scholarly journals Regularized string model for nanofibre formation in centrifugal spinning methods

2017 ◽  
Vol 822 ◽  
pp. 202-234 ◽  
Author(s):  
S. Noroozi ◽  
H. Alamdari ◽  
W. Arne ◽  
R. G. Larson ◽  
S. M. Taghavi
Keyword(s):  
Surface Tension ◽  
String Model ◽  
Inviscid Limit ◽  
Arc Length ◽  
Viscous Forces ◽  
Spiral Trajectory ◽  
Viscous Shear ◽  
Centrifugal Spinning ◽  
Power Law Index ◽  
Arc Lengths

We develop a general regularized thin-fibre (string) model to predict the properties of non-Newtonian fluid fibres generated by centrifugal spinning. In this process the fibre emerges from a nozzle of a spinneret that rotates rapidly around its axis of symmetry, in the presence of centrifugal, Coriolis, inertial, viscous/shear-thinning, surface tension and gravitational forces. We analyse the effects of five important dimensionless groups, namely, the Rossby number ($Rb$), the Reynolds number ($Re$), the Weber number ($We$), the Froude number ($Fr$) and a power-law index ($m$), on the steady state trajectory and thinning of fibre radius. In particular, we find that the gravitational force mainly affects the fibre vertical angle at small arc lengths as well as the fibre trajectory. We show that for small $Rb$, which is the regime of nanofibre formation in centrifugal spinning methods, rapid thinning of the fibre radius occurs over small arc lengths, which becomes more pronounced as $Re$ increases or $m$ decreases. At larger arc lengths, a relatively large $We$ results in a spiral trajectory regime, where the fibre eventually recovers a corresponding inviscid limit with a slow thinning of the fibre radius as a function of the arc length. Viscous forces do not prevent the fibre from approaching the inviscid limit, but very strong surface tension forces may do so as they could even result in a circular trajectory with an almost constant fibre radius. We divide the spiral and circular trajectories into zones of no thinning, intense thinning and slow or ceased thinning, and for each zone we provide simple expressions for the fibre radius as a function of the arc length.

Effects of surface tension and viscosity on airway reopening

1990 ◽  
Vol 69 (1) ◽  
pp. 74-85 ◽  
Author(s):  
D. P. Gaver ◽  
R. W. Samsel ◽  
J. Solway
Keyword(s):  
Surface Tension ◽  
Fluid Viscosity ◽  
Opening Pressure ◽  
Viscous Forces ◽  
Considerable Portion ◽  
Airway Opening ◽  
Wall Compliance ◽  
Large Opening ◽  
Surface Tension Forces ◽  
The Relationship

We studied airway opening in a benchtop model intended to mimic bronchial walls held in apposition by airway lining fluid. We measured the relationship between the airway opening velocity (U) and the applied airway opening pressure in thin-walled polyethylene tubes of different radii (R) using lining fluids of different surface tensions (gamma) and viscosities (mu). Axial wall tension (T) was applied to modify the apparent wall compliance characteristics, and the lining film thickness (H) was varied. Increasing mu or gamma or decreasing R or T led to an increase in the airway opening pressures. The effect of H depended on T: when T was small, opening pressures increased slightly as H was decreased; when T was large, opening pressure was independent of H. Using dimensional analysis, we found that the relative importance of viscous and surface tension forces depends on the capillary number (Ca = microU/gamma). When Ca is small, the opening pressure is approximately 8 gamma/R and acts as an apparent “yield pressure” that must be exceeded before airway opening can begin. When Ca is large (Ca greater than 0.5), viscous forces add appreciably to the overall opening pressures. Based on these results, predictions of airway opening times suggest that airway closure can persist through a considerable portion of inspiration when lining fluid viscosity or surface tension are elevated.

Shape Synthesis and Optimization Using Intrinsic Geometry

1990 ◽  
Author(s):  
Shahriar Tavakkoli ◽  
Sanjay G. Dhande
Keyword(s):  
Optimization Problems ◽  
Piecewise Linear ◽  
Shape Design ◽  
Arc Length ◽  
Intrinsic Geometry ◽  
Shape Model ◽  
Design Variables ◽  
Dimensional Shape ◽  
Variable Geometry Truss ◽  
Arc Lengths

