Electrokinetic Microfluidic Circuit Analysis
Christian Biscombe, Malcolm Davidson and Dalton Harvie
Christian performed a PhD on this topic, supported by a University of Melbourne scholarship. This work was also partially supported by the Australian Research Council Discovery grant, `Electro-viscous effects on pressure-driven liquid flow in microchannels' (DP0665898).
The growing promise of a 'lab-on-a-chip' revolution in chemical and biological analysis has inspired the development here of a new electrokinetic circuit model, named the Ion Current Model (ICM), to facilitate rapid numerical prototyping of electrokinetic microfluidic/nanofluidic devices. The ICM predicts steady, fully developed flow behaviour for binary electrolyte solutions driven through networks of straight charged channels by differences of pressure and/or electrical potential. In contrast to previous circuit theories, the ICM explicitly enforces ion current conservation across circuit nodes, which is necessary to account correctly for concentration changes that occur due to changes in surface conductivity across nodes. Such concentration polarisation effects are expected to be most significant in nanofluidic systems, which are becoming increasingly common.
The ICM is applied to both series and parallel channel networks, these being two of the most commonly encountered channel configurations. ICM predictions are validated by comparison with established analytical models of electrokinetic flow (where possible) and with two-dimensional computational fluid dynamics simulations based on the finite volume method.
Ion current conservation has several important physical consequences. Under conditions of fixed liquid flow rate and ion currents, the ICM predicts the existence of multiple steady states in series networks when the net co-ion flux is in the direction opposite to the net liquid flow. The actual steady state that develops in a physical system depends upon its history and may be predicted in some cases by coupling the ICM with an analysis of concentration shock propagation. For parallel networks, the ICM predicts that there may be infinitely many steady states, regardless of the direction of co-ion transport. The actual steady state that develops is influenced by the formation of concentration polarisation zones near the ends of the parallel channels and is also likely to exhibit history dependence. Contrary to common assumption, the liquid flow and ion currents need not divide equally between identical parallel channels.
The significance of this thesis is that it provides a rigorous, well validated basis for microfluidic/nanofluidic device design. The very fact that many new physical phenomena have been revealed using the ICM is testament to the power of circuit analysis as a design tool, but equally suggests that previously unforeseen difficulties might hinder the development of practical electrokinetic devices.
Electrokinetics at the Silica/Water Interface, with Application to Protein Focusing and Separation in a Silica Nanofluidic Channel
Wei-Lun Hsu, David Dunstan, Malcolm Davidson and Dalton Harvie
Wei-Lun performed a PhD on this topic, supported by a University of Melbourne International Postgraduate Study scholarship. This work was also partially supported by the Australian Research Council Discovery grant, `Simulating two-phase electrodynamics flows in droplet-based microfluidic circuit elements' (DP1097204).
The manipulation of biological macromolecules in a new breed of nanofluidic devices, for applications such as Point-of-Care diagnostics, requires a quantitative understanding of electrokinetics. Using this as motivation, the focus of this research is on electrokinetics within silica nanochannels. It was found that several issues regarding the conventional electric, double layer model at a silica/water interface exist, as evident by a lack of consistency within the literature for properties such as the (i) equilibrium constant of surface silanol groups, (ii) Stern layer capacitance, (iii) zeta potential measured by various electrokinetic methods, and (iv) surface conductivity.
In this work, the silica and water interface model is modified to include the viscoelectric effect - that is, the increase of the local viscosity due to the polarisation of polar solvents. The model is validated by comparing theoretical results with those from previous experiments, conducted using four fundamental electrokinetic phenomena: electrophoresis, electroosmosis, streaming current and streaming potential. This model is then applied to two types of matrix-free protein focusing and separation devices that employ a nanofluidic channel - Concentration Gradient Focusing and Isoelectric Focusing - to better understand how these devices work, and quantitatively predict trapping behaviour. The effects of salt concentration, applied voltage, pH and channel geometry on the electroosmotic flow are examined.
Definitions: Electroosmosis, Electroviscosity, Electrophoresis and Dielectrophoresis
When a charged surface (be it a device wall or another immiscible fluid phase) is brought into contact with an ionic liquid, ions within the liquid redistribute themselves in response to that charge. This produces a region of liquid next to the surface which is itself charged. When an external electrical field is applied to this region then the liquid next to the wall experiences a force. This process defines electrokinetics.
Electrokinetics encompasses electroosmosis, electroviscosity and electrophoresis. During electroosmosis an external field is applied to a single phase ionic liquid that is in contact with a (charged) wall, causing the liquid to flow. Electroviscosity describes the increased flow resistance caused by an induced streaming potential field that develops in response to the pressure driven flow of a single phase ionic liquid through a (charged) channel. Electrophoresis describes the movement of charged particles or droplets within an ionic liquid due to an applied field.
