The extensional viscosity of a dilute suspension of spherical particles at intermediate microscale Reynolds numbers

The extensional viscosity of a dilute suspension of spherical particles (rigid spheres, viscous drops or gas bubbles) is computed for the case when the Reynolds number of the microscale disturbance motion R is not restricted to be small, as in the classical analysis of Einstein and Taylor. However, the present theory is restricted to steady axisymmetric pure straining flow (uniaxial extension). The rate of energy dissipation is expressed using the Bobyleff-Forsythe formula and then conditionally convergent integrals are removed explicitly. The problem is thereby reduced to a determination of the flow around a particle, subject to pure straining at infinity, followed (for rigid particles) by an evaluation of the volume integral of the vorticity squared. In the case of fluid particles, further integrals over the volume and surface of the particle are required. In the present paper, results are obtained numerically for 1 [less-than-or-eq, slant] R [less-than-or-eq, slant] 1000 for a rigid sphere, for a drop whose viscosity is equal to the viscosity of the ambient fluid, and for an inviscid drop (gas bubble). For the last case, limiting results are also obtained for R [rightward arrow] [infinity] using Levich's approach. All of these results show a strain-thickening behaviour which increases with the viscosity of the particle. The possibility of experimental verification of the results, which is complicated by the inapplicability of the approximation of material frame-indifference in this case, is discussed

The measurement of velocity gradients in laminar flow by homodyne light-scattering spectroscopy

A technique for measuring velocity gradients in laminar flows by homodyne light scattering is presented. A theory which describes the light-scattering spectrum is derived that includes the effects of different types of linear flow fields, particle diffusion and the intensity profile in the scattering volume. The conditions which must be satisfied in order that the theory describe the experimental situation are outlined and complementary experiments are performed which both verify the theory and apply the technique. Verification is provided using the flow in a Couette device, and the flow due to single rotating cylinder in a large bath of fluid. The technique is then applied to measure the spatial variation of the shear rate in a four-roll mill

Modeling of droplet breakup in a microfluidic T--shaped junction with a phase--field model

A phase--field method is applied to the modeling of flow and breakup of droplets in a T--shaped junction in the hydrodynamic regime where capillary and viscous stresses dominate over inertial forces, which is characteristic of microfluidic devices. The transport equations are solved numerically in the three--dimensional geometry, and the dependence of the droplet breakup on the flow rates, surface tension and viscosities of the two components is investigated in detail. The model reproduces quite accurately the phase diagram observed in experiments performed with immiscible fluids. The critical capillary number for droplet breakup depends on the viscosity contrast, with a trend which is analogous to that observed for free isolated droplets in hyperbolic flow

The Two Fluid Drop Snap-off Problem: Experiments and Theory

We address the dynamics of a drop with viscosity $\lambda \eta$ breaking up inside another fluid of viscosity $\eta$. For $\lambda=1$, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in excellent agreement with experiment and previous simulations of Lister and Stone. We also investigate the $\lambda$ dependence of the shape and breaking rate.Comment: 4 pages, 3 figure

Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies

The asymptotic frequency $\omega$, dependence of the dynamic viscosity of neutral hard sphere colloidal suspensions is shown to be of the form $\eta_0 A(\phi) (\omega \tau_P)^{-1/2}$, where $A(\phi)$ has been determined as a function of the volume fraction $\phi$, for all concentrations in the fluid range, $\eta_0$ is the solvent viscosity and $\tau_P$ the P\'{e}clet time. For a soft potential it is shown that, to leading order steepness, the asymptotic behavior is the same as that for the hard sphere potential and a condition for the cross-over behavior to $1/\omega \tau_P$ is given. Our result for the hard sphere potential generalizes a result of Cichocki and Felderhof obtained at low concentrations and agrees well with the experiments of van der Werff et al, if the usual Stokes-Einstein diffusion coefficient $D_0$ in the Smoluchowski operator is consistently replaced by the short-time self diffusion coefficient $D_s(\phi)$ for non-dilute colloidal suspensions.Comment: 18 pages LaTeX, 1 postscript figur

Air entrainment through free-surface cusps

In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose a novel mechanism for this phenomenon, based on the instability of cusp singularities that generically form on free surfaces. The air being drawn into the narrow space inside the cusp destroys its stationary shape when the walls of the cusp come too close. Instead, a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory of this instability is confirmed by experimental observation and quantitative comparison with numerical simulations of the flow equations

