Fluctuating viscoelasticity based on a finite number of dumbbells

Stochastic kinetic theory applied to coarse-grained polymer model

A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison with explicit Langevin equation simulations under conditions with analytical solutions. The polymers are modeled as Hookean dumbbells in one dimension, without including hydrodynamic interactions and polymer-polymer interactions. Stochastic moment equations are derived from full field theory. The accuracy of the field theory and moment equations is quantified using autocorrelation functions. The full field theory is only accurate for a large number of polymers due to keeping track of rare occurrences of polymers with a large stretch. The moment equations do not have this error because they do not explicitly track these configurations. The accuracy of both methods depends on the spatial degree of discretization. The timescale of decorrelation over length scales bigger than the spatial discretization is accurate, while there is an error over the scale of single mesh points.

Configurational entropy of a finite number of dumbbells close to a wall

The effect of confinement on the conformation of N dumbbells in D dimensions close to a non-interacting and rigid flat wall is examined. Using statistical mechanics and numerical calculations, the partition coefficient and the confinement-induced change in the configurational entropy are calculated as a function of the conformation tensor [Formula: see text] and of the distance of the dumbbells from the wall. Analytical predictions and numerical results for [Formula: see text] concerning the behavior close to the limiting cases (onset of and saturation of confinement) agree favorably; in one case where an analytical prediction has not been achieved, a thorough numerical study establishes the limiting behavior nevertheless. Beyond these limiting cases, the overall behavior of the partition coefficient and the configurational entropy has been examined as well in detail, for various choices of the parameters. Furthermore, it is shown that the effect of confinement for [Formula: see text] is captured entirely by the partition coefficient determined for [Formula: see text]. In general, the average extension of the dumbbells in the direction perpendicular to the wall is decreased the closer the dumbbells are to the wall. Also, the decay of the partition coefficient with increasing extension of the dumbbells becomes steeper, i.e., more localized, the higher the number of dumbbells N. Finally, it is discussed under what conditions these results can be used also for the case of slab- (i.e., slit-) confinement.

An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

 Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups and additionally study a single sedimenting colloid, also finding good agreement with the literature. Our approach can readily be extended to constitutive equations other than Oldroyd-B. This flexibility and the handling of complex boundaries hold promise for the study of microswimmers in viscoelastic fluids.