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Topic: Weissenberg number

	Weissenberg number: Definition and Links by Encyclopedian.com
		A scientist at Michigan State University has calculated that the production of a single hen egg requires about 120 gallons of water, a loaf of bread requires 300 gallons, and a pound of beef, 3,500.
		...Weissenberg number Weissenberg number The Weissenberg number is a dimensionless...used in the study of Viscoelastic Viscoelastic viscoelastic flows.
		The Weissenberg number is a dimensionless number used in the study of viscoelastic[?] flows.
	www.encyclopedian.com /we/Weissenberg-number.html (118 words)

	Weissenberg number Information
		The dimensionless number is the ratio of a specific process time and the relaxation time of the fluid.
		Since this number is obtained from scaling the evolution of the stress, it contains choices for the shear or elongation rate and the lenghtscale.
		Therefore the exact definition of all non dimensional numbers should be given as well as the number itself.
	www.bookrags.com /Weissenberg_number (108 words)

	[No title]
		Features associated with the high Weissenberg number limit, such as stress boundary layers and corner singularities, have been prominent and troublesome in numerical simulations of viscoelastic flows, and the lack of a mathematical understanding has been a major impediment to progress in the field.
		Rather curiously, for the case of the upper convected Maxwell model, the resulting equations for the infinite Weissenberg number limit can be transformed to the Euler equations, but with a rather unusual ``equation of state," which relates the divergence of the ``velocity field" to the ``density" instead of the usual pressure-density relationship.
		Hence, regardless of the value of the Weissenberg number for the global flow, we should view such flows as having an infinite local Weissenberg number at the corner, and the use of high Weissenberg number asymptotics is appropriate for the analysis of the local behavior.
	www.math.vt.edu /people/renardyy/Research/weissen.html (807 words)

	Guide to Rheological Nomenclature: Measurements in Ceramic Particulate Systems
		Weissenberg effect The tendency of some viscoelastic fluids to flow in a direction normal to the direction of shear.
		Weissenberg number, Wi A measure of the degree of nonlinearity or the degree to which normal stress differences are exhibited in a flow.
		In converging flows it is proportional to the Deborah number.
	ciks.cbt.nist.gov /~garbocz/SP946/node6.htm (1269 words)

	Dimensionlessl Analysis...Measuroo.com (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-17)
		Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all units cancel.
		Dimensionless numbers are widely applied in the field of mechanical and chemical engineering.
		However, a number may be dimensionless in one system of units (e.g., in a nonrationalized cgs system of units with the electric constant e0 = 1), and not dimensionless in another system of units (e.g., the rationalized SI system, with e0 = 8.85419×10
	www.measuroo.com.cob-web.org:8888 /dimensionsnumber.html (516 words)

	Inverse energy cascade
		numbers, the energy growth rate in the viscoelastic case can be reduced to zero when the polymer dissipation balances exactly the forcing input.
		number the energy flux in the cascade is reduced and consequently the friction term stops the cascade at smaller scale.
		number the inverse energy cascade is indeed stopped by friction at smaller scale as shown in Figure (4.12).
	www.ph.unito.it /~smusacch/tesi/node58.html (651 words)

	Polymer dynamics in fluids
		A polymeric molecule consists in a long chain formed by the repetition of a large number of single identical units, the monomers, linked by chemical bonds.
		The relative strength between the relaxation of the polymer and stretching exerted by the flow is measured by the Weissenberg number
		For a turbulent flow the Lyapunov exponent gives an measure of the characteristic gradients of velocity which are determined by the smallest eddies of the turbulent cascade.
	www.ph.unito.it /~smusacch/tesi/node38.html (863 words)

