In this paper we provide analytical solutions for the streaming potential and electroviscous effects in soft nanochannels. The analysis is based on the solution of the linearized Poisson-Boltzmann equation, valid for small electrostatic potentials. We identify the important dimensionless parameters that dictate these two effects. Results are provided for a large range of electric double layer (EDL) thickness values, spanning from the case of very thin to very large overlapped EDL thicknesses. We compare the results with those of a rigid nanochannel, having zeta potential equal to the electrostatic potential at the solid-polyelectrolyte interface of the soft nanochannels. For the soft nanochannel, the streaming potential varies very weakly with the EDL thickness and can be substantially larger than that corresponding to the rigid nanochannel. The electroviscous effects for the soft nanochannel, unlike the rigid nanochannel, virtually always exhibit a monotonic decrease with the EDL thickness, and for certain parameter ranges can be several times larger than that for a rigid nanochannel. Most importantly, for the soft nanochannels the electrochemomechanical energy conversion, associated with the generation of streaming potential, is found to be highly efficient, with the efficiency being several times higher than that of a rigid nanochannel.
We provide a theory to analyze the impact of finite ion sizes (or steric effect) in electrostatic potential distribution for a charged soft surface in contact with an electrolyte solution. The theory is based on a free energy model that appropriately accounts for the contribution of finite ion sizes as well as the structural characteristics of a soft interface, represented by a combination of a rigid surface and a fixed charge layer (FCL), with the FCL being in contact with an electrolyte solution forming an electric double layer (EDL). This FCL contains a particular kind of ion which is impermeable to the electrolyte solution, and this impermeability is quantified in terms of the corresponding Donnan potential of the "membrane" represented by the FCL-electrolyte interface. We find that consideration of the finite ion size increases the magnitude of this Donnan potential, with the extent of increase being dictated by three length scales, namely, the thickness of the FCL, the thickness of the electrolyte EDL, and the thickness of an equivalent EDL within the FCL. Such regulation of the Donnan potential strongly affects the distribution of the permeable electrolyte ions within the FCL, which in turn will have significant implications in several processes involving "soft" biological membranes.
In electrolyte solutions, charged nanoscale pores or channels with overlapping electrical double layers are charge selective, thereby benefiting a wide range of applications such as desalination, bio-sensing, membrane technology, and renewable energy. As an important forcing mechanism, a gradient of electrolyte concentration along a charged nano-confinement can drive flow without an external electrical field or applied pressure difference. In this paper, we numerically investigate such a diffusioosmotic nanoflow, particularly for dilute electrolyte concentrations (0.01 mM–1 mM), and calculate the corresponding electrical and concentration fields in a charged nanochannel connecting two reservoirs of different salt concentrations—a typical fluidic configuration for a variety of experimental applications. Under a wide range of parameters, the simulation results show that the flow speed inside the nanochannel is linearly dependent on the concentration difference between the two reservoir solutions, Δc, whereas the flow direction is primarily influenced by three key parameters: nanochannel length (l), height (h), and surface charge density (σ). Through a comparison of the chemiosmotic (due to ion-concentration difference) and electroosmotic (as a result of the induced electric field) components of this diffusioosmotic flow, a non-dimensional number (C=h/lλGC) has been identified to delineate different nanoscale flow directions in the charged nanochannel, where λGC is a characteristic (so-called Gouy–Chapman) length associated with surface charge and inversely proportional to σ. This critical dimensionless parameter, dependent on the above three key nanochannel parameters, can help in providing a feasible strategy for flow control in a charged nanochannel.
We provide an analytical model to describe the filling dynamics of horizontal cylindrical capillaries having charged walls. The presence of surface charge leads to two distinct effects: It leads to a retarding electrical force on the liquid column and also causes a reduced viscous drag force because of decreased velocity gradients at the wall. Both these effects essentially stem from the spontaneous formation of an electric double layer (EDL) and the resulting streaming potential caused by the net capillary-flow-driven advection of ionic species within the EDL. Our results demonstrate that filling of charged capillaries also exhibits the well-known linear and Washburn regimes witnessed for uncharged capillaries, although the filling rate is always lower than that of the uncharged capillary. We attribute this to a competitive success of the lowering of the driving forces (because of electroviscous effects), in comparison to the effect of weaker drag forces. We further reveal that the time at which the transition between the linear and the Washburn regime occurs may become significantly altered with the introduction of surface charges, thereby altering the resultant capillary dynamics in a rather intricate manner.
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