Dielectrophoresis (DEP) describes a slightly different type of electrodynamic force. The DEP force occurs at the boundary between two mediums that have different dielectric constants, in the presence of a non-uniform electrical field. DEP forces have been used for droplet sorting in droplet-based microfluidic chips and also form the operational basis for digital microfluidics: Digital microfluidics use electrowetting on dieletric (EWOD) forces to move individual droplets around a matrix of electrodes.
Our electrokinetic flow models account for all of these phenomena within multiple phases.
An electrokinetic study of microfluidic drop deformation, breakup and coalescence
Rohit Pillai, Joseph Berry, Dalton Harvie and Malcolm Davidson
Rohit is performing a PhD on this topic. This work is also partially supported by the Australian Research Council Discovery grant, `Simulating two-phase electrodynamics flows in droplet-based microfluidic circuit elements' (DP1097204).
Electric fields have been employed in many industrial processes to produce and manipulate liquid drops, with applications including atomisation, enhanced coalescence and purification of oils. Recent developments in lab-on-a-chip microfluidic devices also provide a host of novel applications for multiphase electrokinetic flow including medical diagnostics and chemical synthesis. Our research focuses on the fundamental understanding of the problem of electrically induced deformation, breakup and coalescence of a microfluidic drop, which is essential prior to proceeding to more complex electrokinetic systems. This is done by numerical modelling of simplified drop scenarios using a two phase electrokinetic model.
The current research focuses on studying the effects of electric fields on coalescence of a drop and a planar interface. Electric fields have been known to accelerate the coalescence process by aiding the rupture of the interfacial film at the point of contact. However, incomplete coalescence can also occur, when a secondary drop pinches off without entering the bulk, the reasons for which are poorly understood. In addition to electric forces, the drop deformation behaviour is influenced by the inertial, viscous and interfacial tension forces. The goal of the project is to characterize the coalescence behaviour of the drop and develop an understanding of the physical mechanisms involved.
Past research has been focused on studying the electrically induced drop deformation and breakup. The effect of electric field strength and drop ion concentration were shown to play a prominent role in the different dynamic behaviours observed. The stability conditions were also characterized.
|||Electrohydrodynamic deformation and interaction of microscale drop pairs ( ), In International Journal of Computational Methods and Experimental Measurements, volume 4, 2016.|
|||Electrophoretically mediated partial coalescence of a charged microdrop ( ), In Chemical Engineering Science, 2016.|
|||Electrokinetics of isolated electrified drops ( ), In Soft Matter, volume 12, 2016.|
|||Viscoelectric Effects in Nanochannels ( ), submitted to Nano Letters, 6/9/16, 2016.|
|||Electrokinetics of the silica and aqueous electrolyte solution interface: Viscoelectric effects ( ), In Advances in Colloid and Interface Science, 2016.|
|||Numerical simulation of two-fluid flow of electrolyte solution with charged deforming interfaces ( ), In Applied Mathematical Modelling, volume 40, 2016.|
|||Electrolytic drops in an electric field: A numerical study of drop deformation and breakup ( ), In Physical Review E, volume 92, 2015.|
|||Electrophoretic Effects on Satellite Droplet Formation during Electrocoalescence of Microdrops ( ), In 11th International Conference on CFD in the Minerals and Process Industries, 2015.|
|||Corrections to `Microfluidic circuit analysis I: Ion current relationships for thin slits and pipes', J. Colloid Interface Sci. 365 (2012) 1-15 and `Microfluidic circuit analysis II: Implications of ion conservation for microchannels connected in series', J. Colloid Interface Sci. 365 (2012) 16-27 ( ), volume 442, 2015.|
|||Electroviscous resistance of nanofluidic bends ( ), In Phys. Rev. E, American Physical Society, volume 90, 2014.|
|||Electroviscous flow through nanofluidic junctions ( ), In Applied Mathematical Modelling, volume 38, 2014.|
|||Numerical simulation of the deformation of charged drops of electrolyte ( ), In Advances in Fluid Mechanics X, 2014.|
|||Multi-Physics Lab-on-a-Chip Simulations ( ), (Zhu, Dr Jonggang; Gu, Prof. Min, eds.), 2014.|
