The stress in a dilute suspension of liquid spheres in a second-order fluid

2012 ◽  
Vol 693 ◽  
pp. 500-507 ◽  
Author(s):  
J. M. Rallison
Keyword(s):  
Normal Stress ◽  
Newtonian Fluid ◽  
Second Order ◽  
Rigid Sphere ◽  
Ensemble Averaging ◽  
Averaging Technique ◽  
Liquid Drops ◽  
Dilute Suspension ◽  
Special Case ◽  
Second Order Fluids

AbstractWe use an ensemble averaging technique to calculate the average stress for a dilute suspension of liquid drops that are instantaneously spherical. The solvent and the drops consist of second-order fluids with differing properties. The suspension is itself a second-order fluid and its viscosity and normal stress coefficients are determined. For the special case of a rigid sphere suspension the results agree with Koch & Subramanian (J. Non-Newtonian Fluid Mech., vol. 138, 2006, p. 87, and vol. 153, 2008, p. 202). Differences from other results in the literature are discussed.

Normal Stress Effects in Second‐Order Fluids

1964 ◽  
Vol 35 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Bernard D. Coleman ◽  
Hershel Markovitz
Keyword(s):  
Normal Stress ◽  
Second Order ◽  
Stress Effects ◽  
Second Order Fluids

Acoustic streaming in second-order fluids

2020 ◽  
Vol 32 (12) ◽  
pp. 123103
Author(s):  
Pradipta Kr. Das ◽  
Arthur David Snider ◽  
Venkat R. Bhethanabotla
Keyword(s):  
Acoustic Streaming ◽  
Second Order ◽  
Second Order Fluids

Trial applications at gymnasiums of in-situ sound absorption measurement method by ensemble averaging technique

2021 ◽  
Vol 263 (2) ◽  
pp. 4532-4537
Author(s):  
Toru Otsuru ◽  
Reiji Tomiku ◽  
Noriko Okamoto ◽  
Siwat Lawanwadeekul
Keyword(s):  
Measurement Method ◽  
Sound Absorption ◽  
Glass Wool ◽  
Absorption Measurement ◽  
Ensemble Averaging ◽  
Averaging Technique ◽  
In Situ Conditions ◽  
Measurement Consistency ◽  
Absorption Characteristics

The authors have been published a series of papers on a measurement method for sound absorption characteristics of materials using ensemble averaging technique, i.e., EA method. The papers' results included measurement mechanisms, measurement uncertainty, and so on. Herein, to examine adaptability, especially in in-situ conditions, the EA method is applied to measure absorption characteristics of materials installed in two gymnasiums. A glass-wool panel with the dimension of 0.5 m by 0.5 m by 0.05 m and with the density of 32 kg m^-3 was brought around and measured to check the measurement consistency. Several measurements were conducted during badminton plays were undergoing. Measured sound absorption coefficients revealed that most results agree well with those measured in reverberation rooms. Certain improvement is necessary for the specimen brought to the in-situ measurement to keep the consistency. The inconsistency is considered to originate from unstable conditions between the specimen and floor.

Numerical Simulation of Die Swell of Second-Order Fluids Using Smoothed Particle Hydrodynamics

2010 ◽  
Author(s):  
Samir Hassan Sadek ◽  
Mehmet Yildiz
Keyword(s):  
Free Surface ◽  
Smoothed Particle Hydrodynamics ◽  
Second Order ◽  
Rheological Parameters ◽  
Die Swell ◽  
Two Dimensional ◽  
Polymeric Fluid ◽  
Particle Hydrodynamics ◽  
Smoothed Particle ◽  
Second Order Fluids

