The influence of frequency and gravity on the orientation of active metallo-dielectric Janus particles translating under a uniform applied alternating-current electric field

Theoretical and numerical models of active Janus particles commonly assume that the metallo-dielectric interface is parallel to the driving applied electric field. However, our experimental observations indicate that the equilibrium angle of orientation of electrokinetically driven Janus particles varies as a function of the frequency and voltage of the applied electric field. Here, we quantify the variation of the orientation with respect to the electric field and demonstrate that the equilibrium position represents the interplay between gravitational, electrostatic and electrohydrodynamic torques. The latter two categories are functions of the applied field (frequency, voltage) as well as the height of the particle above the substrate. Maximum departure from the alignment with the electric field occurs at low frequencies characteristic of induced-charge electrophoresis and at low voltages where gravity dominates the electrostatic and electrohydrodynamic torques. The departure of the interface from alignment with the electric field is shown to decrease particle mobility through comparison of freely suspended Janus particles subject only to electrical forcing and magnetized Janus particles in which magnetic torque is used to align the interface with the electric field. Consideration of the role of gravitational torque and particle-wall interactions could account for some discrepancies between theory, numerics and experiment in active matter systems.

Induced-charge electrophoresis of a tilted metal nanowire near an insulating wall

Electric fields are commonly used to control the orientation and motion of microscopic metal particles in aqueous suspensions. For example, metallodielectric Janus spheres are propelled by the induced-charge electro-osmotic flow occurring on their metallic side, the most common case in electrokinetics of exploiting symmetry breaking of surface properties for achieving net particle motion. In this work, we demonstrate that a homogeneous metal rod can translate parallel to a dielectric wall as a result of the hydrodynamic wall-particle interaction arising from the induced-charge electro-osmosis on the rod surface. The applied electric field could be either dc or low-frequency ac. The only requirement for a nonvanishing particle velocity is that the axis of the rod be inclined with respect to the wall, i.e., it cannot be neither parallel nor perpendicular. We show numerical results of the rod velocity as a function of rod orientation and distance to the wall. The maximum particle velocity is found for an orientation of between ∼30^{∘} and ∼50^{∘}, depending on the position and aspect ratio of the cylinder. Particle velocities of up to tens of µm/s are predicted for typical conditions in electrokinetic experiments.

Low-frequency electrokinetics in a periodic pillar array for particle separation

Deterministic Lateral Displacement (DLD) exploits periodic arrays of pillars inside microfluidic channels for high-precision sorting of micro- and nano-particles. Previously we demonstrated how DLD separation can be significantly improved by the addition of AC electrokinetic forces, increasing the tunability of the technique and expanding the range of applications. At high frequencies of the electric field (>1 kHz) the behaviour of such systems is dominated by Dielectrophoresis (DEP), whereas at low frequencies the particle behaviour is much richer and more complex. In this article, we present a detailed numerical analysis of the mechanisms governing particle motion in a DLD micropillar array in the presence of a low-frequency AC electric field. We show how a combination of Electrophoresis (EP) and Concentration-Polarisation Electroosmosis (CPEO) driven wall-particle repulsion account for the observed experimental behaviour of particles, and demonstrate how this complete model can predict conditions that lead to electrically induced deviation of particles much smaller than the critical size of the DLD array.

Insulating traveling-wave electrophoresis

Traveling-wave electrophoresis (TWE) is a method for transporting charged colloidal particles used in many microfluidic techniques for particle manipulation and fractionation. This method exploits the traveling-wave components of the electric field generated by an array of electrodes subjected to ac voltages with a phase delay between neighboring electrodes. In this article, we propose an alternative way of generating traveling-wave electric fields in microchannels. We apply a rotating electric field around a cylindrical insulating micropillar and the resulting traveling-wave modes induce particle drift around the cylinder. We term this phenomenon insulating traveling-wave electrophoresis (i-TWE) to distinguish it from standard TWE performed with arrays of microelectrodes. We characterized the particle drift experimentally and show a quantitative comparison of the particle velocity with theoretical predictions. Excellent agreement is found when the influence of electro-osmosis on the channel walls is also considered.

