A comparison of boundary element and finite element methods for modeling axisymmetric polymeric drop deformation

A modified boundary element method (BEM) and the DEVSS-G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start-up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd-B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation

Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress)

Large amplitude oscillatory shear (LAOS) is used as a tool to probe the nonlinear rheological response of a model elasto-viscoplastic material (a Carbopol microgel). In contrast to most recent studies, these large amplitude measurements are carried out in a stress-controlled manner. We outline a descriptive framework of characterization measures for nonlinear rheology under stress-controlled LAOS, and this is contrasted experimentally to the strain-controlled framework that is more commonly used. We show that this stress-controlled methodology allows for a physically intuitive interpretation of the yielding behavior of elasto-viscoplastic materials. The insight gained into the material behavior through these nonlinear measures is then used to develop two constitutive models that prescribe the rheological response of the Carbopol microgel. We show that these two successively more sophisticated constitutive models, which are based on the idea of strain decomposition, capture in a compact manner the important features of the nonlinear rheology of the microgel. The second constitutive model, which incorporates the concept of kinematic hardening, embodies all of the essential behaviors exhibited by Carbopol. These include elasto-viscoplastic creep and time-dependent viscosity plateaus below a critical stress, a viscosity bifurcation at the critical stress, and Herschel–Bulkley flow behavior at large stresses

Non-equivalence of Wnt and R-spondin ligands during Lgr5+ intestinal stem-cell self-renewal

The canonical Wnt/β-catenin signaling pathway governs diverse developmental, homeostatic and pathologic processes. Palmitoylated Wnt ligands engage cell surface Frizzled (Fzd) receptors and Lrp5/6 co-receptors enabling β-catenin nuclear translocation and Tcf/Lef-dependent gene transactivation1–3. Mutations in Wnt downstream signaling components have revealed diverse functions presumptively attributed to Wnt ligands themselves, although direct attribution remains elusive, as complicated by redundancy between 19 mammalian Wnts and 10 Fzds1 and Wnt hydrophobicity2,3. For example, individual Wnt ligand mutations have not revealed homeostatic phenotypes in the intestinal epithelium4, an archetypal canonical Wnt pathway-dependent rapidly self-renewing tissue whose regeneration is fueled by proliferative crypt Lgr5+ intestinal stem cells (ISCs)5–9. R-spondin ligands (Rspo1–4) engage distinct Lgr4-6 and Rnf43/Znrf3 receptor classes10–13, markedly potentiate canonical Wnt/β-catenin signaling and induce intestinal organoid growth in vitro and Lgr5+ ISCs in vivo8,14–17. However, the interchangeability, functional cooperation and relative contributions of Wnt versus Rspo ligands to in vivo canonical Wnt signaling and ISC biology remain unknown. Here, we deconstructed functional roles of Wnt versus Rspo ligands in the intestinal crypt stem cell niche. We demonstrate that the default fate of Lgr5+ ISCs is lineage commitment, escape from which requires both Rspo and Wnt ligands. However, gain-of-function studies using Rspo versus a novel non-lipidated Wnt analog reveal qualitatively distinct, non-interchangeable roles for these ligands in ISCs. Wnts are insufficient to induce Lgr5+ ISC self-renewal, but rather confer a basal competency by maintaining Rspo receptor expression that enables Rspo to actively drive and specify the extent of stem cell expansion. This functionally non-equivalent yet cooperative interplay between Wnt and Rspo ligands establishes a molecular precedent for regulation of mammalian stem cells by distinct priming and self-renewal factors, with broad implications for precision control of tissue regeneration

Schizophrenia-associated somatic copy-number variants from 12,834 cases reveal recurrent NRXN1 and ABCB11 disruptions

