addition to the well-known equilibrium solutions for two-dimensional boundary layers there are additionalpossibleequilibrium states for boundary layers with these extra rates-of-strain acting. The necessary constraints for equilibrium are derived and discussed.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Effects of Curvature on Laminar Boundary Layers in Sink-Type Flows

1969 ◽  
Vol 91 (3) ◽  
pp. 353-358 ◽  
Author(s):  
W. A. Gustafson ◽  
I. Pelech
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Momentum Equation ◽  
Similarity Solutions ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Thickness Increase ◽  
Laminar Boundary Layers ◽  
Converging Channel ◽  
Special Case

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

The Relationship Between Atmospheric Boundary Layer Structure, Brown Haze, and Air Pollution in Auckland, New Zealand

2021 ◽  
Author(s):  
Hannah Marley ◽  
Kim Dirks ◽  
Andrew Neverman ◽  
Ian McKendry ◽  
Jennifer Salmond
Keyword(s):  
Boundary Layer ◽  
Air Pollution ◽  
New Zealand ◽  
Atmospheric Boundary Layer ◽  
Boundary Layers ◽  
Layer Structure ◽  
High Surface ◽  
Residual Layer ◽  
Pollution Levels ◽  
Haze Formation

<p><span><span>A brown air pollution haze that forms over some international cities during the winter has been found to be associated with negative health outcomes and high surface air pollution levels. Previous research has demonstrated a well-established link between the structure of the atmospheric boundary layer (ABL) and surface air quality; however, the degree to which the structure of the ABL influences for formation of local-</span></span><span><span>scale</span></span><span><span> brown haze is unknown. Using continuous ceilometer data covering seven consecutive winters, we investigate the influence of the structure of the ABL in relation to surface air pollution and brown haze formation over an urban area of complex coastal terrain in the Southern Hemisphere city of Auckland, New Zealand. Our results suggest the depth and evolution of the ABL has a strong influence on severe brown haze formation. When days with severe brown haze are compared with those when brown haze is expected but not observed (based on favorable meteorology and high surface air pollution levels), days with severe brown haze are found to coincide with significantly shallower daytime convective boundary layers (~ 48% lower), and the nights preceding brown haze formation are found to have significantly shallower nocturnal boundary layers (~ 28% lower). On severe brown haze days the growth rate during the morning transition phase from a nocturnal boundary layer to a convective daytime boundary layer is found to be significantly reduced (70 m h</span></span><sup><span><span>-1</span></span></sup><span><span>) compared to days on which brown haze is expected but not observed (170 m h</span></span><sup><span><span>-1</span></span></sup><span><span>). Compared with moderate brown haze, severe brown haze conditions are found to be associated with a significantly higher proportion of days with a distinct residual layer present in the ceilometer profiles, suggesting the entrainment of residual layer pollutants may contribute to the severity of the haze. This study illustrates the complex interaction between the ABL structure, air pollution, and the presence of brown haze, and demonstrates the utility of a ceilometer instrument in understanding and predicting the occurrence of brown haze events. </span></span></p>

Review: Laminar-to-Turbulent Transition of Three-Dimensional Boundary Layers on Rotating Bodies

1994 ◽  
Vol 116 (2) ◽  
pp. 200-211 ◽  
Author(s):  
Ryoji Kobayashi
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Three Dimensional ◽  
Speed Ratio ◽  
Stream Velocity ◽  
Turbulent Transition ◽  
Centrifugal Instability ◽  
Crossflow Instability ◽  
Dimensional Boundary ◽  
Axisymmetric Bodies

The laminar-turbulent transition of three-dimensional boundary layers is critically reviewed for some typical axisymmetric bodies rotating in still fluid or in axial flow. The flow structures of the transition regions are visualized. The transition phenomena are driven by the compound of the Tollmien-Schlichting instability, the crossflow instability, and the centrifugal instability. Experimental evidence is provided relating the critical and transition Reynolds numbers, defined in terms of the local velocity and the boundary layer momentum thickness, to the local rotational speed ratio, defined as the ratio of the circumferential speed to the free-stream velocity at the outer edge of the boundary layer, for the rotating disk, the rotating cone, the rotating sphere and other rotating axisymmetric bodies. It is shown that the cross-sectional structure of spiral vortices appearing in the transition regions and the flow pattern of the following secondary instability in the case of the crossflow instability are clearly different than those in the case of the centrifugal instability.

On Numerical Prediction of the Stability of Hypersonic Boundary-Layer Flow Over a Row of Microcavities

2003 ◽  
Author(s):  
Vassilios Theofilis ◽  
Michel O. Deville ◽  
Peter W. Duck ◽  
Alexander Fedorov
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Flow Instability ◽  
Viscous Sublayer ◽  
Hypersonic Boundary Layer ◽  
Two Dimensional ◽  
Flow Stabilization ◽  
Two Dimensional Flow ◽  
Dimensional Boundary ◽  
Layer Flow

This paper is concerned with the structure of steady two–dimensional flow inside the viscous sublayer in hypersonic boundary–layer flow over a flat surface in which microscopic cavities (‘microcavities’) are embedded. Such a so–called Ultra Absorptive Coating (UAC) has been predicted theoretically [1] and demonstrated experimentally [2] to stabilize passively hypersonic boundary–layer flow. In an effort to further quantify the physical mechanism leading to flow stabilization, this paper focuses on the nature of the basic flows developing in the configuration in question. Direct numerical simulations are performed, addressing firstly steady flow inside a singe microcavity, driven by a constant shear, and secondly a model of a UAC surface in which the two–dimensional boundary layer over a flat plate and a minimum nontrivial of two microcavities embedded in the wall are solved in a coupled manner. The influence of flow– and geometric parameters on the obtained solutions is illustrated. Based on the results obtained, the limitations of currently used theoretical methodologies for the description of flow instability are identified and suggestions for the improved prediction of the instability characteristics of UAC surfaces are discussed.

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