Contraction Expansion Flow Research Articles

Pressure drop enhancement in a concentrated suspension flowing through an abrupt axisymmetric contraction-expansion

In this work, we investigate the pressure drop of concentrated suspensions flowing through a 4:1:4 axisymmetric contraction-expansion at low Reynolds number. Pressure drop measurements across the narrow tube show an enhanced pressure drop relative to a Newtonian fluid at the same flow rate. A linear increase in pressure drop as a function of flow rate is observed for the suspensions, with a steeper slope at higher particle volume fraction. However, due to shear-induced particle migration, the pressure drop at each concentration is lower than would be expected for a uniform Newtonian fluid of the same viscosity as the bulk suspension viscosity. The Krieger [I. M. Krieger, Adv. Colloid Interface Sci. 3, 111 (1972)] expression for the relative viscosity provides an accurate estimate of the dependence of the normalized suspension pressure drop on particle volume fraction, although the bulk suspension viscosity follows the more rapidly increasing curve of Zarraga [I. E. Zarraga, D. A. Hill, and D. T. Leighton, J. Rheol. 44, 185 (2000)]. As the particle volume fraction increases, the normalized pressure drop rises in a similar manner to the area of the recirculation regions in the corner of the expansion and also to the ratio of suspension viscosities in the tube center and recirculation regions. The pressure measurements, along with nuclear magnetic resonance imaging results, suggest that the viscosity ratio between the center and recirculation regions of the suspension, recirculation region size, and pressure drop are all related in contraction-expansion flows of suspensions.

An efficient algorithm for multiscale flow simulation of dilute polymeric solutions using bead-spring chains

In this study, a computationally efficient algorithm for multiscale flow simulation of dilute polymer solutions using a bead-spring chain description of polymer molecules is presented. The algorithm combines a computationally efficient extension of the earlier BCF-based semi-implicit method (i.e., approximately four-fold speed up) for multiscale flow simulations using a bead-spring dumbbell description [M. Somasi, B. Khomami, Linear stability and dynamics of viscoelastic flows using time-dependent stochastic simulation techniques, J. Non-Newtonian Fluid Mech. 93 (2000) 339–362] with a highly CPU efficient predictor–corrector scheme for BD simulation of bead-spring chains [M. Somasi, B. Khomami, N. Woo, J. Hur, E. Shaqfeh, Brownian dynamics simulations of bead-rod and bead-spring chains: numerical algorithms and coarse-graining issues, J. Non-Newtonian Fluid Mech. 108 (2002) 227–255]. The fidelity and computational efficiency of the parallel implementation of the algorithm are demonstrated via three benchmark flow problems, namely, plane Couette flow, Poiseuille flow and 4:1:4 axisymmetric contraction–expansion flow. The algorithm shows linear speed up with the number of processors and more importantly with the number of chain segments. In addition, the proposed algorithm is approximately 50 times faster in comparison to the only existing fully implicit method [J. Ramirez, M. Laso, Size reduction methods for the implicit time-dependent simulation of micro-macro viscoelastic flow problems, J. Non-Newtonian Fluid Mech. 127 (2005) 41–49].

Polymer Blends in a Contraction−Expansion Flow

We have probed the coupling between flow and concentration fluctuations in polymer blends using small-angle neutron scattering. We utilized a recirculating cell with a slot die, enabling us to measure the behavior at the entrance, within and at the exit of a contraction-expansion flow. While, as expected, anisotropy was observed in all nonquiescent experiments, the correlation lengths associated with the concentration fluctuations are found to be stretched more in the direction perpendicular to the flow at all positions along the centerline of the flow, except at the slot die exit. To gain insight into the observations, we present calculations of the scattering based on a multiscale approach, which bridges the gap between macroscopic Newtonian fluid dynamics and the convection of nanoscale concentration fluctuations. However, we find that this model contains insufficient physics to correctly describe our observations. Consequently, we argue that the deformation of the correlation length is primarily due to the coupling between weakly non-Newtonian stresses and thermodynamics.

Dispersion in microchannels with temporal temperature variations

While amplifying DNA strands in a microfluidic device, the sample is subjected to cyclic changes in temperature. We investigate the dispersion of molecules in a microchannel, as these undergo a contraction–expansion flow that is driven by temporally changing temperatures. In this paper, the method of multiple time scales with regular expansions is used to obtain the effective dispersivity and the analytical results are compared with computational fluid dynamics simulations. Due to the thermal expansion of the carrier fluid, the cyclic temperature variations lead to both axial and lateral velocities. These periodic velocity profiles lead to an increase in axial dispersion. The dispersion coefficient increases as the square of the channel position from the center of the microchannel. Due to the quadratic variation of the dispersion coefficient in the axial direction, the concentration profile is non-Gaussian and a complex function of frequency and magnitude of the temporal oscillations and the dimensions of the microchannel. Analytical expressions for dispersion coefficient are derived for cyclic profiles of any shape; and results are computed and discussed for particular cases of cosine and step-function temperature cycles. The value for effective dispersion is also evaluated for a sample temperature profile that occurs in the microfluidic DNA amplification processes. The dispersion coefficient for step changes in temperature is found to be substantially larger than that for the case of sinusoidal temperature changes at low frequencies. We believe that the results of this study will enhance our understanding of transport in microscale systems that are subjected to temporally changing temperatures, and likely lead to technological advances in diverse areas relevant to microreactor design and DNA amplification.