While germline copy-number variants (CNVs) contribute to schizophrenia (SCZ) risk, the contribution of somatic CNVs (sCNVs)—present in some but not all cells—remains unknown. We identified sCNVs using blood-derived genotype arrays from 12,834 SCZ cases and 11,648 controls, filtering sCNVs at loci recurrently mutated in clonal blood disorders. Likely early-developmental sCNVs were more common in cases (0.91%) than controls (0.51%, p = 2.68e−4), with recurrent somatic deletions of exons 1–5 of the NRXN1 gene in five SCZ cases. Hi-C maps revealed ectopic, allele-specific loops forming between a potential cryptic promoter and non-coding cis-regulatory elements upon 5′ deletions in NRXN1. We also observed recurrent intragenic deletions of ABCB11, encoding a transporter implicated in anti-psychotic response, in five treatment-resistant SCZ cases and showed that ABCB11 is specifically enriched in neurons forming mesocortical and mesolimbic dopaminergic projections. Our results indicate potential roles of sCNVs in SCZ risk

Linear low density polyethylene (LLDPE)/clay nanocomposites. Part I: Structural characterization and quantifying clay dispersion by melt rheology

In this study, linear low density polyethylene (LLDPE)/clay nanocomposites with various clay content were prepared by melt processing using two different compatibilizers, maleic anhydride grafted polyethylene (PE-g-MA) and oxidized polyethylene (OxPE). Effects of structure and physical properties of the compatibilizers on the clay dispersion and clay amount on the microstructure and physical properties of the nanocomposites were investigated. The OxPE was shown to significantly create interfacial interactions between the polymer phase and clay layers. Rheological behavior of the samples was examined by a dynamic oscillatory rheometry in linear viscoelastic region. Percolation threshold (phi(p)) and corresponding aspect ratio (A(f)) values were determined by analyzing the improvement in storage modulus at low frequency region depending on the clay loading. Lower percolation and higher aspect ratio values were obtained for the sample series prepared with the PE-g-MA than that prepared with the OxPE. Moreover, fractal size of the clay network above the percolation point was determined by the scaling law for physical gelation of colloidal flocks to quantify clay dispersion depending on the compatibilizer structure. It was found that the PE-g-MA yielded better clay dispersion and more exfoliated structure compared to the OxPE. Microstructural characterization of the samples was also characterized by XRD and TEM. (c) 2007 Elsevier Ltd. All rights reserved

New Algorithms for 3-D Imaging and Analysis of Open-Celled Foams

ABSTRACT: Open-celled foams are three-dimensional networks of polymeric cells. The mechanical properties of a foam depend on the size and geometry of its cells. Since foams have a three-dimensional polyhedral structure, the two-dimensional characterization techniques currently used provide limited accuracy. Nuclear magnetic resonance and x-ray tomography methods offer opportunities for three-dimensional imaging of these polyhedral structures. Software, which can use digital three-dimensional images to determine structural parameters such as strut length distribution, connectivity, and cell size, is being developed. The image processing approach uses conformal curvature flow (CCF) segmentation to find the surfaces of foam struts in the 3-D images. Once these surfaces have been found, volume thinning is used to find the structural skeleton of the foam. The resulting data set can then be used to determine many statistical characteristics of the foam, including strut length distributions, window size and shape distributions, and cell size information. Analysis of a reticulated polyurethane foam sample using these methods yielded a reasonable approximation of the structural skeleton of the sample

Degradation and Breakdown of Polymer/Graphene Composites under Strong Electric Field

In this work, we study the effect of strong electric fields on a polymer/graphene composite and the resulting morphology upon its dielectric breakdown. Our model system was produced by compounding up to 0.25 wt % graphene nanoplatelets (GNP) into poly(ethylene-co-vinyl acetate) (EVA), which is a soft polymer with low melt viscosity. A strong electric field of up to 400 Vrms/mm was applied to the EVA/GNP composite in the melt. The sample’s resistance over the electric field application was simultaneously measured. Despite the low GNP loading, which was below the theoretical percolation threshold, the electric conductivity of the composite during electric field application dramatically increased to >10−6 S/cm over 5 min of electric field application before reaching the current limit of the experimental apparatus. Conductivity growth follows the same scaling relationship of the theoretical model that predicts the rotation and translation time of GNPs in a polymer melt as a function of electric field strength. Since no significant GNP alignment in the composite was observed under transmission electron microscopy (TEM), we hypothesized that the increase in electrical conductivity was due to local electrical treeing of the polymer matrix, which eventually leads to dielectric breakdown of the composite. Electrical treeing is likely initiated by local GNP agglomerates and propagated through conductive channels formed during progressive dielectric breakdown