Free Surface Effects on Normal Stress Measurements in Cone and Plate Flow

2007 ◽  
Vol 17 (3) ◽  
pp. 36494-1-36494-6 ◽  
Author(s):  
David C. Venerus
Keyword(s):  
Free Surface ◽  
Stress Field ◽  
Normal Stress ◽  
Spherical Shape ◽  
Normal Stress Difference ◽  
Surface Shape ◽  
Stress Difference ◽  
Stress Measurements ◽  
Free Surface Shape ◽  
Normal Stress Differences

Abstract The effects of free surface shape on normal stress difference measurements in cone and plate flow are investigated. The analysis shows that the stress field is significantly altered by deviations of the free surface from an ideal (spherical) shape. For the cone and partitioned plate technique, it is shown how modest deviation from a spherical free surface shape can lead to errors of roughly 10% in the measured normal stress differences.

Thermohydrodynamic Analysis of Journal Bearings Lubricated by Non-Newtonian Fluids—Theory and Experiments

1994 ◽  
Vol 208 (3) ◽  
pp. 173-181 ◽  
Author(s):  
O Sheeja ◽  
B S Prabhu
Keyword(s):  
Film Thickness ◽  
Normal Stress ◽  
Journal Bearing ◽  
Fluid Model ◽  
Normal Stress Difference ◽  
Fluid Film ◽  
Stress Difference ◽  
First Normal Stress Difference ◽  
Cubic Law ◽  
Normal Stress Differences

Viscosity index improvers cause the lubricants to exhibit non-Newtonian flow behaviour and display shear thinning and normal stress differences. Shear thinning behaviour is studied by using a rotary shear viscometer. Owing to the non-availability of a rheogoniometer (for the measurement of normal stress differences), the first normal stress difference is calculated from the viscometric data using the Carreau viscosity function. The influence of the first normal stress difference on the hydrodynamic lubrication is analysed and shows that most of the commercial oils are inelasticoviscous in nature. Regression analysis shows that a large number of commercial lubricants follow the inelasticoviscous cubic law fluid model. Hence the cubic law fluid model is considered for the theoretical analysis. An experimental programme is developed to measure the effect of test parameters on the performance of a journal bearing lubricated with different types of non-Newtonian fluids. The experiments mainly include the measurements of the steady state characteristics like film thickness and fluid film friction. The experimental film thickness values are compared with the respective theoretical ones and are in good agreement. The theoretical performance characteristics are obtained through the simultaneous solution of the modified Reynolds equation using the cubic law fluid model and energy equation. The fluid film friction in a hydrodynamic journal bearing is experimentally determined through coastdown analysis. The results are presented in the form of an apparent Stribeck diagram of friction and are compared with the respective theoretical values.

Normal stress differences in suspensions of rigid  fibres

2014 ◽  
Vol 758 ◽  
pp. 486-507 ◽  
Author(s):  
Braden Snook ◽  
Levi M. Davidson ◽  
Jason E. Butler ◽  
Olivier Pouliquen ◽  
Élisabeth Guazzelli
Keyword(s):  
Normal Stress ◽  
Fibre Length ◽  
Normal Stress Difference ◽  
Contact Forces ◽  
Stress Difference ◽  
Normal Stresses ◽  
First Normal Stress Difference ◽  
Second Normal Stress Difference ◽  
Aspect Ratios ◽  
Normal Stress Differences

AbstractMeasurements of normal stress differences are reported for suspensions of rigid, non-Brownian fibres for concentrations of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}nL^2d=1.5\text {--}3$ and aspect ratios of $L/d=11\text {--}32$, where $n$ is the number of fibres per unit volume, $L$ is the fibre length and $d$ is the diameter. The first and second normal stress differences are determined experimentally from measuring the deformation in the free surface in a tilted trough and in a Weissenberg rheometer. Simulations are performed as well, and the hydrodynamic and contact contributions to the normal stresses are calculated. The experiments and simulations indicate that the second normal stress difference is negative and that its magnitude increases as the concentration is raised and the aspect ratio is lowered. The first normal stress difference is positive and its magnitude is approximately twice that of the second normal stress difference. Simulation results indicate that, for the concentrations and aspect ratios studied, contact forces between fibres form the dominant contribution to the normal stress differences.

