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

Macromolecular interactions during gelatinisation and retrogradation in starch-whey systems as studied by rapid visco-analyser

Gelatinisation and retrogradation of starch-whey mixtures were studied in water (pH 7) using the Rapid Visco-Analyser (RVA). The starch:whey ratios ranged from 0:100 - 100:0. Wheat starch, and whey protein concentrate (about 80% solids basis) and isolate (about 96% solids basis) were used. Mixtures with whey isolates were generally more viscous than those with whey concentrates, and this was attributed to fewer non-protein milk components in the former. Whey protein concentrates and isolates reduced the peak, trough and final viscosities of the mixtures, but the breakdown and setback ratios of the mixtures were increased. The gelatinisation temperature increased with whey substitutions indicating that whey protein delayed starch gelatinisation. The temperature of fastest viscosity development decreased as the amount of whey was increased. Whey protein isolate generally exercised a lesser effect than the concentrate. At between 40 - 50% whey substitutions, the dominant phase changed from starch to protein irrespective of the source of the whey protein. An additive law poorly defined selected RVA parameters. Both macromolecules interacted to define the viscosity of the mixture, and an exponential model predicted the viscosity better than the additive law. The results obtained in this study are discussed to assist the understanding of extrusion processing of starch-whey systems as models for whey-fortified snack and ready-to-eat foods. Copyright ©2006 The Berkeley Electronic Press. All rights reserved.

Differential Priors for Elastic Nets

The elastic net and related algorithms, such as generative topographic mapping, are key methods for discretized dimension-reduction problems. At their heart are priors that specify the expected topological and geometric properties of the maps. However, up to now, only a very small subset of possible priors has been considered. Here we study a much more general family originating from discrete, high-order derivative operators. We show theoretically that the form of the discrete approximation to the derivative used has a crucial influence on the resulting map. Using a new and more powerful iterative elastic net algorithm, we confirm these results empirically, and illustrate how different priors affect the form of simulated ocular dominance columns.

Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

Quantum open-systems approach to current noise in resonant tunneling junctions

A quantum Markovian master equation is derived to describe the current noise in resonant tunneling devices. This equation includes both incoherent and coherent quantum tunneling processes. We show how to obtain the population master equation by adiabatic elimination of quantum coherences in the presence of elastic scattering. We calculate the noise spectrum for a double well device and predict subshot noise statistics for strong tunneling between the wells. The method is an alternative to Green's function methods and population master equations for very small coherently coupled quantum dots.

Modelling the large deformations in stratified media - the Cosserat continuum approach

Methods employing continuum approximation in describing the deformation of layered materials possess a clear advantage over explicit models, However, the conventional implicit models based on the theory of anisotropic continua suffers from certain difficulties associated with interface slip and internal instabilities. These difficulties can be remedied by considering the bending stiffness of the layers. This implies the introduction of moment (couple) stresses and internal rotations, which leads to a Cosserat-type theory. In the present model, the behaviour of the layered material is assumed to be linearly elastic; the interfaces are assumed to be elastic perfectly plastic. Conditions of slip or no slip at the interfaces are detected by a Coulomb criterion with tension cut off at zero normal stress. The theory is valid for large deformation analysis. The model is incorporated into the finite element program AFENA and validated against analytical solutions of elementary buckling problems in layered medium. A problem associated with buckling of the roof and the floor of a rectangular excavation in jointed rock mass under high horizontal in situ stresses is considered as the main application of the theory. Copyright (C) 1999 John Wiley & Sons, Ltd.

