Chemical Engineering and Processing - Process Intensification
Pulsatile flow micromixing coupled with ICEO for non-Newtonian fluids
Introduction
Mixing of two or more species in micron scale is widely utilized in many lab-on-a-chip (LOC) devices. Moreover, it is crucial to handle rapid mixing of fluids for preparation of drugs, a combination of reagents, biofluids as well as macromolecules. However, this is a challenging issue in fluid transport due to uniaxial flow direction for straight channels and dominant viscous forces in low Reynolds number regime. It can also be stated that biological macromolecules such as enzymes, proteins, and cells face the probability of losing their structures and functions due to high shear rates in this flow condition [1]. Therefore, micromixers with sophisticated designs including many components, which activate various phenomena in different disciplines are manufactured to increase mixing efficiency and reduce mixing time/length. The performance of a micromixer is quantified using Peclet number, which is characterized by a ratio between advection and diffusion in fluid transport [2]. The efficiency of fluid mixing can be enhanced using techniques of initiating the chaotic advection [3,4] and the introduction of flow pulsation to the system [5].
Induced-charge electro-osmosis (ICEO) is reported by Squires and Bazant [6], who present the theory with potential applications. ICEO is characterized by four vortices around a circular conductive cylinder suspended in an electrolyte under externally applied alternating (AC) or direct electric (DC) currents. In contrast to electroosmosis (EO), ICEO is a nonlinear electrokinetic phenomenon, which exhibits a nonlinear relation between ICEO flow magnitudes with imposed electric field strength [7]. Therefore, the velocity magnitude of ICEO flow is much higher than that of EO under same electric field strengths. The experimental studies about ICEO suggest that measured velocities are smaller than predicted velocity magnitudes [8,9]. Because of extensive utilization of ICEO in micromixer designs, Canpolat et al. [10] and Canpolat [11] presented flow and vorticity fields of ICEO from experimental measurements. ICEO can be generated around various geometries of conductive objects, such as planar electrodes [13], triangle [14] and circular [15]. ICEO is used efficiently for mixing of two concurrently flowing miscible fluids experimentally [12,14] and numerically [15,16] in the open literature. In addition, Jain et al. [17] performed a shape optimization study of various geometries for determining analogy between mixing efficiency and the shape of a conductive obstacle.
Periodically oscillating flow, which has a time-dependent nature can be generated using pulsation. In addition, it creates perturbation along the interface of concurrently streaming fluids; thus, it comes into play as a tool for mixing of two miscible liquids in micron scale. The presence of pulsation results in a dramatic decrease in mixing length and time. The main parameters affecting the pulsatile flow are the frequency of pulsatile flow, Reynolds number, phase difference and channel geometry [18]. A nondimensional parameter of Strouhal number (St), which is calculated with the equation of St = fL/U is used for determination of the magnitude of frequency of pulsatile flow velocity. In this equation, f is the frequency of the pulse, L is the characteristic length, and U is velocity magnitude. According to related literature, Strouhal number has a profound effect on mixing in microchannels [19]. Since the flow has time-dependent nature, microchannel geometry [20] and microchannel inlet shape [21,22] have significant effects on mixing performance. The impact of the obstructions with various geometries on passive micromixing is numerically investigated by Bhagat et al. [23] and Alam et al. [24]. It is reported that the best mixing performance is obtained with circular microobstruction compared to hexagonal and diamond-shaped obstructions. Park et al. [25] compared micromixing performances of hexahedral obstruction pairs, which are embedded throughout the microchannel.