Scattering of Metal Colloids by a Circular Post under Electric Fields

We consider the scattering of metal colloids in aqueous solutions by an insulating circular post under the action of an AC electric field. We analyze the effects on the particle of several forces of electrical origin: the repulsion between the induced dipole of the particle and its image dipole in the post, the hydrodynamic interaction with the post due to the induced-charge electroosmotic (ICEO) flow around the particle, and the dielectrophoresis arising from the distortion of the applied electric field around the post. The relative influence of these forces is discussed as a function of frequency of the AC field, particle size and distance to the post. We perform numerical simulations of the scattering of the metal colloid by the insulating circular post flowing in a microchannel and subjected to alternating current electric fields. Our simulation results show that the maximum particle deviation is found for an applied electric field parallel to the flow direction. The deviation is also greater at low electric field frequencies, corresponding to the regime in which the ICEO's interaction with the post is predominant over other mechanisms.

Wall Repulsion of Charged Colloidal Particles during Electrophoresis in Microfluidic Channels

Electrophoresis describes the motion of charged particles suspended in electrolytes when subjected to an external electric field. Previous experiments have shown that particles undergoing electrophoresis are repelled from nearby channel walls, contrary to the standard description of electrophoresis that predicts no hydrodynamic repulsion. Dielectrophoretic (DEP) repulsive forces have been commonly invoked as the cause of this wall repulsion. We show that DEP forces can only account for this wall repulsion at high frequencies of applied electric field. In the presence of a low-frequency field, quadrupolar electro-osmotic flows are observed around the particles. We experimentally demonstrate that these hydrodynamic flows are the cause of the widely observed particle-wall interaction. This hydrodynamic wall repulsion should be considered in the design and application of electric-field-driven manipulation of particles in microfluidic devices.

Concentration-Polarization Electroosmosis near Insulating Constrictions within Microfluidic Channels

Electric fields are commonly used to trap and separate micro- and nanoparticles near channel constrictions in microfluidic devices. The trapping mechanism is attributed to the electrical forces arising from the nonhomogeneous electric field caused by the constrictions, and the phenomenon is known as insulator-based-dielectrophoresis (iDEP). In this paper, we describe stationary electroosmotic flows of electrolytes around insulating constrictions induced by low frequency AC electric fields (below 10 kHz). Experimental characterization of the flows is described for two different channel heights (50 and 10 μm), together with numerical simulations based on an electrokinetic model that considers the modification of the local ionic concentration due to surface conductance on charged insulating walls. We term this phenomenon concentration–polarization electroosmosis (CPEO). The observed flow characteristics are in qualitative agreement with the predictions of this model. However, for shallow channels (10 μm), trapping of the particles on both sides of the constrictions is also observed. This particle and fluid behavior could play a major role in iDEP and could be easily misinterpreted as a dielectrophoretic force.

Short communication: A simple and accurate method of measuring the zeta-potential of microfluidic channels

We describe an improved method for determining the electroosmotic mobility and zeta potential of surfaces based on a current-monitoring method. This technique eliminates the requirement for measurements of channel dimensions and sample conductivities, leading to a simple high precision measurement. The zeta potential of PDMS is measured for native surfaces and surfaces treated with a nonionic surfactant in low-conductivity electrolytes.

Continuous Particle Separation in Microfluidics: Deterministic Lateral Displacement Assisted by Electric Fields

Advances in the miniaturization of microelectromechanical systems (MEMS) [...]

Electrorotation of semiconducting microspheres

We study experimentally the electrorotation (ROT) of semiconducting microspheres. ZnO microspheres obtained by a hydrothermal synthesis method are dispersed in KCl aqueous solutions and subjected to rotating electric fields. Two ROT peaks are found in experiments: a counterfield peak and a cofield peak at somewhat higher frequencies. These observations are in accordance with recent theoretical predictions for semiconducting spheres. The counterfield rotation is originated by the charging of the electrical double layer at the particle-electrolyte interface, while the cofield rotation is due to the Maxwell-Wagner relaxation. Additionally, we also found that some microspheres in the sample behaved differently and only showed counterfield rotation. We show that the behavior of these particles can be described by the so-called shell model. The microstructure of the microspheres is analyzed with electron microscope techniques and related to the ROT measurements.