	BIG PAPER
		At the beginning of the mixing process, the capillary number, which is the ratio of the viscous forces to the interfacial forces, is large and interfacial tension is unimportant.
		Although linear stability theory does not predict the correct number and size of drops, the time for breakup is reasonably estimated by the time for the amplitude of the fastest growing disturbance to become equal to the average radius (Tomotika, 1935).
		By analogy with liquid droplets and the capillary number (equation A.8) the dimensionless parameter that characterizes the fragmentation process is the ratio of the viscous shear stress to the strength of the agglomerate.
	mixing.chem-eng.northwestern.edu /papers/Advances/advances.htm (14699 words)

	The Society of Rheology: 70th Annual Meeting (Oct 1998) Paper AN1
		Asymptotic and numerical results indicate that the high frequency, low axial Weissenberg number regime is essentially equivalent to the case without axial flow, implying no stabilization, while at high values of frequency and axial Weissenberg number, the flow is always stable.
		The qualitative effect of adding a steady axial flow is similar to that of the circular Couette geometry for high axial Weissenberg number, with the critical azimuthal Weissenberg number increasing linearly with the axial Weissenberg number.
		For low axial Weissenberg number, the flow is stabilized, in constrast to the circular Couette flow.
	www.rheology.org /sor98a/abstract.asp?PaperID=222 (361 words)

	Dimensionless quantity - Wikipedia, the free encyclopedia
		In dimensional analysis, a dimensionless quantity (or more precisely, a quantity with the dimensions of 1) is a quantity without any physical units and thus a pure number.
		When they attach that dimensionless number (the number of tick marks) to the units that the standard represents, they conceptually are referring to a dimensionful quantity.
		According to the Buckingham π-theorem of dimensional analysis, the functional dependence between a certain number (e.g., n) of variables can be reduced by the number (e.g., k) of independent dimensions occurring in those variables to give a set of p = n − k independent, dimensionless quantity.
	en.wikipedia.org /wiki/Dimensionless_number (982 words)

	Access - Science And Technology
		Another important parameter, known as the Weissenberg or Deborah number, relates the relaxation time of the polymer to how fast the flow can stretch it.
		As this parameter increases, the solution has a stronger tendency to resist extension.
		"It's critical," says Beris, "that the characteristic relaxation time of the material is higher than the characteristic flow time." The simulations show that a high Weissenberg number, 10 or above, is required for drag reduction.
	www.ncsa.uiuc.edu /News/Access/Stories/StretchyMolecules/gasol_3.html (392 words)

	kupferman_abs (Site not responding. Last check: 2007-10-17)
		The high Weissenberg number problem (HWNP) has been a nagging (almost offending) problem in computational rheology for over 30 years.
		For three decades, the computation of flows for such fluids has faced a "wall"--- all computations break down as the degree of elasticity (the dimensionless Weissenberg number) reaches a frustratingly low threshold.
		There has been continual debate whether this breakdown is of numerical nature, or whether the models become ill-posed past certain degree of elasticity.
	www.weizmann.ac.il /math/varlim/kupfer_abs.html (146 words)

	Untitled Document (Site not responding. Last check: 2007-10-17)
		The Weissenberg number was 6.5 for the upper row and 13 for the lower row.
		Its radius was 38 mm and the gap between the plates was 10 mm.
		Efficient mixing is due to a random similar to the elastic turbulence.
	physics.ucsd.edu /~groisman/imagesNEW.htm (522 words)

	Biographical Notes on Karl Weissenberg (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-17)
		Karl Weissenberg was born in Vienna (Austria) on the 11th of June 1893 and he has lived a long life under varied conditions.
		He designed a new type of measuring instrument, known in the literature as the Weissenberg Rheogoniometer, which allowed for the first time to measure in the flowing material the movements and forces and their developments in time in all three directions of space.
		It is widely used for the determination of the strength of materials with respect to their elasticity, viscocity, relaxation, etc. In order to account for the similarity in behaviour of visco-elastic materials he introduced a dimensionless constant, known as the “Weissenberg number”.
	innfm.swan.ac.uk.cob-web.org:8888 /bsr/weissenburg/biography.htm (874 words)

