Filling of charged cylindrical capillaries

Spontaneous Imbibition of Capillaries under the End Effect and Wetting Hysteresis

The phenomenon of spontaneous imbibition is widely present in the development process of tight oil/gas reservoirs. To further explore the spontaneous imbibition behavior of capillary tubes to provide theoretical and methodological references for the study of microscopic porous media imbibition phenomena, the capillaries that can be observed with the naked eye on the order of 10-100 μm were selected as research objects. Based on the theory of interface chemistry, the capillary end effect, and wetting hysteresis, the influence of the additional pressures generated by the two-phase interface on the spontaneous absorption of the horizontal capillary was studied. Some of the capillaries were processed for wettability, and then the water wettability of different capillaries was measured by the introduced concept, which is the conversion height of the self-absorption phase in the capillary. The capillaries were horizontally placed in the liquid for a spontaneous imbibition experiment, and the air-liquid two-phase menisci behavior was observed at the same time, and then the influence of water wettability, surfactant, and capillary diameter on spontaneous imbibition was discussed. It was found that in the equal diameter capillaries, the spontaneous air-liquid imbibition behavior of capillary tubes with different water wetting properties is different in sensitivity to surfactants and tube diameters; when surfactants are used to improve capillary water wettability to increase spontaneous imbibition efficiency, the initial water wettability of the capillary and the comprehensive changes in the capillary pressure caused by interfacial tension should be considered.

Electrokinetics of polymeric fluids in narrow rectangular confinements

The flow of polymeric liquids in narrow confinements with a rectangular cross section, in the presence of electrical double layers is analyzed here. Our analysis is motivated by the fact that many of the previous studies on the flow of complex fluids tend to focus on highly idealized parallel plate channels, which are markedly different from the rectangular ducts, used in many experiments and devices. We consider the combined electroosmotic and pressure driven flows as well as the streaming potential resulting from a mechanically driven flow. We use two distinct constitutive relations to model the polymeric liquids, namely the simplified exponential Phan-Thien-Tanner (sePTT) model and the Giesekus model, both of which are non-linear viscoelastic models, capable of capturing the shear thinning behavior. We establish that the applied electric field may have a strong influence on the overall flow rate, which rapidly increases with the field strength as well as the extent of viscoelasticity of the fluid. Viscoelasticity and shear thinning behavior also enhance the streaming potential by several fold as compared to a Newtonian medium. We demonstrate that the aspect ratio of a channel has a bigger influence on the net throughput and the streaming potential, when the extent of viscoelasticity is relatively large. We illustrate that for sePTT fluids, the flow is strictly unidirectional, while for Giesekus fluids, secondary flows are inevitably present on account of their non-zero second normal stress coefficient. Although the electric field does not change the overall patterns of these secondary flows, their magnitude does depend on the imposed field strength for combined flows.

Space Electroosmotic Thrusters in Ion Partitioning Soft Nanochannels

Space electroosmotic thrusters (EOTs) are theoretically investigated in a soft charged nanochannel with a dense polyelectrolyte layer (PEL), which is considered to be more realistic than a low-density PEL. When the PEL is dense, its permittivity is smaller than the one of the electrolyte solution layer, leading to rearrangement of ions in the channel, which is denoted as the ion partitioning effect. It is noted that fluid viscosity becomes high within the PEL owing to the hydration effect. An analytical solution for electroosmotic velocity through the channel is obtained by utilizing the Debye-Hückel linearization assumption. Based on the fluid motion, thruster performances, including thrust, specific impulse, thrust-to-power ratio, and efficiency, are calculated. The ion partitioning effect leads to enhancement of the thruster velocity, while increase of the dynamic viscosity inside the PEL reduces the flow rate of the fluid. Therefore, these performances are further impacted by the dense soft material, which are discussed in detail. Moreover, changes or improvements of the thruster performances from the dense PEL to the weak PEL are presented and compared, and distributions of various energy items are also provided in this study. There is a good result whereby the increase in electric double layer thickness promotes the development of thruster performances. Ultimately, the simulated EOTs produce thrust of about 0 to 20 μN and achieve thruster efficiency of 90.40%, while maintaining an appropriate thrust-power ratio of about 1.53 mN/W by optimizing all design parameters.

Microfluidic Behavior of Alumina Nanotube-Based Pathways within Hydrophobic CNT Barriers

The use of porous micro-and nanostructured materials within microfluidic devices results in unique fluid transport characteristics. In this paper, we investigate the microfluidic behavior of hybrid alumina nanotube-based pathways within the hydrophobic carbon nanotube (CNT) barriers. These hybrid systems provide unique benefits for potential liquid transport control in porous structures with real-time sensing of fluids. In particular, we examine how the alignment of the alumina nanostructures with high internal porosity enables increased capillary action and sensitivity of detection. Based on the Lucas and Washburn model (LW) and the modified LW models, the microfluidic behavior of these systems is detailed. The time exponent prediction from the models for capillary transport in porous media is determined to be ≤0.5. The experimental results demonstrate that the average capillary rise in the nanostructured media driven by a capillary force follows t^0.7. The hydrophilic/electrically insulating and hydrophobic/electrically conductive patterned structures of the device are used for electronic measurements within the microfluidic channels. The device structure enables the detection of fluid samples of very low analyte concentrations (1 μM) that can be achieved due to the very high surface area of the hybrid structure combined with the electrical conductivity of the CNT support structure.