Electrokinetics of metal cylinders

We study theoretically the rotation induced on an uncharged metal nanocylinder immersed in an electrolyte by AC electric fields. We consider the rotation of the cylinder when subjected to a rotating electric field (electrorotation) and the orientation of the cylinder in an AC field with constant direction (electro-orientation). The cylinder rotation is due to two mechanisms: the electric field interaction with the induced dipole on the particle and the hydrodynamic stress on the particle originated by the induced-charge electro-osmotic (ICEO) flow around the particle. The cylinder rotation induced by the ICEO mechanism can be calculated by using the Lorentz reciprocal theorem, while the rotation due to the induced dipole is calculated from the cylinder polarizability. We employ 3D numerical computations using finite elements for the general case as well as analytical methods for slender cylinders. Both calculations use the thin-double-layer approximation. We compare the results for slender cylinders of both methods showing good agreement. The electro-orientation (EOr) due to dipole torque aligns the axis of slender cylinders with the applied field, but aligns the axis of short cylinders perpendicularly to the field. The EOr due to ICEO torque always aligns the axis of cylinders with the field. The rotation induced by ICEO torque tends to disappear for frequencies of the applied field much greater than the characteristic frequency for charging the double-layer capacitance of the metal-electrolyte interface.

Modeling the AC Electrokinetic Behavior of Semiconducting Spheres

We study theoretically the dielectrophoresis and electrorotation of a semiconducting microsphere immersed in an aqueous electrolyte. To this end, the particle polarizability is calculated from first principles for arbitrary thickness of the Debye layers in liquid and semiconductor. We show that the polarizability dispersion arises from the combination of two relaxation interfacial phenomena: charging of the electrical double layer and the Maxwell⁻Wagner relaxation. We also calculate the particle polarizability in the limit of thin electrical double layers, which greatly simplifies the analytical calculations. Finally, we show the model predictions for two relevant materials (ZnO and doped silicon) and discuss the limits of validity of the thin double layer approximation.

Electrorotation and Electroorientation of Semiconductor Nanowires

A number of experimental studies have shown electric-field manipulation of nanowires dispersed in liquids. We demonstrate from first-principles that the electrical response of semiconductor nanowires in liquids must be described by considering, at least, two mechanisms for interfacial polarization: the classical Maxwell-Wagner interfacial polarization and the formation of an electrical double layer. We compare the theoretical predictions with our experimental data and with data published elsewhere and show that both mechanisms play an important role.

Pumping of electrolytes by electrical forces induced on the diffusion layer: A weakly nonlinear analysis

Pumping of electrolytes in microchannels can be achieved with the use of microelectrodes subjected to AC potentials. Experiments have shown an influence of Faradaic currents in the pumping performance, and theoretical studies for asymmetric electrolytes suggest that induced charges in the diffusion layer play an important role. In this work we consider the case of a diffusion layer induced by an array of electrodes subjected to a traveling wave potential and we include Faradaic currents. Previous theoretical studies considered the case of very small applied voltages, which allowed for two major simplifications: (i) Butler-Volmer (B-V) equation was linearized, and (ii) the presence of gradients in ion concentration was neglected. We extend previous results and used the full nonlinear B-V equation. A comparison with the linear limit shows that the flow rate in both cases coincides for voltages around and below ≈0.25 V. For voltages larger than this, the nonlinear equations show that gradients in ion concentration appear and have an important influence, therefore, the predictions deviate from the linear model. We show that the electrical force in the diffusion layer can induce pumping either in the same or the opposite direction of the applied traveling-wave potential and it could be responsible for the reversal of the flow as observed in experiments.

AC electrified jets in a flow-focusing device: Jet length scaling

We use a microfluidic flow-focusing device with integrated electrodes for controlling the production of water-in-oil drops. In a previous work, we reported that very long jets can be formed upon application of AC fields. We now study in detail the appearance of the long jets as a function of the electrical parameters, i.e., water conductivity, signal frequency, and voltage amplitude. For intermediate frequencies, we find a threshold voltage above which the jet length rapidly increases. Interestingly, this abrupt transition vanishes for high frequencies of the signal and the jet length grows smoothly with voltage. For frequencies below a threshold value, we previously reported a transition from a well-behaved uniform jet to highly unstable liquid structures in which axisymmetry is lost rather abruptly. These liquid filaments eventually break into droplets of different sizes. In this work, we characterize this transition with a diagram as a function of voltage and liquid conductivity. The electrical response of the long jets was studied via a distributed element circuit model. The model allows us to estimate the electric potential at the tip of the jet revealing that, for any combination of the electrical parameters, the breakup of the jet occurs at a critical value of this potential. We show that this voltage is around 550 V for our device geometry and choice of flow rates.