	Materials Technology
		We present a stability analysis in 1D and identify the failure of the numerical scheme to balance exponential growth as a possible source for numerical instabilities at high Weissenberg numbers.
		We provide evidence that the numerical instability identified in the 1D problem is also the actual reason for the failure of the standard FEM implementation of the problem.
		With the log conformation representation we are able to obtain solutions beyond the limiting Weissenberg numbers in the standard scheme.
	www.mate.tue.nl /mate/showabstract.php/5006 (255 words)

	Extrusion Glossary of Terms
		DEBORAH NUMBER (De): The ratio of a characteristic material time to a characteristic process time.
		The flow is turbulent when the Reynolds number is more than 2100 for tubes.
		WEISSENBERG NUMBER: The product of a characteristic material time and shear rate.
	www.polydynamics.com /glossary2.htm (5611 words)

	Preprints
		In the defect step, the constitutive equation is computed with an artificially reduced Weissenberg parameter for stability, and the resulting residual is corrected in the correction step.
		Specifically, at a Weissenberg number larger that a critical value, the iterative nonlinear solver fails to converge.
		In the defect step the Weissenberg number is artifically reduced to solve a stable nonlinear problem.
	www.math.clemson.edu /~vjervin/papers/index.html (1749 words)

	PIV Measurements of Flow Around a Sphere for a Viscoelastic Fluid (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-17)
		The flow for three different extensively characterized, dilute, monodisperse, polystyrene based Boger fluids is mapped as a function of fluid elasticity, which is parameterized by a Weissenberg number, the ratio of elastic and flow time scales (\frac\lambda U_ta), in the range of 0.5 to 14.
		The kinematic structure of the wake is found to scale with the Weissenberg number and the polymer molecular weight, but the drag does not solely correlate with the wake length.
		For the intermediate range of Weissenberg numbers the wake approaches a self-similar structure while at high Weissenberg numbers the features become more complex.
	flux.aps.org.cob-web.org:8888 /meetings/YR00/DFD00/abs/S220005.html (233 words)

	I.2.4 Upwinding
		interpolation and the SUPG technique for the problem of the full set of viscoelastic equations, they have obtained oscillatory extra-stress and velocity at relatively small values of the Weissenberg number, even if interesting accurate results can be obtained for the flow around a sphere or in undulated channels.
		Note that to apply the modified test functions to the advect terms of giverning equations is equivalent to add an artificial diffusivity in the direction of advection.
		(The element Péclet number represents the ratio of advective terms and diffusive terms at element level.) This Number is used for the calculation of additional viscosity in the advection-diffusion equation:
	users.skynet.be /keyFE2/manual/I_2_4_Upwinding.html (622 words)

	OhioLINK ETD: Kang, Kai
		There are many unusual differences from conventional fluidics, such as the significance of surface forces, the high shear/extensional rate, the high heat transfer rate, the low Reynolds number, and the high Weissenberg number.
		In this study, aqueous solutions of high molecular-weight polymers, polyethylene oxide (PEO) and hydroxyethyl cellulose (HEC), as well as biomacromolecules, protein BSA and DNA fragments, have been chosen as the model materials for the complex fluids involved in BioMEMS applications.
		Lastly, the characteristics of high Weissenberg number and strong extensional flow at the entries triggered the study of end (entrance/exit) flow in microfluidics.
	www.ohiolink.edu /etd/view.cgi?acc_num=osu1064325460 (635 words)

	CSCAMM Seminars - Spring 2006
		The kissing number k(n) is the maximal number of equal nonoverlapping spheres in n-dimensional space that can touch another sphere of the same size.
		I will show that the iterative algorithm has an optimal complexity, i.e., the number of iterations is finite and is independent of mesh size, for Eikonal equation which is a nonlinear hyperbolic boundary value problem.
		In many applications materials are modeled by a large number of particles (or atoms) where any one of particles interacting with all others through a pair potential energy.
	www.cscamm.umd.edu /seminars/spring06/index.htm (2862 words)