Specific ion effects on electrocapillarity in aqueous electrolytes confined within nanochannels

A nanoslit is a long, extremely narrow (nanometers apart) opening between two parallel plates. An overlapped electric double layer is formed when an electrolyte is present inside the slit and there exist distributions of the osmotic pressure and the Maxwell stress across the nanoslit, which lead to the electrocapillarity effect. This feature can be incorporated with the specific ion effects by considering the nonelectrostatic interactions between ions and confining walls, as they significantly influence the potential, electric field, and ion distributions across the nanoslit. In the present work, the electromechanical approach is integrated with the concept of specific ion effects to analyze the behavior of an electrolyte confined in a one-dimensional nanochannel. For a nanochannel, the average outward normal stress exerted on the cross section of a channel (P_{zz}[over ¯]) can be regarded as a measure of electrocapillarity and it is the driving force of the flow. This electrocapillarity measure is analyzed by using the solution of the modified Poisson-Boltzmann equation as a function of the bulk concentration of the electrolyte, the boundary potential, and most importantly, the ion-specific interfacial interactions. The significance of the present work can be manifested by the increasing usage of extremely narrow channels in nanoscaled systems, which will require proper consideration of specific ion effects in determining the behavior of the confined electrolyte.

Efficient electrochemomechanical energy conversion in nanochannels grafted with end-charged polyelectrolyte brushes at medium and high salt concentration

We develop a theory to study the generation of the streaming potential and the resulting electrochemomechanical energy conversion (ECMEC) in the presence of pressure-driven transport in nanochannels grafted with end-charged polyelectrolyte (PE) brushes. Our theory gives a thermodynamically self-consistent coupled description of the PE-brush and the electrostatics of the electric double layer (EDL) induced by the PE charges. The end-charged brushes localize the maximum EDL charge density away from the wall, thereby enabling a larger magnitude of pressure-driven transport to stream the ions downstream. This effect is retarded by the drag force imparted by the brushes as well as by the enhanced electroosmotic transport in a direction opposite to the pressure-driven transport. An interplay of these three issues leads to highly non-trivial electrohydrodynamic transport that eventually allows us to converge on appropriate properties of the brushes (e.g., grafting density and the number of monomers) that lead to the generation of a significantly larger streaming potential and a much improved efficiency of the ECMEC as compared to the brush-free nanochannels particularly at medium and high salt concentrations.

Hydroelectric power plant on a paper strip

We exploit the combinatorial advantage of electrokinetics and tortuosity of a cellulose-based paper network on laboratory grade filter paper for the development of a simple, inexpensive, yet extremely robust (shows constant performance for 12 days) 'paper-and-pencil'-based device for energy harvesting applications. We successfully achieve harvesting of a maximum output power of ∼640 pW in a single channel, while the same is significantly improved (by ∼100 times) with the use of a multichannel microfluidic array (maximum of up to 20 channels). Furthermore, we also provide theoretical insights into the observed phenomenon and show that the experimentally predicted trends agree well with our theoretical calculations. Thus, we envisage that such ultra-low cost devices may turn out to be extremely useful in energizing analytical microdevices in resource limited settings, for instance, in extreme point of care diagnostic applications.

Theory of diffusioosmosis in a charged nanochannel

We probe the diffusioosmotic transport in a charged nanofluidic channel in the presence of an applied tangential salt concentration gradient. Ionic salt gradient driven diffusioosmosis or ionic diffusioosmosis (IDO) is characterized by the generation of an induced tangential electric field and a diffusioosmotic velocity (DOSV) that is a combination of an electroosmotic velocity (EOSV) triggered by this electric field and a chemiosmotic velocity (COSV) triggered by an induced tangential pressure gradient. We explain that unlike the existing theories on IDO, it is more appropriate to apply the zero net current conditions (formulation F2) and not more restrictive zero net local flux conditions (formulation F1) particularly for the case where one considers a nanochannel connected to two reservoirs. We pinpoint limitations in the existing literature in correctly predicting the diffusioosmotic behavior even for the case where formulation F1 is used. We address these limitations and establish that (a) the induced electric field is an interplay of the differences in ionic diffusivity, the EDL-induced imbalance in ion concentrations, and the advection effects, (b) formulation F1 may overpredict or underpredict the electric field and the EOSV leading to an overprediction/underprediction of the DOSV and (c) formulation F2 demonstrates remarkable fluid physics of localized backflows owing to a dominant local influence of the COSV, which is missed by formulation F1. We anticipate that our theory will provide the first rigorous understanding of nanofluidic IDO with applications in multiple areas of low Reynolds number transport such as biofluidics, microfluidic separation, and colloidal transport.