|||Effect of interfacial tension and electric field on charge separation dynamics inside stable and unstable microdrops ( ), In 19th Australasian Fluid Mechanics Conference, 2014.|
|||Isoelectric focusing in a silica nanofluidic channel: Effects of electromigration and electroosmosis ( ), In Analytical Chemistry, volume 86, 2014.|
|||Concentration gradient focusing and separation in a silica nanofluidic channel with a non-uniform electroosmotic flow ( ), In Lab Chip, The Royal Society of Chemistry, volume 14, 2014.|
|||Stationary chemical gradients for concentration gradient-based separation and focusing in nanofluidic channels ( ), In Langmuir, volume 30, 2014.|
|||Electrokinetic flow in parallel channels: Circuit modelling for microfluidics and membranes ( ), In Colloids and Surfaces A: Physicochemical and Engineering Aspects, volume 440, 2014.|
|||DNA focusing in nanofluidic channels ( ), In The 17th International Conference on Miniaturized Systems for Chemistry and Life Sciences The 17th International Conference on The 17th International Conference on Miniaturized Systems for Chemistry and Life Sciences (MicroTAS 2013), 2013.|
|||A multiphase electrokinetic flow model for electrolytes with liquid/liquid interfaces ( ), In Journal of Computational Physics, volume 251, 2013.|
|||Electroviscous flow through a microfluidic T-junction ( ), In Ninth International Conference on CFD in the Minerals and Process Industries, 2012.|
|||Deformation of liquid drops containing ions in the presence of an electric field ( ), In HEFAT2012, 9th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, 2012.|
|||Numerical modelling of electrohydrodynamic drops ( ), 2012.|
|||Electroviscous flow through microfluidic contractions, bends and junctions ( ), 2012.|
|||Microfluidic circuit analysis I: Ion current relationships for thin slits and pipes ( ), In Journal of Colloid and Interface Science, volume 365, 2012.|
|||Electrokinetic flow in connected channels: A comparison of two circuit models ( ), In Journal of Microfluidics and Nanofluidics, volume 13, 2012.|
|||Microfluidic circuit analysis II: Implications of ion conservation for microchannels connected in series ( ), In Journal of Colloid and Interface Science, volume 365, 2012.|
|||Electrokinetic development length of electroviscous flow through a contraction ( ), In ANZIAM J. (CTAC2010) (McLean, W.; Roberts, A. J., eds.), volume 52, 2011.|
|||Comparative evaluation of microfluidic circuit model performance for electroviscous flow ( ), In ANZIAM J. (CTAC2010) (McLean, W.; Roberts, A. J., eds.), volume 52, 2011.|
|||Electroviscous flow through a 2D microfluidic contraction with finite dielectric ratio ( ), 2011.|
|||Simulating Lab-on-a-Chip devices ( ), 2011.|
|||Implications of ion conservation for microfluidic circuit analysis ( ), 2011.|
|||Effect of wall permittivity on electroviscous flow through a contraction ( ), In Biomicrofluidics, volume 5, 2011.|
|||Electroviscous effects in a Carreau liquid flowing through a cylindrical microfluidic contraction ( ), In Chemical Engineering Science, volume 65, 2010.|
|||Electroviscous effects in steady flow of a shear-thinning Carreau liquid through a microfluidic contraction ( ), In SEECCM 2009, 2nd South-East European Conference on Computational Mechanics (M. Papadrakakis, M. Kojic V. Papadopoulos, ed.), 2009.|
|||Electro-osmotic effects in low Reynolds number flow through a planar microfluidic contraction-expansion ( ), In Seventh International Conference on CFD in the Minerals and Process Industries, 2009.|
|||Electroviscous effects in low Reynolds number flow through a microfluidic contraction with rectangular cross-section ( ), In World Academy of Science, Engineering and Technology, volume 40, 2009.|
|||Electroviscous effects in steady fully developed flow of a power-law liquid through a cylindrical microchannel ( ), In International Journal of Heat and Fluid Flow, volume 30, 2009.|
|||Fully developed flow of power-law fluid through a cylindrical microfluidic pipe: Pressure drop and electroviscous effects ( ), In ASME Fluids Engineering Division Summer Conference (FEDSM2008), Part A, volume 1, 2008.|
|||Steady flow of ionic liquid through a cylindrical microfluidic contraction-expansion pipe: Electroviscous effects and pressure drop ( ), In Chemical Engineering Science, volume 63, 2008.|
|||Electrokinetic flow resistance in pressure-driven liquid flow through a slit-like microfluidic contraction ( ), In 16th Australasian Fluid Mechanics Conference, 2007.|
|||Electroviscous effects in low Reynolds number liquid flow through a slit-like microfluidic contraction ( ), In Chemical Engineering Science, volume 62, 2007.|