Stress-gradient-induced polymer migration in Taylor–Couette flow

Abstract

We apply our recent continuum theory for stress-gradient-induced migration of polymers in solution (G. Zhu et al., J. Rheol., 2016, 60, 327-343) to rotational shearing flow in the gap between concentric cylinders (the so-called Taylor-Couette flow), where we have also accounted for the effect of polymer depletion from the solid boundaries on migration patterns. The steady-state distribution of dilute solutions of polymer dumbbells, obtained both using a systematic perturbation analysis in terms of the Weissenberg number (Wi) and by solving numerically the transport problem coupled to the upper-convected Maxwell equation, shows accumulation of polymers near the inner cylinder. This accumulation becomes so strong that most polymers are driven near the inner cylinder once Wi > 4. We also show that there is no first-order contribution to the polymer migration in Taylor-Couette flow due to the absence of a velocity component in the r-direction. Brownian dynamics (BD) simulations for a Hookean dumbbell give a concentration distribution in good agreement with the theoretical predictions of our theory, confirming the accuracy of the theory when the dumbbell radius of gyration is around an order of magnitude or much smaller than the gap. The demonstration of the accuracy of our continuum theory by direct molecular simulation opens the door to application of the theory to journal bearing and other lubrication flows containing polymers that may migrate due to stress gradients.

Microfluidic free interface diffusion: Measurement of diffusion coefficients and evidence of interfacial-driven transport phenomena

“…where D is the mutual diffusion coefficient of the mixture, constant for a dilute solution. This equation implies that the polymer mass transport is solely due to molecular diffusion, and thus rules out any other mechanism, such as stress gradient-induced polymer migration, see for instance 38,39 . This hypothesis is very likely because there is no flow in the microfluidic channel closed by valve V 1 , and because it is unlikely that significant mechanical stresses were stored during the filling step described in Fig.…”

Generalized Lagrangian heterogeneous multiscale modelling of complex fluids

“…Further generalization of the LHMM to account for those effects can be attained by including additional evolution equations for compositional fields (Ellero et al 2003) discretized at the macroscopic level, such that microscopic simulations can be generated on the fly accordingly. Stress-driven transport could be also generalized in our LHMM to include the stress-gradient-induced polymer migration models (Zhu et al 2016;Hajizadeh & Larson 2017).…”

Mesoscopic simulations of inertial drag enhancement and polymer migration in viscoelastic solutions flowing around a confined array of cylinders

“…The significant depletion at the wake of the cylinder agrees with description and characteristics of SCI due to the curvature of streamlines in that region. The modeling for SCI (also known as stress-gradient-induced) polymer migration in confined dilute solutions using continuum theory has been recently applied to Taylor-Couette flow [27] and flow between rotating eccentric cylinders [28]. These studies were limited to Wi≤ 1.6 but already found migration towards the inner cylinder with near zero concentration at the outer cylinder wall.…”

“…All mechanisms can be relevant in confined geometries (i.e., when R g and geometry size are comparable). SCI has been shown to govern polymer migration towards the center of curvature in Taylor-vortex flow [26], Taylor-Couette flow [27], and eccentric Taylor-Couette flow [28]. In all these studies SCI is the most relevant mechanism once moderate Wi numbers are reached.…”