Geometric effects on electrocapillarity in nanochannels with an overlapped electric double layer

Unsteady filling of electrolyte solution inside a nanochannel by the electrocapillarity effect is studied. The filling rate is predicted as a function of the bulk concentration of the electrolyte, the surface potential (or surface charge density), and the cross sectional shape of the channel. For a nanochannel, the average outward normal stress exerted on the cross section of a channel (P[over ¯]_{zz}^{}) can be regarded as a measure of electrocapillarity and it is the driving force of the flow. This electrocapillarity measure is first analyzed by using the solution of the Poisson-Boltzmann equation. From the analysis, it is found that the results for many different cross sectional shapes can be unified with good accuracy if the hydraulic radius is adopted as the characteristic length scale of the problem. Especially in the case of constant surface potential, for both limits of κh→0 and κh→∞, it can be shown theoretically that the electrocapillarity is independent of the cross sectional shape if the hydraulic radius is the same. In order to analyze the geometric effects more systematically, we consider the regular N-polygons with the same hydraulic radius and the rectangles of different aspect ratios. Washburn's approach is then adopted to predict the filling rate of electrolyte solution inside a nanochannel. It is found that the average filling velocity decreases as N increases in the case of regular N-polygons with the same hydraulic radius. This is because the regular N-polygons of the same hydraulic radius share the same inscribing circle.

Rapid capillary filling via ion-water interactions over the nanoscale

Giant frictional resistances are grand challenges against the rapid filling of nanoscale capillaries, as encountered in a wide variety of applications ranging from nature to energy. It is commonly believed that partially wettable charged nanocapillaries fill up considerably slower, compared to completely wettable ones, under the influence of a complex interplay between interfacial tension and electrical interactions. In sharp contrast to this common belief, here we discover a new non-intuitive regime of rapid filling of charged capillaries over the nanometer scale, by virtue of which a partially wettable capillary may fill up comparatively faster than a completely wettable one. We attribute the fundamental origin of this remarkable behavior to ion-water interactions over interfacial scales. The underlying novel electro-hydrodynamic mechanism, as unveiled here, may provide deeper insights into the physico-chemical interactions leading to augmentations in the rates of nanocapillary filling over hydrophobic regimes, bearing far-reaching implications in the transport of biological fluids, enhanced oil recovery, and miniaturized energy harvesting applications.

Streaming potential-modulated capillary filling dynamics of immiscible fluids

The pressure driven transport of two immiscible electrolytes in a narrow channel with prescribed surface potential (zeta potential) is considered under the influence of a flow-induced electric field. The latter consideration is non-trivially and fundamentally different from the problem of electric field-driven motion (electroosmosis) of two immiscible electrolytes in a channel in a sense that in the former case, the genesis of the induced electric field, termed as streaming potential, is the advection of ions in the absence of any external electric field. As the flow occurs, one fluid displaces the other. Consequently, in cases where the conductivities of the two fluids differ, imbibition dynamically alters the net conductivity of the channel. We emphasize, through numerical simulations, that the alteration in the net conductivity has a significant impact on the contact line dynamics and the concomitant induced streaming potential. The results presented herein are expected to shed light on multiphase electrokinetics devices.

Electro-capillary effects in capillary filling dynamics of electrorheological fluids

The flow of electrorheological fluids is characterized by an apparent increase in viscosity manifested by the yield stress property of the fluid, which is a function of the applied electric field and the concentration of the suspended solute phase within the dielectric medium. This property of electrorheological fluids generally hinders flow through a capillary if the imposed shear stress is lower than the induced yield stress. This results in a plug-like zone in the flow profile, thus giving the fluid Bingham plastic properties. In the present work, we study such influences of the yield stress on the capillary filling dynamics of an electrorheological fluid by employing a rheologically consistent reduced order formalism. One important feature of the theoretical formalism is its ability to address the intricate interplay between the surface tension and viscous forces, both of which depend sensitively on the electric field. Our analysis reveals that the progress of the capillary front is hindered at an intermediate temporal regime, which is attributable to the increase of the span of the plug-zone across the channel width with time. With a preliminary understanding on the cessation of the capillary front advancement due to the yield stress property of the electrorheological fluids, we further strive to achieve a basic comparison with an experimental study made earlier. Reasonable agreements with the reported data support our theoretical framework. Comprehensive scaling analysis brings further insight to our reported observations over various temporal regimes.

Combined electroosmotically and pressure driven flow in soft nanofluidics

The present study is devoted to the analysis of mixed electroosmotic and pressure driven flows through a soft charged nanochannel considering boundary slip and constant charge density on the walls of the slit channel. The sources of the fluid flow are the pressure gradient along the channel axis and the electrokinetic effects that trigger an electroosmotic flow under the influence of a uniformly applied electric field. The polyelectrolyte layer (PEL) is denoted as a fixed charge layer (FCL) and the electrolyte ions can be present both inside and outside the PEL i.e., the PEL-electrolyte interface acts as a semi-penetrable membrane. The Poisson-Boltzmann equation is solved assuming the Debye-Hückel linearization for the low electric potential to provide us with analytical closed form solutions for the conservation equations. The conservation equations are solved to obtain the electric potential and velocity distributions in terms of governing dimensionless parameters. The results for the dimensionless electric potential, the dimensionless velocity and Poiseuille number are presented graphically and discussed in detail.