Newtonian Jet Research Articles

The Oscillation of Slender Elliptical Inviscid and Newtonian Jets: Effects of Surface Tension, Inertia, Viscosity, and Gravity

The motion of inviscid and Newtonian jets issuing from elliptical orifices is analyzed. The analysis is not confined to small departures of the jet free surface from a circular cylindrical mean surface, but rather is fully nonlinear. Two types of behavior are predicted: (1) In the presence of surface tension the major axis of the elliptical jet cross-section alternates between perpendicular directions with distance down the jet. In this case the system is described as a single-degree-of-freedom nonlinear oscillator, conservative for the inviscid elliptical jet in the absence of gravity, and nonconservative for the Newtonian jet. (2) When surface tension is neglected, the transformation occurs only once, after which the jet flattens into a sheet perpendicular to the major axis of the orifice. The effect of gravity is discussed both for downward flowing jets and fountains.

Die geometrical effect on annular die swelling

AbstractDie geometrical effect on Newtonian annular jet swelling was studied using a finite element method. Numerical result shows what we expected in the limiting cases of die swelling with annular die geometries, i.e., variation of the die gap for straight dies follows the limiting behavior of capillary and planar die swellings. Also the effect of upstream die geometry was investigated. The result shows that final extrudate dimensions are generally influenced by its previous history in the die, i.e., not only by shearing action but also by elongational effect caused by narrowing die gap.

Three‐dimensional extrudate swell of creeping Newtonian jets

AIChE JournalVolume 34, Issue 12 p. 2088-2094 R & D Note Three-dimensional extrudate swell of creeping Newtonian jets A. Karagiannis, A. Karagiannis Department of Chemical Engineering, McMaster University, Hamilton, Ontario, CANADA L8S 4L7Search for more papers by this authorA. N. Hrymak, A. N. Hrymak Department of Chemical Engineering, McMaster University, Hamilton, Ontario, CANADA L8S 4L7Search for more papers by this authorJ. Vlachopoulos, J. Vlachopoulos Department of Chemical Engineering, McMaster University, Hamilton, Ontario, CANADA L8S 4L7Search for more papers by this author A. Karagiannis, A. Karagiannis Department of Chemical Engineering, McMaster University, Hamilton, Ontario, CANADA L8S 4L7Search for more papers by this authorA. N. Hrymak, A. N. Hrymak Department of Chemical Engineering, McMaster University, Hamilton, Ontario, CANADA L8S 4L7Search for more papers by this authorJ. Vlachopoulos, J. Vlachopoulos Department of Chemical Engineering, McMaster University, Hamilton, Ontario, CANADA L8S 4L7Search for more papers by this author First published: December 1988 https://doi.org/10.1002/aic.690341222Citations: 26AboutRelatedInformationPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessClose modalShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume34, Issue12December 1988Pages 2088-2094 RelatedInformation RecommendedExtrudate swell of Newtonian fluids from annular diesE. Mitsoulis, AIChE JournalExperimental study on wetting of fibers with non‐Newtonian liquidsMamdouh T. Ghannam, M. Nabil Esmail, AIChE JournalWall normal stresses and die swell behavior of viscoelastic polymeric melts in flow through converging ductsChang Dae Han, AIChE JournalExperimental and linear analysis for the instability of non-Newtonian liquid jets issuing from a pressurized vibrating nozzleCristina Rodríguez-Rivero, Eva M. M. Del Valle, Miguel A. Galán, AIChE JournalComputational study of planar extrudate swell flows with a viscous liquid–gas interfacePaulo Roberto C. Mendes Junior, Ivan R. Siqueira, Roney L. Thompson, Marcio S. Carvalho, AIChE Journal

Laminar Newtonian jets at high Reynolds number and high surface tension

AIChE JournalVolume 34, Issue 9 p. 1559-1562 R & D Note Laminar Newtonian jets at high Reynolds number and high surface tension G. C. Georgiou, G. C. Georgiou Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109Search for more papers by this authorT. C. Papanastasiou, Corresponding Author T. C. Papanastasiou Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109Search for more papers by this authorJ. O. Wilkes, J. O. Wilkes Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109Search for more papers by this author G. C. Georgiou, G. C. Georgiou Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109Search for more papers by this authorT. C. Papanastasiou, Corresponding Author T. C. Papanastasiou Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109Search for more papers by this authorJ. O. Wilkes, J. O. Wilkes Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109Search for more papers by this author First published: September 1988 https://doi.org/10.1002/aic.690340918Citations: 42AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume34, Issue9September 1988Pages 1559-1562 RelatedInformation

On the behavior of viscoelastic free jets with elliptical cross section

In [1,2] we develop a comprehensive theory of one space dimensional closure models (closed systems of 1-D equations for the unknown, or modal, variables) for free viscoelastic jets. These closure models are derived via asymptotics from the full 3-D boundary value problem under the conditions of a Von Kármán-like flow geometry, a Maxwell-Jeffreys constitutive model, elliptical free surface cross section, and a slender jet scaling. The focus of the present paper is to determine the consequences and predictions of the lowest order system of equations in this asymptotic analysis. For the special cases of elliptical inviscid and Newtonian free jets, subject to the effects of surface tension and gravity, our model predicts oscillation of the major axis of the free surface elliptical cross section between perpendicular directions with distance down the jet, and draw-down of the cross section, in agreement with observed behavior. In the absence of surface tension the transformation from a cross section with major axis in one direction to a cross section with major axis in the perpendicular direction occurs only once, in agreement with the observation of Taylor [4]. In viscoelastic regimes, our model predicts swell of the elliptical extrudate and distortion of the elliptical extrudate cross section from the dimensions of the die aperture.