	The Second Israeli Mini-Workshop in Applied and Computational Mathematics
		For those arriving by car, there are parking lots outside, but close to, the campus (the big white things on the map next to building 1401).
		A large number of bus routes serve the university.
		We also demonstrate our new approach by predicting the flow of an Oldroyd B fluid at high Weissenberg numbers in a 4:1 planar abruplty contracting channel.
	www.math.biu.ac.il /~schiff/wrkshpam.html (1531 words)

	Flow Stability and Dynamics: Graham (1998) Abstract (Site not responding. Last check: 2007-10-17)
		Circular Couette flow displays the prototypical instability of this type, when the azimuthal Weissenberg number We t
		We consider here the effect of superimposed steady axial Couette or Poiseuille flow on this instability.
		The numerical results are consistent with a scaling analysis for We
	www.engr.wisc.edu /groups/fsd/research/vetc/graham98.html (279 words)

	Short wave inertialess interfacial instabilities at large Weissenberg number (Site not responding. Last check: 2007-10-17)
		A considerable amount of attention has been paid to instabilities of Couette flow of inertialess viscoelastic fluids with an interface.
		Long and short wave instabilities are fairly well understood and some recent work has investigated a new intermediate wavelength mode at large Wi.
		The large Wi number limit can be acheived by speeding up the flow or by bringing the walls closer together.
	flux.aps.org /meetings/YR04/DFD04/baps/abs/S890008.html (147 words)

	Citations: the high Weissenberg number problem - Keunings (ResearchIndex) (Site not responding. Last check: 2007-10-17)
		Keunings, R.: On the high Weissenberg number problem.
		One way to deal with this problem is to consider the corresponding time dependent problem and use operator splitting methods such as Peaceman Rachford type or the methods of time discretization, Saramito [2] Saramito and Piau [3] Sureshkumar et al.
		One way to deal with this problem is to consider the corresponding time dependent problem and use operator splitting methods such as Peaceman Rachford type or the methods of time discretization, Saramito [4] Saramito and Piau [5] Sureshkumar et al.
	citeseer.ist.psu.edu /context/1826963/0 (273 words)

	Journal of Rheology: Volume 49, Issue 1 (Jan-Feb 2005)
		We characterize the configurations and concentration of λ-phage DNA molecules in shear flow near a glass surface in a microchannel through epi-fluorescence microscopy.
		We also find that the concentration of DNA molecules in this same region is notably lower than in the bulk, to a degree that increases with increasing Weissenberg number.
		A simplified explanation is proposed for the behavior of DNA molecules near the glass surface based on wall influences on hydrodynamic interaction within the chain, motivated by the recent theoretical work of Jendrejack et al.
	www.rheology.org /sor/publications/J_Rheology/Abstract/a0512.htm (3280 words)

	Amazon.com: "number asymptotics": Key Phrase page (Site not responding. Last check: 2007-10-17)
		See all pages with references to number asymptotics.
		chosen three topics to which he has made substantial con- tributions over the past ten years, they are: high Weissenberg number asymptotics, stability of viscoelastic flows and breakup of viscoelastic jets.
		Approximation by Algebraic Numbers (Cambridge Tracts in Mathematics) by Yann Bugeaud
	www.amazon.com /phrase/number-asymptotics (413 words)

	Mathematics Preprints
		This is the Preprint Collection of the Department of Mathematical Sciences at the University of Bath.
		Click on the preprint number to see a copy of the paper (the files are stored as gzipped PostScript: we assume your Web Browser knows what to do with this!).
		maths0601: High Weissenberg number boundary layer structures for UCM fluids
	www.maths.bath.ac.uk /MATHEMATICS/preprints.html (2609 words)

	Past 2004 Seminars
		Subject: ``Tamagawa Numbers and the Cohomology of Bun_G''
		Event: PIMS Distinguished Lecture Series in Number Theory
		Subject:``Linear Stability of Uniform Shear Flow in High Weissenberg Number Boundary Layers
	www.math.ubc.ca /Dept/Events/2004sem.shtml (5385 words)

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