Analysis of dynamic mechanical response in torsion

We investigate the dynamic response of industrial rubbers (styrene-butadiene random copolymers, SBR) in torsion and compare against common small amplitude oscillatory shear measurements by using a torsion rectangular fixture, a modified torsion cylindrical fixture, and a conventional parallel plate fixture, respectively, in two different rheometers (ARES 2kFRTN1 from TA Instruments, USA and MCR 702 from Anton Paar-Physica, Austria). The effects of specimen geometry (length-to-width aspect ratio) on storage modulus and level of clamping are investigated. For cylindrical specimens undergoing torsional deformation, we find that geometry and clamping barely affect the shear moduli, and the measurements essentially coincide with those using parallel plates. In contrast, a clear dependence of the storage modulus on the aspect ratio is detected for specimens having rectangular cross section. The empirical correction used routinely in this test is based on geometrical factors and can account for clamping effects, but works only for aspect ratios above a threshold value of 1.4. By employing a finite element analysis, we perform a parametric study of the effects of the aspect ratio in the cross-sectional stress distribution and the linear viscoelastic torsional response. We propose a new, improved empirical equation for obtaining accurate moduli values in torsion at different aspect ratios, whose general validity is demonstrated in both rheometers. These results should provide a guideline for measurements with different elastomers, for which comparison with dynamic oscillatory tests may not be possible due to wall slip issues

Locomotion of a microorganism in weakly viscoelastic liquids

In the present work we study the motion of microorganisms swimming by an axisymmetric distribution of surface tangential velocity in a weakly viscoelastic fluid. The second-order fluid constitutive equation is used to model the suspending fluid, while the well-known squirmer model [M. J. Lighthill, Comm. Pure Appl. Math. 5, 109 (1952); J. R. Blake, J. Fluid Mech. 46, 199 (1971)] is employed to describe the organism propulsion mechanism. A regular perturbation expansion up to first order in the Deborah number is performed, and the generalized reciprocity theorem from Stokes flow theory is then used, to derive analytical formulas for the squirmer velocity. Results show that neutral squirmers are unaffected by viscoelasticity, whereas pullers and pushers are slowed down and hastened, respectively. The power dissipated by the swimming microorganism and the swimming efficiency are also analytically quantified

The effect of wall slip on the dynamics of a spherical particle in Newtonian and viscoelastic fluids subjected to shear and Poiseuille flow

\u3cbr/\u3eWe address the effect of wall slip on the dynamics of a spherical particle suspended in an inertialess Newtonian or viscoelastic shear-thinning fluid under shear or Poiseuille flow. The study is performed through 3D direct finite element simulations by employing an Arbitrary Lagrangian-Eulerian method for the particle motion.\u3cbr/\u3eIn both shear and Poiseuille flows, wall slip reduces the difference between the particle translational velocity along the flow direction and the velocity of the unperturbed fluid, and slows down the particle rotational velocity. Remarkably, in a viscoelastic fluid, the presence of wall slip reverses the migration direction as compared to the no-slip case. Hence, for sufficiently high slip coefficients, all the particles migrate toward the channel midplane in shear flow and toward the channel centerline in Poiseuille flow, regardless of their initial position through the channel.\u3cbr/\u3

Viscoelasticity-induced migration of a rigid sphere in confined shear flow

Suspensions of solid particles in liquids are often made to flow in devices with characteristicdimensions comparable to that of the suspended particles, the so-called confined situation, as in thecase of several microfluidic applications. Combination of confinement with viscoelasticity of thesuspending liquid can lead to peculiar effects. In this paper we present the first 3D simulation of thedynamics of a particle suspended in a viscoelastic liquid under imposed confined shear flow. The fullsystem of equations is solved through the finite element method. A DEVSS/SUPG formulation with alog-representation of the conformation tensor is implemented, assuring stable and convergent resultsup to high flow rates. Particle motion is handled through an ALE formulation. To optimize thecomputational effort and to reduce the remeshing and projection steps required when the meshbecomes too distorted, a rigid motion of the grid in the flow direction is performed, so that, in fact, theparticle moves along the cross-streamline direction only.Confinement and viscoelasticity are found to induce particle migration, i.e., transverse motion acrossthe main flow direction, towards the closest wall. Under continuous shearing, three different dynamicalregimes are recognized, related to the particle-wall distance. A simple heuristic argument is given tolink the crossflow migration to normal stresses in the suspending liquid.The analysis is then extended to a time-dependent shear flow imposed by periodically inverting thedirection of wall motion. A slower migration is found for higher forcing frequency. A peculiar effectarises if the inversion period is chosen close to the fluid relaxation time: the migration velocityoscillates around zero, and the overall migration is suppressed. Such novel prediction of a dynamicinstability scenario, with the particle escaping the center plane of the channel, and many features of thecomputed results, are in nice agreement with recent experiments reported in the literature(B.M.~Lormand and R.J.~Phillips, J. Rheol. 48 (2004) 551-570)

A closure approximation for nematic liquid crystals based on the canonical distribution subspace theory

A closure approximation for nematic polymers is presented. It approximates the fourth rank order tensor in terms of lower rank tensors, and is derived in the framework of the canonical distribution subspace theory. This approach requires a choice of the class of distributions: Here the set of Bingham distributions is chosen, as already introduced by Chaubal and Leal (1998). The closure is written in a generic frame of reference, and in an explicit form, so that it can be easily implemented. Such formulation also permits studying the closure approximation with continuation tools, which rather completely describe the system dynamics. The predictions can then be compared with those obtained with the exact model. The shear flow is considered as a test, since this flow condition appears to be the most demanding for closure approximations for nematic polymers

Numerical design of a T-shaped microfluidic device for deformability-based separation of elastic capsules and soft beads

\u3cp\u3eWe propose a square cross-section microfluidic channel with an orthogonal side branch (asymmetric T-shaped bifurcation) for the separation of elastic capsules and soft beads suspended in a Newtonian liquid on the basis of their mechanical properties. The design is performed through three-dimensional direct numerical simulations. When suspended objects start near the inflow channel centerline and the carrier fluid is equally partitioned between the two outflow branches, particle separation can be achieved based on their deformability, with the stiffer ones going straight and the softer ones being deviated to the side branch. The effects of the geometrical and physical parameters of the system on the phenomenon are investigated. Since cell deformability can be significantly modified by pathology, we give a proof of concept on the possibility of separating diseased cells from healthy ones, thus leading to illness diagnosis.\u3c/p\u3

Numerical simulations of deformable particle lateral migration in tube flow of Newtonian and viscoelastic media

The deformation and cross-streamline migration of an elastic particle in pressure-driven flows of Newtonian and viscoelastic (Oldroyd-B, Giesekus) fluids in a cylindrical tube are studied through 3D finite element method numerical simulations. The dependences of particle deformation and migration on geometric confinement, flow strength, and fluid rheology are investigated. If the particle is initially not at the channel axis, it attains an asymmetric shape and migrates. In a Newtonian liquid, the migration is always directed towards the tube axis. A project equation is proposed for the design of a microfluidic cylindrical device aimed at focusing elastic particles on the cylinder centerline. In a viscoelastic liquid, the migration direction and velocity depend on the competition among particle deformability, fluid elasticity, and fluid viscosity shear thinning (if any). In a certain range of parameters, an unstable radial position appears, which separates the region where the migration is directed towards the axis from the region where it is directed towards the wall