Abstract The present paper outlines a method of shape synthesis using intrinsic geometry to be used for two-dimensional shape optimization problems. It is observed that the shape of a curve can be defined in terms of intrinsic parameters such as the curvature as a function of the arc length. The method of shape synthesis, proposed here, consists of selecting a shape model, defining a set of shape design variables and then evaluating Cartesian coordinates of a curve. A shape model is conceived as a set of continuous piecewise linear segments of the curvature; each segment defined as a function of the arc length. The shape design variables are the values of curvature and/or arc lengths at some of the end-points of the linear segments. The proposed method of shape synthesis and optimization is general in nature. It has been shown how the proposed method can be used to find the optimal shape of a planar Variable Geometry Truss (VGT) manipulator for a pre-specified position and orientation of the end-effector. In conclusion, it can be said that the proposed approach requires fewer design variables as compared to the methods where shape is represented using spline-like functions.

scholarly journals On the origin of the circular hydraulic jump in a thin liquid film

2018 ◽  
Vol 851 ◽  
Author(s):  
Rajesh K. Bhagat ◽  
N. K. Jha ◽  
P. F. Linden ◽  
D. Ian Wilson
Keyword(s):  
Thin Film ◽  
Surface Tension ◽  
Liquid Film ◽  
Thin Liquid Film ◽  
Capillary Waves ◽  
Hydraulic Jumps ◽  
Planar Surface ◽  
Normal Impact ◽  
Viscous Forces

This study explores the formation of circular thin-film hydraulic jumps caused by the normal impact of a jet on an infinite planar surface. For more than a century, it has been believed that all hydraulic jumps are created due to gravity. However, we show that these thin-film hydraulic jumps result from energy loss due to surface tension and viscous forces alone. We show that, at the jump, surface tension and viscous forces balance the momentum in the liquid film and gravity plays no significant role. Experiments show no dependence on the orientation of the surface and a scaling relation balancing viscous forces and surface tension collapses the experimental data. A theoretical analysis shows that the downstream transport of surface energy is the previously neglected critical ingredient in these flows, and that capillary waves play the role of gravity waves in a traditional jump in demarcating the transition from the supercritical to subcritical flow associated with these jumps.

scholarly journals Nonlinear rotating viscoelastic jets during forcespinning process

2018 ◽  
Vol 474 (2220) ◽  
pp. 20180346 ◽  
Author(s):  
Daniel N. Riahi
Keyword(s):  
Surface Tension ◽  
Strain Rate ◽  
Tensile Force ◽  
Arc Length ◽  
Rotation Surface ◽  
Speed Increase ◽  
Nonlinear Viscoelastic ◽  
Steady Solutions ◽  
Effects Of Rotation ◽  
Viscoelastic Jets

In the usual forcespinning (FS) process, a fluid jet is forced through an orifice of a rotating spinneret leading to the formation of a jet with curved centreline. In this paper, we investigate the properties of nonlinear viscoelastic jets during the FS process. We apply scaling and perturbation techniques to determine the modelling system for the viscoelastic jets, subjected to the Giesekus constitutive equations for the stress tensor. We calculate numerically the expressions for the nonlinear steady solutions for the jet quantities such as radius, speed, stretching rate, strain rate, tensile force and trajectory. We determine these quantities for different values of the parameters such as those representing the effects due to rotation, surface tension, viscosity, jet drag and viscoelasticity. We find, in particular, that the fibre jet radius decreases and the tensile force increases with the jet arc length as well as with increasing the effects of rotation and viscoelasticity. Both viscosity and surface tension indicate stabilizing effect on the viscoelastic jet. In addition, strain rate, stretching rate and the jet speed increase with the arc length, viscoelasticity and rotation rate.

Film spreading from a miscible drop on a deep liquid layer

2017 ◽  
Vol 829 ◽  
pp. 304-327 ◽  
Author(s):  
Raj Dandekar ◽  
Anurag Pant ◽  
Baburaj A. Puthenveettil
Keyword(s):  
Surface Tension ◽  
Water Layer ◽  
Reynolds Numbers ◽  
Capillary Waves ◽  
Water Mixture ◽  
Inertial Forces ◽  
Viscous Forces ◽  
Dimensionless Velocity ◽  
Deep Water Layer ◽  
Film Spreading