A non-Newtonian fluid is characterized by a nonlinear trend of the curve in the plot of shear stress versus deformation at a given temperature and pressure. Apparent viscosity exhibits highly dependent behavior on flow conditions, such as channel geometry and shear rate [26]. In microfluidics, it is worth to state that many fluids/biofluids, i.e., blood, saliva, DNA solutions, etc., employed in LOC devices, such as polymer solutions, cell suspensions, and colloids have non-Newtonian characteristics [27]. Therefore, investigation of fluid mixing for non-Newtonian fluids has crucial importance. An extensive review of electrokinetics of non-Newtonian fluids is presented by Zhao and Yang [28]. Zimmerman et al. [29] performed two dimensional numerical simulations for electrokinetic flow through a microchannel, which had a working fluid with Carreau-type viscosity behavior. An analytical solution of electrokinetic motion of power-law fluids in micron scale is derived by Das and Chakraborty [30]. Note that, Carreau-type viscosity equation differs from power-law viscosity model by taking into account of limiting values of viscosities, such as zero shear viscosity and infinite shear viscosity [27]. Berli and Olivares [31] present a theory of electroosmosis through slits and cylindrical channels for non-Newtonian fluids. According to these theories, Hadigol et al. [32] utilize electroosmotic flow through a microchannel with nonuniform zeta potential for mixing of power-law fluids. In this numerical study, they report that the fluid mixing of shear thinning fluids is very efficient than that of shear thickening fluids. Shamloo et al. [33] test the performance of electroosmotic micromixer for non-Newtonian fluids numerically. Electrothermal effects, which is generated under alternating current electric field are utilized for micromixing by Kunti et al. [34]. Their study results that the flow rate through the microchannel depends on flow behavior index of power-law fluids. Galletti et al. [35] conduct numerical work for studying the mixing of non-ideal liquids with composition dependent viscosity using direct numerical simulations (DNS). Alipanah and Ramiar [36] investigate micromixing efficacy of induced-charge electro-osmosis, which is propelled using AC electric fields. The floating electrodes are located on channel walls at the entrance of T-shaped microchannel in this study. It is concluded that their mixer design provides high mixing efficiency for Newtonian and non-Newtonian fluids. Particularly, ICEO around a conductive cylinder of polymer solutions are measured by Canpolat et al. [37] using micro particle image velocimetry.
In this study, pulsatile flow micromixing which is coupled with induced-charge electro-osmosis for non-Newtonian fluids is quantified. In the light of previous studies, we select to investigate shear thinning behavior for the present numerical study. Moreover, the results are compared to the cases of a Newtonian fluid. Rectangular obstruction and pulsatile flow conditions are also introduced to the system to decrease the required time and length for mixing. Channel geometry, electric field strength, and frequency of pulsatile flow are varied to reveal their effects on mixing index under Reynolds number of Re = 2 × 10−2 based on channel width. On the other hand, mixed species are considered as chemically inactive for each other, and Joule heating effects, which derive from external potential difference are neglected. For the qualitative presentation of the results, instantaneous streamline topologies and related concentration distributions are demonstrated. Mixing indexes of instantaneous time steps within the last period of pulsatile flow as well as their average values are plotted for quantitative evaluation. To the best of the author’s knowledge, this is the first study that utilizes ICEO and pulsatile flow effects on mixing of two fluids in the open literature.
Section snippets
Theory
The fluid motion is described by Navier – Stokes Equation and continuity equation, which are presented below, respectively.where u is the velocity of the fluid, ρ is the density of the fluid, p is the pressure, f is the body force, and bold characters are preferred for indicating the vector quantity. These equations are modified due to incompressible nature of the fluid.
The transport of diluted species is governed by Nernst – Planck Equation which is:
Results and discussions
Prior to the detailed investigation of micromixer design parametrically, each variable in the system is evaluated individually. For this purpose, micromixers working with only ICEO and pulsatile flows are simulated and mixing index values are calculated for Newtonian and Non-Newtonian fluids. It is observed that the species could not be transported completely to the outlet of the channel under these conditions. For instance, maximum concentration is obtained at a location, where it corresponds
Conclusions
The current numerical work aims to reveal the characteristics of a pulsatile micromixer coupled with induced-charge electro-osmosis (ICEO), which is initiated around a flat electrode for the fluids with various rheology models, such as Newtonian, Power-law, and Carreau. The parameters evaluated in this study are the magnitude of the external electric field, the frequency of pulsatile flow and the width of rectangular obstruction. The following conclusions are drawn from this study:
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Pulsatile
Acknowledgment
This work is supported by Cukurova University Scientific Research Office financially under contract no FBA-2017-7960.
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