Transition in flexible tubes and channels

Abstract

A combination of experiments, flow simulations and linear stability analysis is used to develop a fundamental understanding of the instability and transition in flows through flexible tubes and channels. The present study is divided into four parts as follows:

Transition in a flexible tube A tubular bore (diameter range from 1200 ?m to 800 ?m) was prepared in soft polydimethylsiloxane (PDMS) polymer and used for this study. The shear modulus of the PDMS gel was varied from 18 kPa to 0.55 MPa by changing the cross-linker percentage in the pre-polymer. A pressure drop between the inlet and outlet of the tube is used to drive fluid flow. Transition is inferred using both friction factor (pressure drop) measurements, dye-stream experiments where the break-up of a dye-stream inserted at the center of the tube is observed, and observations of wall oscillations using a laser scattering technique. The experimental observations show that the flow becomes unstable at Reynolds numbers as low as 500 in flexible tubes, which is significantly lower than the transition value of 2100 for a rigid tube of equivalent diameter. The results show that the transition is qualitatively different from those in a rigid tube, in that there is a continuous increase in the friction factor at transition in a flexible tube, in contrast to the discontinuous change in a rigid tube. The transition Reynolds number is also lower, by an order of magnitude, than that predicted by previous linear stability analyses based on a parabolic profile and a constant pressure gradient.

Transition in a microchannel due to a soft wall Experiments are conducted in rectangular microchannels with a flexible bottom wall. Microchannels of height 100 ?m, 160 ?m and width 1.5 mm are prepared using soft lithography technique. The onset of transition from laminar flow is detected using dye-stream experiments where the break-up of a dye-stream inserted at the center of the channel is observed, pressure drop measurements, and detection of wall oscillations by embedding fluorescent microbeads in the soft wall. We also carry out experiments on mixing between two inlet streams across a width of 1.5 mm, and mixing is quantified using image analysis as well as conductance measurements of tannic acid solutions at the outlet. Two important observations in both sets of experiments are that the transition Reynolds number is much smaller than that for the flow in rigid channels of equivalent dimension, and there is a substantial deformation of the channel wall due to the applied pressure gradient. The transition Reynolds number is found to be lower, by more than an order of magnitude, in comparison to previous linear stability analyses based on a parabolic flow profile and a constant pressure gradient.

CFD simulations and linear stability analysis In order to determine whether the discrepancy in the transition Reynolds number can be explained by the tube/channel deformation, leading to a non-parabolic velocity profile and non-constant pressure gradient, a combination of Computational Fluid Dynamics (CFD) studies of flow in the deformed tube/channel along with the linear stability studies for a generalized velocity profile and pressure gradient were undertaken. The CFD simulation of flow through flexible tube and channel was carried out using Ansys 13 (Fluent) software package. The dimensions for tube and channel geometry were extracted from experiments for different flow rates. The deformed shape is reconstructed numerically, and CFD simulations were carried out to obtain the pressure gradient and the velocity profiles at different locations for different flow rates. The simulation results for the pressure difference across the tube/channel are in agreement with experimental results when the flow is laminar in the experiments, but are significantly lower than the experimental results when transition is observed in the experiments. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modeled as a neo-Hookean elastic solid. The theoretical model was developed for generalized velocity and pressure fields, and is not restricted to a parabolic flow and a constant pressure gradient. The mean velocity and the pressure profiles obtained from CFD simulations are used as inputs for the linear stability calculations. The stability analysis accurately predicts the onset of transition from laminar where dye-stream goes unstable, and it also predicts the location at which the instability first takes place at the downstream converging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation.

Nanoparticle synthesis in a microchannel with a soft wall The effect of mixing due to a soft wall on the size and polydispersity of gold nanoparticles synthesized by the room-temperature reduction of chloroauric acid, with tannic acid as the reducing agent and stabilizer, has been studied. The polydispersity does vary with the mixing conditions in flexible channels. The polydispersity is lower, and does not vary much with flow velocity, when the tannic acid is in excess compared to the chloroauric acid, due to the production of a large number of small nanoparticle seeds. This indicates that the conditions in the microchannel can be optimized to obtain minimum nanoparticle polydispersity.