A new model for Brownian dynamics simulations of entangled polymeric liquids is proposed here. Chains are coarse grained at the level of segments between consecutive entanglements; hence, the system is in fact a network of primitive chains. The model incorporates not only the “individual” mechanisms of reptation and tube length fluctuation, but also collective contributions arising from the 3D network structure of the entangled system, such as constraint release. Chain coupling is achieved by fulfilling force balance on the entanglement nodes. The Langevin equation for the nodes contains both the tension in the chain segments emanating from the node and an osmotic force arising from density fluctuations. Entanglements are modeled as slip links, each connecting two chain strands. The motion of monomers through slip links, which ultimately generates reptation as well as tube length fluctuations, is also described by a suitable Langevin equation. Creation and release of entanglements is controlled by the number of monomers at the chain ends. In a creation event, the partner chain segment is chosen randomly among those spatially close to the advancing chain end. To validate the model, equilibrium dynamics simulations were run for monodisperse linear chains containing up to Z=40 entanglements. The results show, in agreement with experiments, (i) a Z3.5±0.1 dependence of the longest relaxation time, (ii) a Z−2.4±0.2 dependence of the self-diffusion coefficient, and (iii) a relaxation modulus proportional to the square of the end-to-end vector correlation function, consistently with the dynamic tube dilation concept.

We perform 3D numerical simulations, heuristic modeling and microfluidic experiments to demonstrate, for the first time, the presence of a bistability scenario for transversal migration of particles suspended in a viscoelastic liquid flowing in a pipe. Our results show that particle migration, either at the centerline or at the wall, can be controlled by the rheological properties of the suspending liquid and by the relative dimensions of the particle and tube. Proper selection of these parameters can promote strict aligning of particles on a line, i.e., 3-D focusing. Simple design rules are given to rationally control particle focusing under flow in micropipes.

The fast growth of microfluidic applications based on complex fluids is a result of the unique fluid dynamics of these systems, enabling the creation of devices for health care or biological and chemical analysis. Microchannels designed to focus, concentrate, or separate particles suspended in viscoelastic liquids are becoming common. The key fluid dynamical issue on which such devices work is viscoelasticity-induced lateral migration. This phenomenon was discovered in the 1960s in macroscopic channels and has received great attention within the microfluidic community in the past decade. This review presents the current understanding, both from experiments and theoretical analysis, of viscoelasticity-driven cross-flow migration. Examples of promising microfluidic applications show the unprecedented capabilities offered by such technology based on geometrically simple microchannels and rheologically complex liquids

Brownian dynamics simulations of the linear viscoelastic response of entangled polymers have been performed, and compared quantitatively with some existing solution data at a fixed concentration and variable molecular weight. The model is a three-dimensional network where the nodes are sliplinks connecting chains in pair. The simulations make use of Langevin equations both for the node motion in space, and for the one-dimensional monomer sliding through sliplinks. Comparison with data is very satisfactory, but the molecular weight between entanglements that emerges from the model is unconventionally small.

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A novel method to estimate the relaxation time of viscoelastic fluids, down to milliseconds, is here proposed. The adopted technique is based on the particle migration phenomenon occurring when the suspending viscoelastic fluid flows in microfluidic channels. The method is applied to measure the fluid relaxation times of two water-glycerol polymer solutions in an ample range of concentrations. A remarkable improvement in the accuracy of the measure of the relaxation time is found, as compared with experimental data obtained from shear or elongational experiments available in the literature. Good agreement with available theoretical predictions is also found. The proposed method is reliable, handy and does not need a calibration curve, opening an effective way to measure relaxation times of viscoelastic fluids otherwise not easily detectable by conventional techniques.

We demonstrate the possibility to achieve 3D particle focusing in a straight microchannel with a square cross-section by exploiting purely viscoelastic effects. Experiments are carried out by considering an elastic, constant-viscosity aqueous solution of PVP (polyvinylpyrrolidone) as the suspending liquid. Several flow rates and two channel dimensions (with a fixed particle size to channel dimension ratio) are investigated. A novel technique combining particle tracking measurements and numerical simulations is used to reconstruct the position of the flowing particles over the channel cross-section. The results show that, for all the investigated experimental conditions, particles migrate towards the channel centerline. Flow-focusing is enhanced by higher flow rates. The measured particle fractions can be rescaled according to a single dimensionless parameter, as already reported in the literature for the case of cylindrical channels. The so-obtained master curve can be used as a guide to predict the required focusing length. The effect of the entrance on the focusing channel length is also addressed. Finally, analogies and discrepancies with similar previous works are discussed.