Electrorotation of a metal sphere immersed in an electrolyte of finite Debye length

We theoretically study the rotation induced on a metal sphere immersed in an electrolyte and subjected to a rotating electric field. The rotation arises from the interaction of the field with the electric charges induced at the metal-electrolyte interface, i.e., the induced electrical double layer (EDL). Particle rotation is due to the torque on the induced dipole, and also from induced-charge electro-osmostic flow (ICEO). The interaction of the electric field with the induced dipole on the system gives rise to counterfield rotation, i.e., the direction opposite to the rotation of the electric field. ICEO generates co-field rotation of the sphere. For thin EDL, ICEO generates negligible rotation. For increasing size of EDL, co-field rotation appears and, in the limit of very thick EDL, it compensates the counter-field rotation induced by the electrical torque. We also report computations of the rotating fluid velocity field around the sphere.

Modelling a Human-Like Bot in a First Person Shooter Game

Autonomous agents in videogames, usually called bots, have tried to behave as human players from their emergence more than 20 years ago. They normally try to model a part of a human expert player's knowledge with respect to the game, trying to become a competitive opponent or a good partner for other players. This paper presents a deep description of the design of a bot for playing 1 vs. 1 Death Match mode in the first person shooter Unreal Tournament™ 2004 (UT2K4). This bot uses a state-based Artificial Intelligence model which emulates a big part of the behavior/knowledge (actions and tricks) of an expert human player in this mode. This player has participated in international UT2K4 championships. The behavioral engine considers primary and secondary actions, and uses a memory approach. It is based in an auxiliary database for learning about the fighting arena, so it stores weapons and items locations once the bot has discovered them, as a human player would do. This so-called Expert Bot has yielded excellent results, beating the game default bots even in the hardest difficulty, and being a very hard opponent for medium-level human players.

Electro-orientation of a metal nanowire counterbalanced by thermal torques

The rotational diffusion of electrically polarized metal nanowires suspended in an electrolyte is studied. The alignment of a Brownian nanowire in an ac field with a given direction is not complete due to thermal (fluctuating) torques. The orientation distribution allows us to examine the electrokinetic torques acting on the nanowire for smaller voltages than in previous deterministic experiments. In addition, the torques are obtained without recurring to the rotational friction coefficient as in dynamic deterministic experiments. The present results are in accordance with previous deterministic results of electro-orientation of metal nanowires. Nanowire rotation is originated by both the electrical torque on the induced dipole and by induced-charge electro-osmotic flow around the particle. At low frequencies of the applied ac field, induced-charge electro-osmotic orientation dominates while induced dipole torque orientation dominates at high frequencies. The angular standard deviation and the rotational rate are calculated from the measured fluctuating angle as a function of time, and good agreement with theoretical predictions is found. The experiments at high frequency indicate that the electrical torque on a nanowire near an insulating wall is reduced with respect to the bulk.

The microfluidic Kelvin water dropper

The so-called "Kelvin water dropper" is a simple experiment demonstrating the spontaneous appearance of induced free charge in droplets emitted through a tube. As Lord Kelvin explained, water droplets spontaneously acquire a net charge during detachment from a faucet due to the presence of electrical fields in their surroundings created by any metallic object. In his experiment, two streams of droplets are allowed to drip from separate nozzles into separate buckets, which are, at the same time, interconnected through the dripping needles. In this paper, we build a microfluidic water dropper and demonstrate that the droplets get charged and break up due to electrohydrodynamic instabilities. A comparison with recent simulations shows the dependence of the acquired charge in the droplets on different parameters of the system. The phenomenon opens a door to cheap and accessible transformation of pneumatic pressure into electrical energy and to an enhanced control in microfluidic and biophysical manipulation of capsules, cells and droplets via self-induced charging of the elements.

Electro-orientation and electrorotation of metal nanowires

The physical mechanisms responsible for the electrical orientation and electrical rotation of metal nanowires suspended in an electrolyte as a function of frequency of the applied ac electric field are examined theoretically and experimentally. The alignment of a nanowire in an ac field with a fixed direction is called electro-orientation. The induced constant rotation of a nanowire in a rotating electric field is called electrorotation. In both situations, the applied electric field interacts with the induced charge in the electrical double layer at the metal-electrolyte interface, causing rotation due to the torque on the induced dipole, and also from induced-charge electro-osmotic flow around the particle. First, we describe the dipole theory that describes electro-orientation and electrorotation of perfectly polarizable metal rods. Second, based on a slender approximation, an analytical theory that describes induced-charge electro-orientation and electrorotation of metal nanowires is provided. Finally, experimental measurements of the electro-orientation and electrorotation of metal nanowires are presented and compared with theory, providing a comprehensive study of the relative importance between induced-dipole rotation and induced-charge electro-osmotic rotation.