The influence of secondary flows induced by normal stress differences on the shear-induced migration of particles in concentrated suspensions

2008 ◽  
Vol 603 ◽  
pp. 207-243 ◽  
Author(s):  
ARUN RAMACHANDRAN ◽  
DAVID T. LEIGHTON
Keyword(s):  
Normal Stress ◽  
Secondary Flow ◽  
Cross Section ◽  
Concentration Distribution ◽  
Normal Stress Difference ◽  
Secondary Flows ◽  
Stress Difference ◽  
Second Normal Stress Difference ◽  
Normal Stress Differences ◽  
The Cross

It was first demonstrated experimentally by H. Giesekus in 1965 that the second normal stress difference in polymers can induce a secondary flow within the cross-section of a non-axisymmetric conduit. In this paper, we show through simulations that the same may be true for suspensions of rigid non-colloidal particles that are known to exhibit a strong negative second normal stress difference. Typically, the magnitudes of the transverse velocity components are small compared to the average axial velocity of the suspension; but the ratio of this transverse convective velocity to the shear-induced migration velocity is characterized by the shear-induced migration Péclet number χ which scales as B2/a2, B being the characteristic length scale of the cross-section and a being the particle radius. Since this Péclet number is kept high in suspension experiments (typically 100 to 2500), the influence of the weak circulation currents on the concentration profile can be very strong, a result that has not been appreciated in previous work. The principal effect of secondary flows on the concentration distribution as determined from simulations using the suspension balance model of Nott & Brady (J. Fluid Mech. vol. 275, 1994, p. 157) and the constitutive equations of Zarraga et al. (J. Rheol. vol. 44, 2000, p. 185) is three-fold. First, the steady-state particle concentration distribution is no longer independent of particle size; rather, it depends on the aspect ratio B/a. Secondly, the direction of the secondary flow is such that particles are swept out of regions of high streamsurface curvature, e.g. particle concentrations in corners reach a minimum rather than the local maximum predicted in the absence of such flows. Finally, the second normal stress differences lead to instabilities even in such simple geometries as plane-Poiseuille flow.

Normal Stress Differences of Human Blood in Unidirectional Large-Amplitude Oscillatory Shear Flow

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
Chaimongkol Saengow ◽  
Alan Jeffrey Giacomin ◽  
Andrea Stephanie Dimitrov
Keyword(s):  
Shear Flow ◽  
Normal Stress ◽  
Human Blood ◽  
Stress Responses ◽  
Large Amplitude ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
Large Amplitude Oscillatory Shear ◽  
Oscillatory Shear Flow ◽  
Normal Stress Differences

Abstract This work analyzes normal stress difference responses in blood tested in unidirectional large-amplitude oscillatory shear flow (udLAOS), a novel rheological test, designed for human blood. udLAOS mimics the pulsatile flow in veins and arteries, in the sense that it never reverses, and yet also nearly stops once per heartbeat. As for our continuum fluid model, we choose the Oldroyd 8-constant framework for its rich diversity of popular constitutive equations, including the corotational Jeffreys fluid. This work arrives at exact solutions for normal stress differences from the corotational Jeffreys fluid in udLAOS. We discover fractional harmonics comprising the transient part of the normal stress difference responses, and both integer and fractional harmonics, the alternant part. By fractional, we mean that these occur at frequencies other than integer multiples of the superposed oscillation frequency. More generally, predictions from the Oldroyd 8-constant framework are explored by means of the finite difference method. Finally, the generalized versions of both the Oldroyd 8-constant framework and the corotational Jeffreys fluid are employed to predict the nonlinear normal stress responses for the model parameters fitted to udLAOS measurements from three very different donors, all healthy. From our predictions, we are led to expect less variation in normal stress differences in udLAOS from healthy donor to donor, than for the corresponding measured shear stress responses.

