On the use of viscous micropumps for the transport of thixotropic fluids

Abstract

A cylinder rotating in an off-center position across a microchannel is known to generate a net flow for highly viscous Newtonian fluids. The mechanism is also known to be a viable option for the transport of viscoelastic or viscoplastic fluids albeit with a slight drop in performance. In the present work, the applicability of this mechanism is numerically investigated for the transport of (inelastic) time-dependent fluids obeying the structural-based Quemada model. By numerically solving the equations of motion, it is predicted that viscous micropumps can be used for the transport of thixotropic fluids although the obtained numerical results suggest that there exists a critical thixotropy number (a dimensionless number related to the fluid’s natural time) at which the flow rate is at its lowest value. It is shown that the critical thixotropy number can be avoided from the response of the fluid by properly choosing the geometrical parameters of the device. The general conclusion is that viscous micropumps can be deemed as an efficient mechanism for the transport of thixotropic fluids in microfluidic systems provided that the thixotropy number is sufficiently small, i.e., the fluid is strongly thixotropic. The device is predicted to be more suitable for anti-thixotropic fluids.

Appendices

Appendix A: Anti-thixotropic fluids

Time-dependent fluids encountered in the real world are often realized to be thixotropic. Having said this it should be conceded that there are time-dependent fluid that are anti-thixotropic (or, rheopectic). In other words, their viscosity increases with time at any given shear rate. In such fluids, upon structure breakdown by shear stresses, larger microstructures are formed through bridging between the micelles thereby giving rise to an increased viscosity as time progresses. In this Appendix, we investigate the possibility of transporting such fluids by viscous micropumps. Here, we just compare the response of the two types of time-dependent fluids in a typical test case. As earlier mentioned, Quemada model can represent anti-thixotropic fluids provided αβ < 0 and $\mu_{0} < \mu_{\infty }$. Figure 22 shows a comparison between thixotropic fluids (β = 2) with anti-thixotropic results (β = − 2) for a typical α = 1. The behavior of the two fluids is seen to be completely at odds although both types of fluids exhibit a critical Tx which appears to be around 2 (for this set of parameters). Interestingly, for any given Tx, the average velocity is larger for anti-thixotropic fluids suggesting that they are more suitable than thixotropic fluids for being transported in microfluidic channels by viscous micropumps.

Fig. 22

A comparison between thixotropic fluid (β =  + 2) and anti-thixotropic fluid (β =  − 2) in predicting the average velocity (u*) as a function of the thixotropy number, Tx (Δp^* = 0, ϵ = 0.95, S = 1.5, Re = 1, ζ = 2).

Appendix B: Plane Poiseuille flow of quemada fluid

In the main body of the text, it has been shown that COMSOL is well capable of recovering the analytical velocity profiles in pipe flow for Quemada fluids [24]. We could not find similar velocity profiles for the plane Poiseuille flow of Quemada fluids. In this Appendix, we use COMSOL to obtain these velocity profiles, which are needed to ensure that at the exit plane of the viscous micropump the flow is indeed fully developed. With this in mind, Fig. 23 shows typical velocity profiles (made dimensionless using the centerline velocity) in plane Poiseuille flow for thixotropic fluids obeying the Quemada model at several viscosity ratios, with one of them representing Newtonian fluids. This figure shows that by an increase in the viscosity ratio, the flow rate is decreased. This is not surprising realizing the fact that for a given infinite-shear viscosity, an increase in the viscosity ratio means a larger zero-shear viscosity which reduces the flow rate for a given pressure gradient.

Fig. 23

Effect of the viscosity ratio (ζ) on the axial velocity profiles for fully-developed plane Poiseuille flow of thixotropic fluids obeying the Quemada model (Tx = 1)