Novel vascular graft grown within recipient's own peritoneal cavity

A method by which to overcome the clinical symptoms of atherosclerosis is the insertion of a graft to bypass an artery blocked or impeded by plaque. However, there may be insufficient autologous mammary artery for multiple or repeat bypass, saphenous vein may have varicose degenerative alterations that can lead to aneurysm in high-pressure sites, and small-caliber synthetic grafts are prone to thrombus induction and occlusion. Therefore, the aim of the present study was to develop an artificial blood conduit of any required length and diameter from the cells of the host for autologous transplantation. Silastic tubing, of variable length and diameter, was inserted into the peritoneal cavity of rats or rabbits. By 2 weeks, it had become covered by several layers of myofibroblasts, collagen matrix, and a single layer of mesothelium. The Silastic tubing was removed from the harvested implants, and the tube of living tissue was everted such that it now resembled a blood vessel with an inner lining of nonthrombotic mesothelial cells (the intima), with a media of smooth muscle-like cells (myofibroblasts), collagen, and elastin, and with an outer collagenous adventitia. The tube of tissue (10 to 20 mm long) was successfully grafted by end-to-end anastomoses into the severed carotid artery or abdominal aorta of the same animal in which they were grown. The transplant remained patent for at least 4 months and developed structures resembling elastic lamellae. The myofibroblasts gained a higher volume fraction of myofilaments and became responsive to contractile agonists, similar to the vessel into which they had been grafted. It is suggested that these nonthrombogenic tubes of living tissue, grown in the peritoneal cavity of the host, may be developed as autologous coronary artery bypass grafts or as arteriovenous access fistulae for hemodialysis patients.

Wall material properties of yeast cells. Part II. Analysis

In the preceding paper (Part I) force-deformation data were measured with the compression experiment in conjunction with the initial radial stretch ratio and the initial wall-thickness to cell-radius ratio for baker's yeast (Saccharomyces cerevisiae). In this paper, these data have been analysed with the mechanical model of Smith et al. (Smith, Moxham & Middelberg (1998) Chemical Engineering Science, 53, 3913-3922) with the wall constitutive behaviour defined a priori as incompressible and linear-elastic. This analysis determined the mean Young's modulus ((E) over bar), mean maximum von Mises stress-at-failure (<(sigma)over bar>(VM,f)) and mean maximum von Mises strain-at failure (<(epsilon)over bar>(VM,f)) to be (E) over bar = 150 +/- 15 MPa, <(sigma)over bar>(VM,f) = 70 +/- 4 MPa and <(epsilon)over bar>(VM,f) = 0.75 +/- 0.08, respectively. The mean Young's modulus was not dependent (P greater than or equal to 0.05) on external osmotic pressure (0-0.8 MPa) nor compression rate (1.03-7.68 mu m/s) suggesting the incompressible linear-elastic relationship is representative of the actual cell-wall constitutive behaviour. Hydraulic conductivities were also determined and were comparable to other similar cell types (0-2.5 mu m/MPa s). The hydraulic conductivity distribution was not dependent on external osmotic pressure (0-0.8 MPa) nor compression rate (1.03-7.68 mu m/s) suggesting inclusion of cell-wall permeability in the mechanical model is justified. <(epsilon)over bar>(VM,f) was independent of cell diameter and to a first-approximation unaffected (P greater than or equal to 0.01) by external osmotic pressure and compression rate, thus providing a reasonable failure criterion. This criterion states that the cell-wall material will break when the strain exceeds <(epsilon)over bar>(VM,f) = 0.75 +/- 0.08. Variability in overall cell strength during compression was shown to be primarily due to biological variability in the maximum von Mises strain-at-failure. These data represent the first estimates of cell-wall material properties for yeast and the first fundamental analysis of cell-compression data. They are essential for describing cell-disruption at the fundamental level of fluid-cell interactions in general bioprocesses. They also provide valuable new measurements for yeast-cell physiologists. (C) 2000 Elsevier Science Ltd. All rights reserved.

Blood vessels from bone marrow

Lengths of silastic tubing were inserted into the peritoneal cavity of rats or rabbits. By two weeks the free-floating implants had become covered by a capsule consisting of several layers of macrophage-derived myofibroblasts and collagen matrix overlaid by a single layer of mesothelial cells. The tubing was removed from the harvested implant and the tissue everted. This now resembled an artery with an inner lining of mesothelial cells (the intima), a media of myofibroblasts, and an outer collagenous adventitia. The tube of living tissue was grafted by end-to-end anastomoses into the transected carotid artery or abdominal aorta of the same animal in which the tissue had been grown, where it remained parent for four months and developed structures resembling elastic lamellae, The myofibroblasts developed a high volume fraction of myofilaments and became responsive to contractile and relaxing agents similar to smooth muscle cells of the adjacent artery wall.