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We investigate theoretically the steady incompressible viscoelastic flow in a rigid axisymmetric tube (cylindrical pipe) with varying cross-section. We use the Oldroyd-B viscoelastic constitutive equation to model the fluid viscoelasticity. First, we derive new exact results expressed in the form of general formulas: for the average pressure-drop through the pipe as a function of the wall shear rate and the viscoelastic axial normal extra-stress, for the viscoelastic extra-stress tensor at the axis of symmetry and the Trouton ratio of the fluid as function of the fluid velocity at the axis, and for the viscoelastic extra-stress tensor along the wall in terms of the tangential shear rate at the wall. We then proceed by exploiting the classic lubrication approximation, valid for small values of the square of the aspect ratio of the pipe, to simplify the original governing equations. The final equations are solved analytically using a regular perturbation scheme in terms of the Deborah number, De, up to eight order in De. For the specific case of a hyperbolic pipe, we reveal that the pressure-drop and the Trouton ratio (when reduced by their corresponding Newtonian values) can be recast in terms of a modified Deborah number, Dem, and the polymer viscosity ratio, {\eta}, only. Furthermore, we enhance the convergence and accuracy of the eight-order solutions by deriving transformed analytical formulas using Pad\'e diagonal approximants. The results show the decrease of the pressure drop and the enhancement of the Trouton ratio with increasing Dem and/or increasing {\eta}. Comparison of the transformed solutions with numerical simulations of the lubrication equations using pseudospectral methods shows excellent agreement between the results revealing the robustness, validity and efficiency of the theoretical methods and techniques developed in this work.

Chronic Obstructive Pulmonary Disease (COPD) is a progressive lung disease characterized by airflow limitation. This study develops a systems engineering framework for representing important mechanistic details of COPD in a model of the cardio-respiratory system. In this model, we present the cardio-respiratory system as an integrated biological control system responsible for regulating breathing. Four engineering control system components are considered: sensor, controller, actuator, and the process itself. Knowledge of human anatomy and physiology is used to develop appropriate mechanistic mathematical models for each component. Following a systematic analysis of the computational model, we identify three physiological parameters associated with reproducing clinical manifestations of COPD - changes in the forced expiratory volume (FEV), lung volumes, and pulmonary hypertension. We quantify the changes in these parameters (airway resistance, lung elastance, and pulmonary resistance) as the ones that result in a systemic response that is diagnostic of COPD. A multivariate analysis reveals that the changes in airway resistance have a broad impact on the human cardio-respiratory system, and that the pulmonary circuit is stressed beyond normal under hypoxic environments in most COPD patients., Comment: 25 pages, 15 figures

Due to the potential impact on the diagnosis and treatment of various cardiovascular diseases, work on the rheology of blood has significantly expanded in the last decade, both experimentally and theoretically. Experimentally, blood has been confirmed to demonstrate a variety of non-Newtonian rheological characteristics, including pseudoplasticity, viscoelasticity, and thixotropy. New rheological experiments and the development of more controlled experimental protocols on more extensive, broadly physiologically characterized, human blood samples demonstrate the sensitivity of aspects of hemorheology to several physiological factors. For example, at high shear rates to the red blood cells elastically deformation, imparting viscoelasticity, while and at low shear rates, they form rouleaux structures that impart additional, thixotropic behavior. In addition to these advances in experimental methods and validated data sets, significant advances have also been made in both microscopic simulations and macroscopic, continuum, modeling, as well as novel, multiscale approaches. We outline and evaluate the most promising of these recent advances. Although we primarily focus on human blood rheology, we also discuss recent observations on variations across some animal species that provide some indication on evolutionary effects., Comment: 22 pages, 14 figures, submitted to "Soft Matter"

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary Newtonian fluids are stable, owing to the nonlinear coupling of the elastic and viscous stresses. Perhaps more surprisingly, the instabilities produce flows with the hallmarks of turbulence -- even though the effective Reynolds numbers may be $O(1)$ or smaller. We provide perspectives on viscoelastic flow instabilities by integrating the input from speakers at a recent international workshop: historical remarks, characterization of fluids and flows, discussion of experimental and simulation tools, and modern questions and puzzles that motivate further studies of this fascinating subject. The materials here will be useful for researchers and educators alike, especially as the subject continues to evolve in both fundamental understanding and applications in engineering and the sciences., Comment: A perspective article based on a virtual workshop of the Princeton Center for Theoretical Sciences that took place in January 2021

We present here the systematic development of quantitative lattice simulations of dense polymers through a novel computational technique that allows for an efficient accounting of the chain conformations. Our approach is based on the decomposition of the original lattice into sublattices of optimal size. We develop and validate the method here for 2-D lattices using sublattices of 4x4 nodes. For each possible connectivity, i.e. arrangement of bonds connecting the 4x4 nodes of a sublattice with the rest of the nodes of the lattice, all possible sublattice microstates (submicrostates) are evaluated. We apply this technique to study the interlamellar amorphous phase in dense semicrystalline polymers where in polymer chains conform to a 2-D square lattice. For lattices of moderate size (up to 8x8 nodes), exact results can be obtained from an exhaustive enumeration of all the microstates corresponding to the fully dense (i.e. with no free chain ends) interlamellar amorphous phase of a semicrystalline system. For larger lattices, a stochastic enumeration technique (purely entropic) and an efficient Metropolis Monte Carlo scheme were developed. A large selection of Monte Carlo moves makes the correlation between the Monte Carlo moves especially short. Thus, statistical quantities of interest can be obtained with tight error bars (calculated concurrently with the averages) using small number of steps., Comment: 24 pages

In this work we illustrate our novel quantitative simulation approach for dense amorphous polymer systems, as discussed in our previous work[Kulkarni et al., A Novel Approach for Lattice Simulations of Polymer Chains in Dense Amorphous Polymer Systems: Method Development and Validation with 2-D Lattices, arXiV, 2008] in applications involving large lattice sizes and high energetic bias. We first demonstrate how the topology of the microstate ensemble in 2-D lattices presents a serious challenge for the collection of accurate and reliable quantitative results (i.e., with simultaneous determination of error bars) for large lattices. This necessitates a further enhancement of our Monte Carlo simulation scheme to sample effectively a meaningful 2-D lattice configurational subspace. Two techniques were investigated: simulated annealing and parallel tempering, to avoid trapping near a local free energy minimum in simulations at high energetic bias. Extensive results of the prediction of various chain conformation statistics and thermodynamic quantities, in the thermodynamic limit (i.e. infinite lateral sizes) are presented., Comment: 19 pages