We study the spreading of a film from ethanol–water droplets of radii $0.9~\text{mm}<r_{d}<1.1~\text{mm}$ on the surface of a deep water layer for various concentrations of ethanol in the drop. Since the drop is lighter ($\unicode[STIX]{x1D709}=\unicode[STIX]{x1D70C}_{l}/\unicode[STIX]{x1D70C}_{d}>1.03$), it stays at the surface of the water layer during the spreading of the film from the drop; the film is more viscous than the underlying water layer since $\unicode[STIX]{x1D712}=\unicode[STIX]{x1D707}_{l}/\unicode[STIX]{x1D707}_{d}>0.38$. Inertial forces are not dominant in the spreading since the Reynolds numbers based on the film thickness $h_{f}$ are in the range $0.02<Re_{f}<1.4$. The spreading is surface-tension-driven since the film capillary numbers are in the range $0.0005<Ca_{f}<0.0069$ and the drop Bond numbers are in the range $0.19<Bo_{d}<0.56$. We observe that, when the drop is brought in contact with the water surface, capillary waves propagate from the point of contact, followed by a radially expanding, thin circular film of ethanol–water mixture. The film develops instabilities at some radius to form outward-moving fingers at its periphery while it is still expanding, till the expansion stops at a larger radius. The film then retracts, during which time the remaining major part of the drop, which stays at the centre of the expanding film, thins and develops holes and eventually mixes completely with water. The radius of the expanding front of the film scales as $r_{f}\sim t^{1/4}$ and shows a dependence on the concentration of ethanol in the drop as well as on $r_{d}$, and is independent of the layer height $h_{l}$. Using a balance of surface tension and viscous forces within the film, along with a model for the fraction of the drop that forms the thin film, we obtain an expression for the dimensionless film radius $r_{f}^{\ast }=r_{f}/r_{d}$, in the form $fr_{f}^{\ast }={t_{\unicode[STIX]{x1D707}d}^{\ast }}^{1/4}$, where $t_{\unicode[STIX]{x1D707}d}^{\ast }=t/t_{\unicode[STIX]{x1D707}d}$, with the time scale $t_{\unicode[STIX]{x1D707}d}=\unicode[STIX]{x1D707}_{d}r_{d}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$ and $f$ is a function of $Bo_{d}$. Similarly, we show that the dimensionless velocity of film spreading, $Ca_{d}=u_{f}\unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x0394}\unicode[STIX]{x1D70E}$, scales as $4f^{4}Ca_{d}={r_{f}^{\ast }}^{-3}$.

Rheological Properties of Liquid Metals and Semisolid Materials at Low Solid Fraction

2016 ◽  
Vol 256 ◽  
pp. 133-138 ◽  
Author(s):  
Marialaura Tocci ◽  
Christoph Zang ◽  
Ines Cadòrniga Zueco ◽  
Annalisa Pola ◽  
Michael Modigell
Keyword(s):  
Surface Tension ◽  
Rheological Properties ◽  
Liquid Metals ◽  
High Surface ◽  
Measuring System ◽  
High Surface Tension ◽  
Viscous Forces ◽  
Low Viscosity ◽  
Semi Solid ◽  
Low Shear

Rheological properties of liquid metals are difficult to investigate experimentally because of the extreme border conditions to consider. One difficulty is related to the low viscosity of liquid metals. Surface tension effects can cause forces that can be considerably higher than the viscous forces in the liquid metals. Evaluating the experimental data without considering these effects leads to an apparent shear thinning behavior of the material. In the present study, experiments were performed by means of a Searle rheometer changing the dimension of the measuring system with metals of high surface tension, as mercury and tin. It became evident that surface tension plays a significant role in the effects that falsify measurements at low shear rate. Conclusions can be drawn to what extent measurements of semi-solid metals are affected.

Covering the circle with random arcs of random sizes

1982 ◽  
Vol 19 (2) ◽  
pp. 373-381 ◽  
Author(s):  
Andrew F. Siegel ◽  
Lars Holst
Keyword(s):  
Finite Number ◽  
Uniform Distribution ◽  
Special Class ◽  
Arc Length ◽  
Asymptotic Results ◽  
Arc Lengths

Consider the random uniform placement of a finite number of arcs on the circle, where the arc lengths are sampled from a distribution on (0, 1). We provide exact formulae for the probability that the circle is completely covered and for the distribution of the number of uncovered gaps, extending Stevens's (1939) formulae for the case of fixed equal arc lengths. A special class of arc length distributions is considered, and exact probabilities of coverage are tabulated for the uniform distribution on (0, 1). Some asymptotic results for the number of gaps are also given.