The mechanisms of ‘neck-like’ deformation in high-speed melt spinning. 1. Rheological and dynamic factors

In the search for mechanisms responsible for abrupt (‘neck-like’) deformation of polymer jets in high-speed fibre spinning, two groups of factors are analyzed. Kinematics of inertialess jets from Newtonian, Reiner-Rivlin, ‘power-law’ and co-rotational Maxwell fluids are studied. It is shown that the main factor responsible for S-shaped velocity profiles and concentrated deformation (‘necking’), is a positive viscosity gradient along the fluid jet. Elasticity, and non-linear (elongation-rate dependent) viscosity do not admit ‘necking’ under isothermal conditions, and reduce the necking effects produced by temperature-controlled viscosity increase. A similar study of Newtonian jets with inertial, surface tension, gravity and air drag effects, confirmed the controlling role of the viscosity gradient. Inertia, surface tension and air drag slightly reduce necking in non-isothermal jets; gravity exerts a small positive effect. Necking effects modelled by exponentially varying viscosity cannot quantitatively reproduce the experimental observations on high-speed fibre spinning. An additional source of viscosity gradient — stress-induced crystallization — will be discussed in a separate paper.

The mechanisms of ‘neck-like’ deformation in high-speed melt spinning. 2. Effects of polymer crystallization

As is shown in the first paper of the series, the main factor responsible for concentrated (‘neck-like’) deformation in high-speed melt spinning is the gradient of elongational viscosity along the spinline. In the present paper, stress-induced polymer crystallization is analyzed as a potential source of the rapid viscosity increase. A model of crystallization-controlled solidification is proposed, in which viscosity of the polymer increases with the degree of crystallinity, Θ, as ▪, reaching infinity (complete solidification) at Θ  Θ cr. The critical crystallinity level has been interpreted as one required for ‘crosslinking’ of polymer chains present in the melt. In addition to viscosity increase, crystallization modifies the local temperature in the spinline and reduces viscosity. The analysis of stress effects shows that critical crystallization temperature, T m, and crystallization rate, K, increase with the square of normal stress difference in the spinline, Δ p = p xx − p rr . The onset of crystallization can be shifted by 20–40 K towards higher temperatures, and crystallization rate can increase by orders of magnitude when high take-up speeds increase the stress level. A simple model illustrating velocity profiles in crystallizing Newtonian jets is discussed. The analysis strongly supports the hypothesis that the high viscosity gradient resulting from rapid stress-induced crystallization provides the major mechanism of ‘neck-like’ deformation.

Breakup of non‐newtonian emulsion jets

AbstractThe breakup of non‐Newtonian emulsion jets into drops was experimentally studied by ejecting both O/W and W/O emulsions vertically downward into stagnant air through nozzles. Breakup lengths of non‐Newtonian emulsion jets were found to be almost equivalent to those of Newtonian jets. Experimental breakup data establish that the static surface tension of the oil phase can be used as the surface tension of W/O emulsion jets, whereas the dynamic surface tension of aqueous surfactant solutions is used as that of O/W emulsion jets. Diameters of drops formed from non‐Newtonian emulsion jets are in good agreement with the prediction from the stability theory previously developed by the authors. When the rheological index in a power law model is appreciably smaller than unity and the Ohnesorge number is significantly large, however, drop sizes are larger than the prediction because of the profile relaxation in jets. The critical velocity of emulsion jets, either O/W or W/O emulsion, is significantly lower than that of homogeneous Newtonian jets.

Extrudate swell of Newtonian and non-Newtonian fluids—the effect of gravitational body force

In this investigation, the shape and the amount of swelling were measured for several Newtonian and viscoelastic fluids. The effect of the gravitational body force was investigated systematically. In the case of Newtonian jets, experimental measurements were compared with numerical solutions obtained by a combination of finite-element computation and analytical solution. For viscoelastic jets, the fluids was a carefully characterized Boger fluid. Experimental data were compared with finite-element solutions reported in recent literature for Oldroyd-B fluids.

Die swell experiments for newtonian fluids

AbstractThe swelling and shrinking of Newtonian jets issuing from circular orifices or slits are examined. Equations predicting the die swell ratio and downstream flow characteristics are developed. It is found that the cause of swelling at low Reynolds numbers is related to a negative pressure (below the free stream pressure) at the slit exit. The scatter of experimental data has been studied and the factors contributing to this phenomenon are discussed. The die swell ratios and jet shapes versus Reynolds number for Newtonian liquids issuing from tubes are empirically shown.