Electric-field-induced rotation of Brownian metal nanowires

We describe the physical mechanism responsible for the rotation of Brownian metal nanowires suspended in an electrolyte exposed to a rotating electric field. The electric field interacts with the induced charge in the electrical double layer at the metal-electrolyte interface, causing rotation due to the torque on the induced dipole and to the induced-charge electro-osmotic flow around the particle. Experiments demonstrate that the primary driving mechanism is the former of these two. Our analysis contrasts with previous work describing the electrical manipulation of metallic particles with electric fields, which neglected the electrical double layer. Theoretical values for the rotation speed are calculated and good agreement with experiments is found.

Alternating current electrokinetic properties of gold-coated microspheres

We present dielectrophoresis (DEP) and electrorotation (ROT) measurements of gold-coated polystyrene microspheres as a function of frequency and for several electrolyte conductivities. Particle rotation was counterfield with a maximum rotation rate observed at a single characteristic frequency. Negative DEP was observed for frequencies lower than this characteristic frequency and positive DEP for signal frequencies higher than this. These experimental observations are in agreement with predictions for the force and torque on the induced dipole of a perfectly polarizable metal sphere. We present a theoretical model for this case, and good agreement is found for both ROT and DEP measurements if we take into account the viscous friction for a spherical particle near a wall. From the characteristic frequency for rotation, we obtain the capacitance of the electrical double layer at the electrolyte-particle interface. Remarkably, no effect of induced charge electroosmosis around the particles can be inferred from DEP measurements.

Electrothermally driven flows in ac electrowetting

Mixing within sessile drops can be enhanced by generating internal flow patterns using ac electrowetting. While for low ac frequencies, the flow patterns have been attributed to oscillations of the drop surface, we provide here the driving mechanism of the hitherto unexplained high-frequency flows. We show that: (1) the electric field in the liquid bulk becomes important, leading to energy dissipation due to Joule heating and a temperature increase of several degrees Celsius, and (2) the fluid flow at these frequencies is generated by electrothermal effect, i.e., gradients in temperature give rise to gradients in conductivity and permittivity, the electric field acting on these inhomogeneities induces an electrical body force that generates the flow. We solved numerically the equations for the electric, temperature and flow fields. The temperature is obtained from a convection-diffusion equation where Joule heating is introduced as a source term. From the solution of the electric field and the temperature, we compute the electrical force that acts as a body force in Stokes equations. Our numerical results agree with previous experimental observations.

Effect of the combined action of Faradaic currents and mobility differences in ac electro-osmosis

In this work, we extend previous analyses of ac electro-osmosis to account for the combined action of two experimentally relevant effects: (i) Faradaic currents from electrochemical reactions at the electrodes and (ii) differences in ion mobilities of the electrolyte. In previous works, the ac electro-osmotic motion has been analyzed theoretically under the assumption that only forces in the diffuse (Debye) layer are relevant. Here, we first show that if the ion mobilities of a 1-1 aqueous solution are different, the charged zone expands from the Debye layer to include the diffusion layer. We later include the Faradaic currents and, as an attempt to explore both factors simultaneously, we perform a thin-layer, low-frequency, linear analysis of the system. Finally, the model is applied to the case of an electrolyte actuated by a traveling-wave signal. A steady liquid motion in opposite direction to the applied signal is predicted for some ranges of the parameters. This could serve as a partial explanation for the observed flow reversal in some experiments.

Flow reversal in traveling-wave electrokinetics: an analysis of forces due to ionic concentration gradients

Pumping of electrolytes using ac electric fields from arrays of microelectrodes is a subject of current research. The behavior of fluids at low signal amplitudes (<2-3 V(pp)) is in qualitative agreement with the prediction of the ac electroosmosis theory. At higher voltages, this theory cannot account for the experimental observations. In some cases, net pumping is generated in the direction opposite to that predicted by the theory (flow reversal). In this work, we use fluorescent dyes to study the effect of ionic concentration gradients generated by Faradaic currents. We also evaluate the influence of factors such as the channel height and microelectrode array shape in the pumping of electrolytes with traveling-wave potentials. Induced charge beyond the Debye length is postulated to be responsible for the forces generating the observed flows at higher voltages. Numerical calculations are performed in order to illustrate the mechanisms that might be responsible for generating the flow.

