A parametric study of droplet deformation through a microfluidic contraction: Low viscosity Newtonian droplets

Numerical simulations are conducted to investigate how a droplet of Newtonian liquid. entrained in a higher viscosity Newtonian liquid, behaves when passing through an axisymmetric microfluidic contraction. Simulations are performed using a transient Volume of Fluid finite volume algorithm, and cover ranges of Reynolds and Weber numbers relevant to microfluidic flows. Results are presented for a droplet to surrounding fluid viscosity ratio of 0.001. In contrast to behaviour at higher viscosity ratios obtained previously by the authors, shear and interfacial tension driven instabilities often develop along the droplet Surface. leading to complex shape development, and in some instances, droplet breakup. (c) 2006 Elsevier Ltd. All rights reserved.

Development of a quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system. Part 1. Description of the model and its application to the MgO, MgO-SiO2, Al2O3-MgO and CaO-MgO sub-systems

A structurally-based quasi-chemical viscosity model for fully liquid slags in the Al2O3 CaO-'FeO'-MgO-SiO2 system has been developed. The model links the slag viscosities to the internal structures of the melts through the concentrations of various Si0.5O, Me2/nn+O and Me1/nn+Si0.25O viscous flow structural units. The concentrations of these structural units are derived from a quasi-chemical thermodynamic model of the system. The model described in this series of papers enables the viscosities of liquid slags to be predicted within experimental uncertainties over the whole range of temperatures and compositions in the Al2O3 CaOMgO-SiO2 system.

Development of a quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system. Part 2. A review of the experimental data and the model predictions for the Al2O3-CaO-MgO, CaO-MgO-SiO2 and Al2O3-MgO-SiO2 systems

A structurally-based quasi-chemical viscosity model has been developed for the Al2O3 CaO-'FeO'-MgO-SiO2 system. The model links the slag viscosity to the internal structure of melts through the concentrations of various anion/cation Si0.5O, Me2/nn+O and Me1/nn+Si0.25O viscous flow structural units. The concentrations of structural units are derived from the quasi-chemical thermodynamic model. The focus of the work described in the present paper is the analysis of experimental data and the viscosity models for fully liquid slags in the Al2O3-CaO-MgO, Al2O3 MgO-SiO2 and CaO-MgO-SiO2 systems.

Development of a quasi-chemical viscosity model for fully liquid slags in the Al2O3-CaO-'FeO'-MgO-SiO2 system. Part 3. Summary of the model predictions for the Al2O3-CaO-MgO-SiO2 system and its sub-systems

A structurally-based quasi-chemical viscosity model for fully liquid slags in the Al2O3 CaO-'FeO'-MgOSiO2 system has been developed. The focus of the work described in the present paper is the analysis of the experimental data and viscosity models in the quaternary system Al2O3 CaO-MgO-SiO2 and its subsystems. A review of the experimental data, viscometry methods used and viscosity models available in the Al2O3 CaO-MgO-SiO2 and its sub-systems is reported. The quasi-chemical viscosity model is shown to provide good agreement between experimental data and predictions over the whole compositional range.

Comparison of apparent ileal amino acid digestibility of feed ingredients measured with broilers, layers, and roosters

The apparent ileal digestibility of amino acids in 7 feed ingredients was determined using broilers, layers, and roosters. The ingredients included 3 cereals (wheat, sorghum, and corn), 3 oilseed meals (canola, cottonseed, and soybean meals), and 1 animal protein meal (meat and bone meal). Dietary protein in the assay diets was supplied solely by the test ingredient. All diets contained 20 g/kg of acid-insoluble ash as an indigestible marker, and each diet was offered ad libitum in mash form to 5 replicate pens of broilers and layers, and 4 replicate pens of roosters. The digestibility coefficients of individual amino acids for wheat, corn, and sorghum were higher (P < 0.05) in broilers than in layers and roosters. The digestibility of most amino acids for corn and sorghum was higher (P < 0.05) in roosters compared with those in layers, whereas the digestibility for wheat in layers and roosters was similar. In general, the digestibility of amino acids in canola meal, cottonseed meal, and meat and bone meal was similar among the 3 classes of chickens. The digestibility of amino acids in soybean meal was higher (P < 0.05) for layers compared with those for broilers and roosters but similar between broilers and roosters. These results suggest that the class of chickens significantly influenced the apparent ileal digestibility of amino acids in some feed ingredients.

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical "pinch time" t(p), an inertial-capillary balance leads to the expected 2/3-power scaling of the minimum radius with time: R-min similar to(t(p)-t)(2/3). However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>t(p). In this region, the filament radius decreases exponentially with time R-min similar to exp[(t(p)-t)/lambda(1)], where lambda(1) is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions. (C) 2006 American Institute of Physics

Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.

Local geometric changes in left ventricular remodeling post-infarction can lead to apparent reduction in scar thickness

Serial reduction in scar thickness has been shown in animal models. We sought whether this reduction in scar thickness may be a result of dilatation of the left ventricle (LV) with stretching and thinning of the wall. Contrast enhanced magnetic resonance imaging (CMRI) was performed to delineate radial scar thickness in 25 patients (age 63±10, 21 men) after myocardial infarction. The LV was divided into 16 segts and the absolute radial scar thickness (ST) and percentage scar to total wall thickness (%ST) were measured. Regional end diastolic (EDV) and end systolic volumes (ESV) of corresponding segments were measured on CMRI. All patients underwent revascularization and serial changes in ST, %ST, and regional volumes were assessed with a mean follow up of 15±5 months. CMRI identified a total of 93 scar segments. An increase in EDV or ESV was associated with a serial reduction inST(versusEDV, r =−0.3, p = 0.01; versusESV, r =−0.3, p = 0.005) and%ST(versusEDV, r =−0.2, p = 0.04; versus ESV, r =−0.3, p = 0.001). For segts associated with a positive increase in EDV (group I) or ESV (group II) there was a significant decrease in ST and %ST, but in those segts with stable EDV (group III) or ESV (group IV) there were no significant changes in ST and %ST (Table).