This work presents the development of both weakly compressible and incompressible Smoothed Particle Hydrodynamics (SPH) models for simulating two-dimensional transient viscoelastic free surface flow which has extensive applications in polymer processing industries. As an illustration with industrial significance, we have chosen to model the extrudate swell of a second-order polymeric fluid. The extrudate or die swell is a phenomenon that takes place during the extrusion of polymeric fluids. When a polymeric fluid is forced through a die to give a polymer its desired shape, due to its viscoelastic non-Newtonian nature, it shows a tendency to swell or contract at the die exit depending on its rheological parameters. The die swell phenomenon is a typical example of a free surface problem where the free surface is formed at the die exit after the polymeric fluid has been extruded. The swelling process leads to an undesired increase in the dimensions of the extrudate. To be able to obtain a near-net shape product, the flow in the extrusion process should be well-understood to shed some light on the important process parameters behind the swelling phenomenon. To this end, a systematic study has been carried out to compare constitutive models proposed in literature for second-order fluids in terms of their ability to capture the physics behind the swelling phenomenon. The effect of various process and rheological parameters on the die swell such as the extrusion velocity, normal stress coefficients, and Reynolds and Deborah numbers have also been investigated. The models developed here can predict both swelling and contraction of the extrudate successfully. The die swell problem was solved for a wide range of Deborah numbers and for two different Re numbers. The numerical model was validated through the solution of fully developed Newtonian and Non-Newtonian viscoelastic flows in a two-dimensional channel, and the results of these two benchmark problems were compared with analytic solutions, and good agreements were obtained.

The stress generated in a non-dilute suspension of elongated particles by pure straining motion

1971 ◽  
Vol 46 (4) ◽  
pp. 813-829 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Theoretical Formula ◽  
Rigid Sphere ◽  
Cross Sectional ◽  
Outer Flow ◽  
Rigid Particles ◽  
Bulk Stress ◽  
Order Of Magnitude ◽  
Sectional Plane ◽  
Dilute Suspension ◽  
A Minor

In a pure straining motion, elongated rigid particles in suspension are aligned parallel to the direction of the greatest principal rate of extension, provided the effect of Brownian motion is weak. If the suspension is dilute, in the sense that the particles are hydrodynamically independent, each particle of length 2l makes a contribution to the bulk deviatoric stress which is of roughly the same order of magnitude as that due to a rigid sphere of radius l. The fractional increase in the bulk stress due to the presence of the particles is thus equal to the concentration by volume multiplied by a factor of order l2/b2, where 2b is a measure of the linear dimensions of the particle cross-section. This suggests that the stress due to the particles might be relatively large, for volume fractions which are still small, with interesting implications for the behaviour of polymer solutions. However, dilute-suspension theory is not applicable in these circumstances, and so an investigation is made of the effect of interactions between particles. It is assumed that, when the average lateral spacing of particles (h) satisfies the conditions b [Lt ] h [Lt ] l, the disturbance velocity vector is parallel to the particles and varies only in the cross-sectional plane. The velocity near a particle is found to have the same functional form as for an isolated particle, and the modification to the outer flow field for one particle is determined by replacing the randomly placed neighbouring particles by an equivalent cylindrical boundary. The resulting expression for the contribution to the bulk stress due to the particles differs from that for a dilute suspension only in a minor way, viz. by the replacement of log 2l/b by log h/b, and the above suggestion is confirmed. The relative error in the expression for the stress is expected to be of order (log h/b)−1. Some recent observations by Weinberger of the stress in a suspension of glass-fibre particles for which 2l/h = 7·4 and h/2b = 7·8 do show a particle stress which is much larger than the ambient-fluid stress, although the theoretical formula is not accurate under these conditions.

ON TAYLOR'S SCRAPING PROBLEM AND FLOW OF A SISKO FLUID

2009 ◽  
Vol 14 (4) ◽  
pp. 515-529 ◽  
Author(s):  
Abdul M. Siddiqui ◽  
Ali R. Ansari ◽  
Ahmed Ahmad ◽  
N. Ahmad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Viscous Fluid ◽  
Normal Stress ◽  
Partial Differential ◽  
Sisko Fluid ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Special Case

The aim of the present investigation is to study the properties of a Sisko fluid flowing between two intersecting planes. The problem is similar to Taylor's scraping problem for a viscous fluid. We determine the solution of the complicated set of non‐linear partial differential equations describing the flow analytically. The analysis is carried out in detail reflecting the effects of varying the angle of the scraper on the flow. In addition, the tangential and normal stress are also computed. We also show the well known Taylor scraper problem as a special case.

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