Traveling-wave electrokinetic micropumps: velocity, electrical current, and impedance measurements

An array of microelectrodes covered in an electrolyte and energized by a traveling-wave potential produces net movement of the fluid. Arrays of platinum microelectrodes of two different characteristic sizes have been studied. For both sizes of arrays, at low voltages (<2 V pp) the electrolyte flow is in qualitative agreement with the linear theory of ac electroosmosis. At voltages above a threshold, the direction of fluid flow is reversed. The electrical impedance of the electrode-electrolyte system was measured after the experiments, and changes in the electrical properties of the electrolyte were observed. Measurements of the electrical current during pumping of the electrolyte are also reported. Transient behaviors in both electrical current and fluid velocity were observed. The Faradaic currents probably generate conductivity gradients in the liquid bulk, which in turn give rise to electrical forces. These effects are discussed in relation to the fluid flow observations.

A linear analysis of the effect of Faradaic currents on traveling-wave electroosmosis

Net fluid flow of electrolytic solutions induced by a traveling-wave potential applied to an array of co-planar interdigitated microelectrodes has been reported. At low applied voltages the flow is driven in the direction of the traveling-wave potential, as expected by linear and weakly nonlinear theoretical studies. The flow is driven at the surfaces of the electrodes by electrical forces acting in the diffuse electrical double layer. The pumping mechanism has been analyzed theoretically under the assumption of perfectly polarizable electrodes. Here we extend these studies to include the effect of Faradaic currents on the electroosmotic slip velocity generated at the electrode/electrolyte interface. We integrate the electrokinetic equations under the thin-double-layer and low-potential approximations. Finally, we analyze the pumping of electrolyte induced by a traveling-wave signal applied to a microelectrode array using this linear model.

Electroviscous Effect of Moderately Concentrated Colloidal Suspensions: Stern-Layer Influence

A previous model for the viscosity of moderately concentrated suspensions has been extended. The influence of a dynamic Stern layer (DSL), which produces an additional surface conductance at the electrolyte-particle interface, is included. The theoretical treatment is based on Happel's cell model with Simha's boundary conditions for the interparticle hydrodynamic interactions and on a dynamic Stern-layer model for ionic conduction on the particle surface according to Mangelsdorf and White (ref 39). The results are valid for arbitrary zeta potentials and double-layer thickness. Extensive theoretical predictions are shown and interesting new behaviors are found. The comparison with the results in the absence of additional surface conductance shows a great influence of this mechanism in the energy dissipation during the laminar flow of these suspensions. We conclude that the inclusion of a dynamic Stern layer will be required to match the predictions with the experimental results.

Electroviscous Effect of Moderately Concentrated Colloidal Suspensions under Overlapping Conditions

In this work we present a theoretical model for the calculation of the electroviscous coefficient of a colloidal suspension. The treatment is not limited for dilute suspensions and includes the contribution of the overlapping between adjacent ionic layers. The development here used is based on a cell model, which is applicable to Newtonian suspensions under low shear conditions and without crystalline ordering. Also presented are a complete study of the new numerical results and comparisons with previous results. We find new behaviors for the case of moderate volume fractions that do not appear in the dilute limit.

Stern-layer parameters of alumina suspensions

The specific adsorption of Mg(+2) and S(2)O(-2)(8) ions onto the gamma-alumina particle surface has been demonstrated. An estimation algorithm based upon the correlation between electrophoretic mobility and conductivity increment experimental data, employing a dynamic Stern-layer theory, has been developed and used to get the adsorption parameters into the Stern layer for different gamma-alumina/Mg(+2) and S(2)O(-2)(8) aqueous solutions interface.

An experimental test of Booth's primary electroviscous effect theory

The primary electroviscous effect has been investigated in dilute suspensions of titanium oxide (anatase), the viscosities of which were measured by means of a capillary viscometer with automatic timing. The linear relation between viscosity and solids volume fraction was first determined at the isoelectric point of the particles when the particles are uncharged, and the electroviscous contribution to the intrinsic viscosity was then determined at other values of pH. Booth's theory (Proc. R. Soc. London Ser. A203, 533 (1950)) agrees well with the experimental results when the particle zeta potential is small and the double layer is thin (kappa alpha approximately 7.3), but agreement is poor when the double layer is thick (kappa alpha approximately 0.6).