Deformation of a Droplet in a Channel Flow

2008 ◽  
Vol 5 (4) ◽  
Author(s):  
Ebrahim Shirani ◽  
Shila Masoomi
Keyword(s):  
Surface Tension ◽  
Channel Flow ◽  
Polymer Electrolyte Membrane ◽  
Droplet Deformation ◽  
Navier Stokes Equation ◽  
Droplet Shape ◽  
Viscous Forces ◽  
Electrolyte Membrane ◽  
Wide Range ◽  
Surrounding Fluid

Formation of droplets especially in microchannels, micro-electro-mechanical systems (MEMS) and polymer electrolyte membrane fuel cells and their effects on the performance of these devises, as well as scientific aspect of the droplet behavior in the fluid flow motion, makes the subject of the droplet deformation and motion an attractive problem. In this work, we numerically simulate the deformation of a drop of water attached to the wall of a channel flow using full two-dimensional Navier–Stokes equation and the volume-of-fluid method for capturing the interface. The effects of channel inlet velocity, the density and viscosity of the surrounding fluid, and the surface tension coefficient on the flow structures both inside and outside of the droplet as well as the deformation of the droplets are examined. Several test cases, which cover rather wide range of the Reynolds and capillary numbers, based on the surrounding fluid properties and the diameter of the droplet are performed. The Reynolds number, Re, range is from 24 to 1800 and the capillary number, Ca, is from 0.014 to 0.219. It is found that the droplet shape changes and depending on the capillary and Reynolds numbers, it eventually reaches an equilibrium state when there is balance between the surface tension, inertia, and the viscous forces. It is also found that the deformation of the droplet does not depend on the capillary numbers, when Ca is small, but it is a strong function of Ca, when it is large.

On the Law of Spontaneous Spreading of Liquid Droplets on Solid Substrates

2002 ◽  
Author(s):  
Abdullatif M. Alteraifi ◽  
Dalia Sherif ◽  
Abdelsamie Moet
Keyword(s):  
Surface Tension ◽  
Spherical Shape ◽  
Soda Lime ◽  
Solid Substrate ◽  
Contact Radius ◽  
Soda Lime Glass ◽  
Image Analysis System ◽  
Liquid Droplets ◽  
Viscous Forces ◽  
Wide Range

Several theories deal with the spreading kinetics of liquids on solid substrate, notable amongst which is de Gennes’ law, which relates the contact radius, R, to the droplet volume, V, the surface tension, σ, and the viscosity, µ, by the equation R3m+1 = (σ/µ) t Vm and ascertains that m = 3 is “indeed expected theoretically for all cases of dry spreading”. Validity of the proposed models is examined by measurements of the spreading of a number of liquids exhibiting a wide range of surface tension and viscosity on dry soda-lime glass. The measurements used a small droplet of constant volume to minimize gravitational effects. The droplet was released near the glass surface from automatic micro syring, supported on micromanipulator. The contact radius was acquired as a function of time by an image analysis system. Analyzed in terms of de Gennes law, it was noted that the m values for silicone oils fall within the suggested variance i.e., m = 3.0±0.5. However, significant disagreements were noted in the case of other liquids, where m ranged from 5.2 to 15.0 with no correlation with the parameters included. Mechanistic considerations suggest that whereas the surface tension acts to retain the spherical shape of the droplet, interfacial tension acts to maximize the contact area whereas the viscous forces determine the kinetics. The magnitude of the difference between the interfacial and surface energies likely determines whether spreading is complete or incomplete.

scholarly journals A genetic algorithm for the fuzzy shortest path problem in a fuzzy network

2020 ◽  
Author(s):  
Lihua Lin ◽  
Chuzheng Wu ◽  
Li Ma
Keyword(s):  
Genetic Algorithm ◽  
Shortest Path ◽  
Ad Hoc ◽  
Real Life ◽  
Shortest Path Problem ◽  
Arc Length ◽  
Routing Problem ◽  
Path Lengths ◽  
Fuzzy Network ◽  
Arc Lengths

Abstract The shortest path problem (SPP) is an optimization problem of determining a path between specified source vertex s and destination vertex t in a fuzzy network. Fuzzy logic can handle the uncertainties, associated with the information of any real life problem, where conventional mathematical models may fail to reveal proper result. In classical SPP, real numbers are used to represent the arc length of the network. However, the uncertainties related with the linguistic description of arc length in SPP are not properly represented by real number. We need to address two main matters in SPP with fuzzy arc lengths. The first matter is how to calculate the path length using fuzzy addition operation and the second matter is how to compare the two different path lengths denoted by fuzzy parameter. We use the graded mean integration technique of triangular fuzzy numbers to solve this two problems. A common heuristic algorithm to solve the SPP is the genetic algorithm. In this manuscript, we have introduced an algorithmic method based on genetic algorithm for determining the shortest path between a source vertex s and destination vertex t in a fuzzy graph with fuzzy arc lengths in SPP. A new crossover and mutation is introduced to solve this SPP. We also describe the QoS routing problem in a wireless ad hoc network.

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