Journal ArticleDOI
On the flow due to a rotating disk
TLDR
In this paper, the von Karman problem is extended to the case of flow started impulsively from rest; also, the steady-state problem is solved to a higher degree of accuracy than previously by a simple analytical-numerical method which avoids the matching difficulties in Cochran's (1934) well-known solution.Abstract:
The von Karman (1921) rotating disk problem is extended to the case of flow started impulsively from rest; also, the steady-state problem is solved to a higher degree of accuracy than previously by a simple analytical-numerical method which avoids the matching difficulties in Cochran's (1934) well-known solution. Exact representations of the non-steady velocity field and pressure are given by suitable power-series expansions in the angle of rotation, Ωt, with coefficients that are functions of a similarity variable. The first four equations for velocity coefficient functions are solved exactly in closed form, and the next six by numerical integration. This gives four terms in the series for the primary flow and three terms in each series for the secondary flow.The results indicate that the asymptotic steady state is approached after about 2 radians of the disk's motion and that it can be approximately obtained from the initial-value, time-dependent analysis. Furthermore, the non-steady flow has three phases, the first two of which are accurately and fully described with the terms computed. During the first-half radian (phase 1), the velocity field is essentially similar in time, with boundary-layer thickening the only significant effect. For 0·5 [lsim ] Ωt [lsim ] 1·5 (phase 2), boundary-layer growth continues at a slower rate, but simultaneously the velocity profiles adjust towards the shape of the ultimate steady-state profiles. At about Ωt = 1·5, some flow quantities overshoot the steady-state values by small amounts. In analogy with the ‘Greenspan-Howard problem’ (1963) it is believed that the third phase (Ωt > 1·5) consists of a small amplitude decaying oscillation about the steady-state solution.read more
Citations
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Journal ArticleDOI
Shear-dependent changes in the three-dimensional structure of human von Willebrand factor
Christopher A. Siedlecki,Brian J. Lestini,Brian J. Lestini,Kandice Kottke-Marchant,Kandice Kottke-Marchant,Steven J. Eppell,Steven J. Eppell,David L. Wilson,David L. Wilson,Roger E. Marchant +9 more
TL;DR: Shear stress-induced structural changes to vWF suggest a close conformation-function relationship in vWF properties for thrombogenesis in regions of high shear stress.
Journal ArticleDOI
Nanofluid flow and heat transfer due to a rotating disk
TL;DR: In this article, the nanofluid boundary layer flow over a rotating disk is the main concern of the present paper and a comparative analysis is made in terms of shear stress and cooling properties of considered nanoparticles.
Journal ArticleDOI
Investigation of entropy generation in MHD and slip flow over a rotating porous disk with variable properties
TL;DR: In this paper, the effects of magnetic interaction number, slip factor and relative temperature difference on velocity and temperature profiles as well as entropy generation in magnetohydrodynamic (MHD) flow of a fluid with variable properties over a rotating disk are investigated using numerical methods.
Journal ArticleDOI
Cell adhesion to a series of hydrophilic-hydrophobic copolymers studied with a spinning disc apparatus
TL;DR: The existence of a critical shear stress for 3T3 cell detachment suggests that cell adhesion to surfaces cannot be fully understood with singleShear stress methods because cells may attach with a wide range of strengths which are either all above or all below the applied shear Stress.
Cell adhesion to a series of hydrophilichydrophobic copolymers studied with a spinning disc apparatus.
TL;DR: In this article, the authors measured 3T3 cell detachment from a chemically homologous series of copolymers based on HEMA and ethylmethacrylate (EMA) with a spinning-disc apparatus.
References
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Difference methods for initial-value problems
Robert D. Richtmyer,K. W. Morton +1 more
TL;DR: In this article, differentielles and stabilite were used for differentiable transport in the context of transfert de chaleur and ondes Reference Record created on 2005-11-18, modified on 2016-08-08
Journal ArticleDOI
Über laminare und turbulente Reibung
Journal ArticleDOI
The flow due to a rotating disc
TL;DR: In this paper, the steady motion of an incompressible viscous fluid due to an infinite rotating plane lamina was considered, and it was shown that the equations of motion and continuity are satisfied by taking
Journal ArticleDOI
On a time-dependent motion of a rotating fluid
H. P. Greenspan,L. N. Howard +1 more
TL;DR: In this article, the authors consider the way in which the state of rigid rotation of a contained viscous fluid is established, and they find that the motion consists of three distinct phases, namely, the development of the Ekman layer, the inviscid fluid spin-up, and the viscous decay of residual oscillations.
Journal ArticleDOI
Boundary layer growth
S. Goldstein,L. Rosenhead +1 more
TL;DR: In this paper, it was shown that the initial motion of a viscous incompressible fluid is irrotational, without circulation, when the fluid is started impulsively from rest.