Laminar length of a non-Newtonian fluid jet

The laminar length of a submerged jet of a non-Newtonian fluid is measured employing a flow visualization technique, which makes use of the birefringent property of the fluid and a circular polariscope. Fluids of two different concentrations are studied. The results indicate that the concentration, hence the non-Newtonian nature of the fluid, has no influence on the laminar length of the jet for 600 〈 Re 〈 1100. In the Reynolds number range of 50 to 200 the laminar length is affected by the viscous properties of the fluid. The results also indicate that there is not much difference in the laminar length of a Newtonian and non-Newtonian jet for 600 〈 Re 〈 1100. The experimental facility is also used as a “falling head” capillary viscometer. The laminar length data and the viscosity data are taken simultaneously. The viscosity obtained from the present test facility is found to agree with that obtained using a standard rotary viscometer in trend only.

An Alternative Analysis of the Plane Stick-Slip Problem

The plane stick-slip problem has been solved analytically using the separation of variable technique. The essence of the mathematical procedure is to solve the problem separately for the “stick” and the “slip” regions and then to match the two solutions at the exit plane. The present solution, which is relatively easy to evaluate, yields results that compare favorably with those obtained by the Wiener-Hopf technique. Furthermore, the stick-slip solution has been used to estimate the expansion of a two-dimensional plane Newtonian jet at very low Reynolds numbers. For capillary numbers less than 0.1, the approximate method predicts swell ratios that are in fairly good agreement with those obtained from a more elaborate numerical solution of the jet swell problem.

Breakup of jets in power law non‐newtonianndashnewtonian liquid systems

AbstractNon‐Newtonian effects on the breakup of jets into drops were experimentally studied for power law fluidNdashNewtonian systems under the condition of zero jet velocity relative to the continuous phase. While laminar breakup lengths of Newtonian jets in non‐Newtonian liquids agree with the prediction from the stability analysis for Newtonian systems, non‐Newtonian jets in Newtonian liquids are less stable than Newtonian jets. Experimental diameters of drops formed from jets in NewtonianNdashnon‐Newtonian and in non‐NewtonianNdashNewtonian systems are in good agreement with the prediction based on stability analysis for Newtonian systems.

Inertia and surface tension effects in newtonian liquid jets

Inertia and surface tension effects in newtonian liquid jets

Dynamics of a creeping Newtonian jet with gravity and surface tension: A finite difference technique for solving steady free‐surface flows using orthogonal curvilinear coordinates

AbstractA finite difference technique capable of simulating steady, incompressible, viscous, free‐surface flows has been successfully applied to the motion of a creeping Newtonian jet, including both surface tension and gravitational forces. In accordance with experimental results, the numerical solutions predict either a 12 or 16% increase in the jet dimensions depending on whether the jet emerges from a circular or a slit die. Both gravity and surface tension inhibit the swelling behavior.

Finite difference simulation of die swell for a newtonian fluid

AbstractThe phenomenon of die swell for Newtonian fluids has been successfully simulated using a finite difference numerical method. The calculations predict the surface shape of Newtonian jets over a range of Reynolds numbers from 4.2 to 92.3 for both rectangular slits and cylindrical tubes. The calculated die swells for tubes compare favourably to experimental data. Velocity profiles and pressure distributions in jets exiting from slits or tubes are also predicted. The numerical data were incorporated into a momentum balance expression to demonstrate factors influencing this phenomenon. Other solutions were calculated to predict the effect of gravity and a sudden perturbation in flow on the resulting jet shape.

On the die-swell of an axisymmetric Newtonian jet

This paper investigates the behaviour of an axisymmetric Newtonian jet of incompressible viscous fluid. Numerical solutions are obtained via the Galerkin formulation of the finite element method for values of Reynolds number between 0.0001 and 1000, and for various values of the surface tension parameter. Attention is focussed on the shape of the free surface profile and the die-swell ratio. The numerical solutions are subjected to tests for validity based upon the momentum balance and mass balance equations. The satisfaction of stress boundary condition is also tested. The numerical are compared with experimental results.

Computer solutions of a plane newtonian jet with surface tension

Computer solutions of a plane newtonian jet with surface tension

An upper and lower bound for the die swell of the plane jet

A lower and upper bound for the die swell of a plane jet of a viscoelastic liquid is obtained and applied to a Newtonian jet. Extension of the bounds for other fluids is suggested.

Finite element methods for the solution of some incompressible non-newtonian fluid mechanics problems with free surfaces

A finite element scheme suitable for incompressible fluid flow in plane and axisymmetric geometries is constructed by using a Galerkin method. Principal features of the associated computer program are that it can be used for problems with or without free surfaces, with or without inertia, and for many types of non-Newtonian flow. Here we describe the use of the program in solving Poiseuille flow, a 2:1 contraction tube flow, free non-Newtonian jets without inertia, and a Newtonian free jet problem at a Reynolds number of 10. Comparison with exact solutions, other computer solutions and experiment is given where such information is available.