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Electrokinetics of non-Newtonian fluids: A review ABSTRACT
This work presents a comprehensive review of electrokinetics pertaining to non-Newtonian fluids. The topic covers a broad range of non-Newtonian effects in electrokinetics, including electroosmosis of non-Newtonian fluids, electrophoresis of particles in non-Newtonian fluids, streaming potential effect of non-Newtonian fluids and other related non-Newtonian effects in electrokinetics. Generally, the coupling between non-Newtonian hydrodynamics and electrostatics not only complicates the electrokinetics but also causes the fluid/particle velocity to be nonlinearly dependent on the strength of external electric field and/or the zeta potential. Shear-thinning nature of liquids tends to enhance electrokinetic phenomena, while shear-thickening nature of liquids leads to the reduction of electrokinetic effects. In addition, directions for the future studies are suggested and several theoretical issues in non-Newtonian electrokinetics are highlighted.
1. Introduction
The recently growing interests in electrokinetic phenomena are triggered by their diverse applications in microfluidic devices which could have the potential to revolutionize conventionalways of chemical analysis,medical diagnostics, material synthesis, drug screening and delivery aswell as environmental detection andmonitoring. The prevalent use of electrokinetic techniques in microfluidic devices is ascribed to their several distinctive advantages: (i) the devices are energized by electricitywhich is widely available and ease of control; (ii) the devices involve no moving parts and thus less mechanical failures; (iii) the induced velocity of liquid or particle is independent of geometric dimensions of devices; (iv) the devices can be readily integrated with other electronic controlling units to achieve fully-automated operation. In addition to its useful applications in microfluidics, electrokinetics is also a basis for understanding various phenomena, such as ionic transport and rectification in nanochannels [1,2], thermophoresis in
aqueous solutions [3,4], electrowetting of electrolyte solutions [5,6] and so on. When a solid surface is brought into contact with an electrolyte solution, the solid surface obtains electrostatic charges. The presence of such surface charges causes redistribution of ions and then forms a charged diffuse layer in the electrolyte solution near the solid surface to naturalize the electric charges on solid surface. Such electrically nonneutral diffuse layer is usually dubbed electric double layer (EDL) which is responsible for two categories of electrokinetic phenomena, (i) electrically-driven electrokinetic phenomena and (ii) nonelectrically-driven electrokinetic phenomena. The basic physics behind the first category is as follows: when an external electric field is applied tangentially along the charged surface, the charged diffuse layer experiences an electrostatic body force which produces relativemotion between the charged surface and the liquid electrolyte solution. The liquid motion relative to the stationary charged surfaces is known as electroosmosis (Fig. 1a), and the motion of charged particles relative to the stationary liquid is known as electrophoresis (Fig. 1b). The classic electroosmosis occurs around solids with fixed surface charges (or, equivalently, zeta potential ζ) for given physiochemical properties of surface and solution, and then the effective liquid slip at the solid surface under the situation of thin EDLs is quantified by the well-known Helmholtz–Smoluchowski velocity, i.e., us = ?εζE0/μ (ε is the electric permittivity of the electrolyte solution, ζ is the zeta potential of the solid surface, E0 is the external electric field strength and μ is the dynamic viscosity of electrolyte solution). When a charged particle with a thin EDL is freely suspended in a stationary liquid electrolyte solution, electroosmotic slip motion of solution molecules on the particle surface induces the electrophoretic motion of particle with a velocity given by the Smoluchowski equation, U =εζE0/μ (Note that here ζ denotes the zeta potential of particle). One typical behavior of the second category is the generation of streaming potential effect in pressure-driven flows (Fig. 1c). There are surplus counterions in EDLs adjacent to the channel walls, and the pressuredriven flow convects these counterions downstream to gives rise to a streaming current. Simultaneously, the depletion (accumulation) of counterions in the upstream (downstream) sets up a streaming potential which drives a conduction current in opposite direction to the streaming current. At the steady state, the conduction current exactly counter-balances the streaming current, and the streaming potential built up across the channel under the limit of thin EDLs is given
by Es = Pεζ/(σ0μ) (P is externally applied pressure gradient and σ0 represents the bulk conductivity of electrolyte solution). More fundamental and comprehensive descriptions of electrokinetic phenomena are given in textbooks and reviews [7–13].
Previous description of electrokinetics usually assumes Newtonian fluids with constant liquid viscosity, and most studies of electrokinetics in literature adopt such assumption. But in reality, microfluidic devices are more frequently involved in analyzing and/or processing biofluids (such as solutions of blood, saliva, protein and DNA), polymeric solutions and colloidal suspensions. These fluids cannot be treated as Newtonian fluids. Therefore, the characterization of hydrodynamics of such non-Newtonian fluids relies on the general Cauchy momentum equation in conjunction with proper constitutive equations which generally define the viscosity of liquid to vary with the rate of hydrodynamic shear, rather than the Navier–Stokes equation which is only applicable to Newtonian fluids. Since electrokinetics results from the coupling of hydrodynamics and electrostatics, it is straightforward to believe that non-Newtonian hydrodynamics would modify the conventional Newtonian electrokinetics. In this review, non-Newtonian effects on electrokinetics are comprehensively summarized and discussed. This review is organized as follows: Section 2 provides a review on the most widelystudied electroosmosis of non-Newtonian fluids. Section 3 presents a review for the electrophoresis of particles in non-Newtonian fluids, and Section 4 discusses the streaming potential effects of non-Newtonian fluids. Other non-Newtonian effects of particular interest on electrokinetics are given in Section 5. Lastly, Section 6 concludes the review and identifies the directions for the future studies.
2. Electroosmosis of non-Newtonian fluids
The pioneering contribution to this field is probably attributed to Bello et al. [14] who experimentally measured an electroosmotic flow of a polymer (methyl cellulose) solution in a capillary. Their investigation showed that the electroosmotic velocity of such polymer solution is much higher than that predicted with the classic Helmholtz–Smoluchowski velocity. It was then proposed that the shear-thinning induced by polymermolecules lowers the effective fluid viscosity inside the EDL. About a decade later, more interests were paid to such phenomenon
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