Normal stress differences, their origin and constitutive relations for a sheared granular fluid

2016 ◽  
Vol 795 ◽  
pp. 549-580 ◽  
Author(s):  
Saikat Saha ◽  
Meheboob Alam
Keyword(s):  
Normal Stress ◽  
Constitutive Relations ◽  
Moment Tensor ◽  
Normal Stress Difference ◽  
Stress Difference ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
Sign Change ◽  
Normal Stress Differences ◽  
Dilute Limit

The rheology of the steady uniform shear flow of smooth inelastic spheres is analysed by choosing the anisotropic/triaxial Gaussian as the single-particle distribution function. An exact solution of the balance equation for the second-moment tensor of velocity fluctuations, truncated at the ‘Burnett order’ (second order in the shear rate), is derived, leading to analytical expressions for the first and second ($\unicode[STIX]{x1D615}_{1}$ and $\unicode[STIX]{x1D615}_{2}$) normal stress differences and other transport coefficients as functions of density (i.e. the volume fraction of particles), restitution coefficient and other control parameters. Moreover, the perturbation solution at fourth order in the shear rate is obtained which helped to assess the range of validity of Burnett-order constitutive relations. Theoretical expressions for both $\unicode[STIX]{x1D615}_{1}$ and $\unicode[STIX]{x1D615}_{2}$ and those for pressure and shear viscosity agree well with particle simulation data for the uniform shear flow of inelastic hard spheres for a large range of volume fractions spanning from the dilute regime to close to the freezing-point density (${\it\nu}\sim 0.5$). While the first normal stress difference $\unicode[STIX]{x1D615}_{1}$ is found to be positive in the dilute limit and decreases monotonically to zero in the dense limit, the second normal stress difference $\unicode[STIX]{x1D615}_{2}$ is negative and positive in the dilute and dense limits, respectively, and undergoes a sign change at a finite density due to the sign change of its kinetic component. It is shown that the origin of $\unicode[STIX]{x1D615}_{1}$ is tied to the non-coaxiality (${\it\phi}\neq 0$) between the eigendirections of the second-moment tensor $\unicode[STIX]{x1D648}$ and those of the shear tensor $\unicode[STIX]{x1D63F}$. In contrast, the origin of $\unicode[STIX]{x1D615}_{2}$ in the dilute limit is tied to the ‘excess’ temperature ($T_{z}^{ex}=T-T_{z}$, where $T_{z}$ and $T$ are the $z$-component and the average of the granular temperature, respectively) along the mean vorticity ($z$) direction, whereas its origin in the dense limit is tied to the imposed shear field.

Measurements of the viscometric functions for a fluid in steady shear flows

1971 ◽  
Vol 270 (1208) ◽  
pp. 507-556 ◽  
Keyword(s):  
Normal Stress ◽  
Couette Flow ◽  
Direct Method ◽  
Normal Stress Difference ◽  
Optical Measurements ◽  
Measuring Error ◽  
Stress Difference ◽  
Concentric Cylinders ◽  
Plate Apparatus ◽  
Good Agreement

This paper describes a series of experiments in which the three material functions of steady viscometric flows were measured for a given polyisobutene solution. A number of instruments and measuring techniques were used in order to check the experimental method. The shear stress was determined from the torque transmitted by the fluid in a cone-and-plate apparatus and in Couette flow between concentric cylinders. The results obtained from these measurements were in good agreement with each other. The primary normal-stress difference was determined from the normal force acting on the plate of a cone-and-plate apparatus, and from stress-optical measurements on Couette flow between concentric cylinders. These results are in good agreement with each other. Detailed measurements of the distribution f Permanent address: Fluid Mechanics Research Institute, University of Essex, Colchester, Essex. of the normal stress acting on the plate of the cone-and-plate apparatus were made for three cone angles and for two boundary configurations at the rim of the apparatus: from these results a combination of the primary and the secondary normal-stress differences was deduced, thereby making possible the computation of the secondary normal-stress difference. When the normal stress acting on a rigid surface is measured by means of a hole leading to a pressure transducer the results are in error by an amount roughly proportional to the primary normal-stress difference of the fluid (cf. Kaye, Lodge & Vale 1968). In the present experiments this error was determined from measurements of the distribution of the normal stress acting on the plates of a plate-and-plate apparatus, together with the assumption that the error is a function only of the shear rate at the position o the hole in the undisturbed viscometric flow. The values of the measuring error thus obtained are in goo agreement with measurements made in Gouette flow between concentric cylinders. The secondary normal-stress difference, P2, was measured in a number of different ways. From the results it is suggested that the methods of Jackson & Kaye and of Marsh & Pearson may be imprecise and, in particular, may yield incorrect values for P2- A new, direct, method of estimating P2, suggested by Higashitani & Pritchard (1971) and outlined in appendix A, may provide a more convenient means of determining P2.

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