Autonomous filling of a viscoelastic fluid in a microfluidic channel: Effect of streaming potential

Highlights

• Autonomous filling of viscoelastic fluid in a capillary.

• sPTT model is used to describe the rheology of viscoelastic fluid.

• Effect of streaming potential on the filling dynamics is investigated.

• Oscillations are seen in the temporal evolution of the filling dynamics.

• A unique scale $\left(x\sim \sqrt{t}\right)$ at a later stage of filling in the capillary is established.

Abstract

We study the streaming potential modulated autonomous filling dynamics of a viscoelastic fluid in a microfluidic channel. To describe the rheology of viscoelastic fluid, we consider a simplified Phan-Thien-Tanner (sPTT) model. Considering the electroviscous effect, along with the effects of surface tension force and viscous resistance, we derive a reduced-order model for obtaining the variations in the filling dynamics for different physical parameters of the system. We observe that a complex competition between the viscoelasticity and the electroviscous effect leads to the non-trivial behaviour in the temporal evolution of the filling dynamics. Moreover, our analysis unveils that an enhancement in the electroviscous effect due to increasing viscoelasticity of the fluid leads to a non-linear reduction in the filling length of the fluid in the channel. Consequently, the notion of having a higher filling length for more elastic nature of the fluid is contradicted here due to the presence of the electroviscous effect. Finally, we establish a regime $\left(x\sim \sqrt{t}\right)$ at the later stage of filling in the channel. We show that this regime is unique to the surface tension driven filling of viscoelastic fluids in a charged fluidic pathways under the influence of electroviscous effect.

Introduction

The surface tension driven capillary filling in microscale conduits has overwhelmingly expedited the up-gradation of the multifarious Micro-Electro-Mechanical systems (MEMS) and the assays in Point-of-Care (POC) diagnostics [1], [2], [3]. These systems are acknowledged as the Autonomous capillary filling systems (ACS) [2,4] and find considerable applications in miniaturized devices/systems. Examples include sandwich immunoassays, test strips used in pregnancy and HIV diagnostics, protein analysis, capillary electrophoresis, to name a few [4]. Acknowledging this significance of ACSs, several studies have been carried out following numerical methods [5], [6], [7], [8], [9], [10], analytical calculations [11], [12], [13], [14], [15], [16], [17], [18] as well as experimental investigations [2,4,[19], [20], [21], [22], [23], [24]]. Out of the methods mentioned above, a reduced-order model developed by Washburn [11], which is experimentally proven as well as a numerically validated approach [6,9], has been promoted widely by the research community. It may be added here that a few researchers have done salient modifications in this method considering the extraneous aspects [12], [13], [14], [15], [16], [17], [18].

In such ACSs, we can deploy two novel features to tune the filling characteristics of the samples being transported. These features include the effect of streaming potential and the viscoelasticity of the fluid on the underlying filling dynamics. In streaming potential modulated ACSs, the convection of ions inside the charged test strips gives rise to the accumulation of ions at the meniscus of the liquid. This phenomenon further gives rise to the development of streaming potential across the liquid column, which opposes the advancement of filling fluid in the capillary [13]. Note that to explore the underlying flow physics involved with this phenomenon, the effect of streaming potential on the filling dynamics in a microfluidic channel has been studied in recent times [13]. The electroviscous effect was found to be the best parameter to control the filling phenomenon, as discussed in the reported study. Given the insights in the reported analysis, in ACSs, the streaming potential is expected to play a prominent role.

It is important to mention here that the shear-thinning nature of the viscoelastic fluid offers a higher flow velocity and results in an increase in the streaming of the counter-ions. This phenomenon leads to an enhancement in the magnitude of streaming potential to a greater extent with the underlying transport [25]. It is worth adding here that some viscoelastic fluids respond well to the electrokinetic activity, and following this rheology modulated alteration in electromechanics at a small scale, the underlying transport features get changed non trivially. For example, the polymer- polyethylene glycol (PEG) is used as a crowding agent for the in-vitro assays to mimic highly crowded cellular conditions, precipitant for plasmid DNA isolation, protein crystallization with the objectives of concentrating on the viruses and for detection of antigens/antibodies [26,27]. The compound PEG also triggers the electrokinetic phenomenon as the Debye length of the PEG varies from 2.2 nm to 3.93 nm when the molecular weight of the compound is varied from 600 to 10000. Note that the electrolytic salt, such as NaCl can be added to reduce the Debye length as well as to increase the electrokinetic effect. The Debye length in PEG solution can be reduced to 1.48 nm with the addition of 10 mM of NaCl salt in the solution [28]. Another polymeric compound, Polyacrylamide (PAA) can be used to separate the charged particles from the bio-fluidic samples and to find a small amount of DNA [29]. Recently, the electrokinetics of PAA solution having 1mM KCl has been studied following experimental investigations [30]. To summarize, the viscoelastic fluids of these kinds, as mentioned above, can trigger electrokinetic activity during their transportation in the micro-capillaries having charged surface.

A closer look into the paradigm of capillary filling dynamics pertaining to rheology-based revisions reveals that the effect of streaming potential on the underlying capillary filling dynamics of a viscoelastic fluid is not explored in the literature to date. The surface tension driven filling of a viscoelastic fluid in a capillary under the influence of streaming potential in tandem may bring about non-intuitive flow features, attributed primarily to the complex coupling between electroviscous effect generated in the process and the fluid rheology. The higher relaxation time of the fluid reduces the drag and shows a shear-thinning behaviour. Because of this shear-thinning effect, the streaming rate of the counter-ions increases and results in an enhancement in the streaming potential.

In this article, we study the influence of electroviscous effect on the filling dynamics of a viscoelastic fluid in a horizontal microfluidic channel. For depicting the viscoelastic nature, we consider a simplified Phan-Thien-Tanner (sPTT) model, while for filling dynamics, we consider the reduced ordered model, derived from Newton's second law. In addition to the surface tension force and viscous resistance at the walls, we take into account the electric force generated by the streaming potential in the underlying analysis. To obtain the inferences pertinent to the change in the viscoelasticity, we show the variations in the filling characteristics with relaxation time, whereas to show the influence of streaming potential, we vary the physical parameters of the system such as Debye length, the height of the channel and the conductivity of the viscoelastic electrolyte.