Dynamics of Fluid Vesicles in Oscillatory Shear Flow

The dynamics of fluid vesicles in oscillatory shear flow was studied using differential equations of two variables: the Taylor deformation parameter and inclination angle $\theta$. In a steady shear flow with a low viscosity $\eta_{\rm {in}}$ of internal fluid, the vesicles exhibit steady tank-treading motion with a constant inclination angle $\theta_0$. In the oscillatory flow with a low shear frequency, $\theta$ oscillates between $\pm \theta_0$ or around $\theta_0$ for zero or finite mean shear rate $\dot\gamma_{\rm m}$, respectively. As shear frequency $f_{\gamma}$ increases, the vesicle oscillation becomes delayed with respect to the shear oscillation, and the oscillation amplitude decreases. At high $f_{\gamma}$ with $\dot\gamma_{\rm m}=0$, another limit-cycle oscillation between $\theta_0-\pi$ and $-\theta_0$ is found to appear. In the steady flow, $\theta$ periodically rotates (tumbling) at high $\eta_{\rm {in}}$, and $\theta$ and the vesicle shape oscillate (swinging) at middle $\eta_{\rm {in}}$ and high shear rate. In the oscillatory flow, the coexistence of two or more limit-cycle oscillations can occur for low $f_{\gamma}$ in these phases. For the vesicle with a fixed shape, the angle $\theta$ rotates back to the original position after an oscillation period. However, it is found that a preferred angle can be induced by small thermal fluctuations.Comment: 11 pages, 13 figure

Autoimmune thyroiditis in antinuclear antibody positive children without rheumatologic disease

<p>Abstract</p> <p>Background</p> <p>Children are commonly referred to a pediatric rheumatology center for the laboratory finding of an Anti-nuclear antibody (ANA) of undetermined significance. Previous studies regarding adult rheumatology patients have supported an association between ANA and anti-thyroid antibodies, with the prevalence of thyroid antibodies being significantly higher in patients referred to a rheumatology center for an ANA without evidence of connective tissue disease compared to the general population. The purpose of the present study was to determine the frequency of thyroid antibodies in children referred to a pediatric rheumatology center for a positive ANA without evidence of a connective tissue disease.</p> <p>Methods</p> <p>A retrospective chart review was performed on children who were referred to our pediatric rheumatology center between August 2003 and March 2007 for positive ANA with concurrent thyroid antibody and thyroid function tests performed who did not fulfill criteria for a specific connective tissue disease. Laboratory and clinical features were recorded and analyzed. Mean and standard deviation were used to describe continuous data. Chi-square or Fisher's exact tests were used to compare proportions between variables.</p> <p>Results</p> <p>One-hundred and four ANA-positive patients with concurrent thyroid studies were evaluated (88% female, 93% Caucasian, mean age 11.9 ± 4.0 years). Half of patients had an ANA titer ≥ 1:320. The ANA pattern was speckled in 60% of the patients. Thyroid antibodies were detected in 30% of the patients. Anti-Thyroglobulin (ATG) was detected in 29% and Anti-thyroid peroxidase (ATPO) in 21% of the patients; of these children, 14% had hypothyroidism. ANA pattern and titer were not associated with anti-thyroid antibody positivity.</p> <p>Conclusion</p> <p>Thyroid antibodies associated with chronic lymphocytic thyroiditis, ATG and ATPO, were detected significantly higher in ANA-positive children without a rheumatologic condition (30%) as compared to the general pediatric population (1.3 - 3.4%). ANA titer and pattern did not help predict the presence or absence of thyroid antibodies. Given the high frequency of thyroid antibodies and increased risk of developing hypothyroidism over time, routine evaluation of ATG and ATPO with thyroid function tests in ANA-positive children is recommended.</p

Numerical study of chemical reaction effects in magnetohydrodynamic Oldroyd B oblique stagnation flow with a non-Fourier heat flux model

Reactive magnetohydrodynamic (MHD) flows arise in many areas of nuclear reactor transport. Working fluids in such systems may be either Newtonian or non-Newtonian. Motivated by these applications, in the current study, a mathematical model is developed for electrically-conducting viscoelastic oblique flow impinging on stretching wall under transverse magnetic field. A non-Fourier Cattaneo-Christov model is employed to simulate thermal relaxation effects which cannot be simulated with the classical Fourier heat conduction approach. The Oldroyd-B non-Newtonian model is employed which allows relaxation and retardation effects to be included. A convective boundary condition is imposed at the wall invoking Biot number effects. The fluid is assumed to be chemically reactive and both homogeneous-heterogeneous reactions are studied. The conservation equations for mass, momentum, energy and species (concentration) are altered with applicable similarity variables and the emerging strongly coupled, nonlinear non-dimensional boundary value problem is solved with robust well-tested Runge-Kutta-Fehlberg numerical quadrature and a shooting technique with tolerance level of 10−4. Validation with the Adomian decomposition method (ADM) is included. The influence of selected thermal (Biot number, Prandtl number), viscoelastic hydrodynamic (Deborah relaxation number), Schmidt number, magnetic parameter and chemical reaction parameters, on velocity, temperature and concentration distributions are plotted for fixed values of geometric (stretching rate, obliqueness) and thermal relaxation parameter. Wall heat transfer rate (local heat flux) and wall species transfer rate (local mass flux) are also computed and it is observed that local mass flux increases with strength of heterogeneous reactions whereas it decreases with strength of homogeneous reactions. The results provide interesting insights into certain nuclear reactor transport phenomena and furthermore a benchmark for more general CFD simulations