Hydraulic fracturing for production of oil and gas from shale formations releases fluid waste, by-products that must be managed carefully to avoid significant harm to human health and the environment. These fluids are presumed to result from a variety of fracture relaxation processes, and are commonly referred to as ‘flowback’ and ‘produced water’, depending primarily on the time scale of their appearance. Here, a model is presented for investigating the dynamics of backflows caused by the elastic relaxation of a pre-strained medium, namely a single fracture and two model fracture network systems: a single bifurcated channel and its generalization for $n$ bifurcated fracture generations. Early- and late-time asymptotic solutions are obtained for the model problems and agree well with numerical solutions. In the late-time period, the fracture apertures and backflow rates exhibit a time dependence of $t^{-1/3}$ and $t^{-4/3}$ , respectively. In addition, the pressure distributions collapse to universal curves when scaled by the maximum pressure in the system, which we calculate as a function of $n$ . The pressure gradient along the network is steepest near the outlet while the bulk of the network serves as a ‘reservoir’. Fracture networks with larger $n$ are less efficient at evicting fluids, manifested through a longer time required for a given fractional reduction of the initial volume. The developed framework may be useful for informing engineering design and environmental regulations.

Wet thermoacoustic engines (WTEs) are simple, robust energy conversion devices that employ a condensable vapor to generate acoustic power from heat. While previous studies focused on the potential of WTE technology to convert low-grade heat to power, this work focuses on the WTE's dependence on the working gas mixture, unique mass transport, and low working temperature properties, which make it a potential candidate for thermally driven separation processes, e.g., distillation and water desalination. In a set of experiments, the steady-state behavior of a water-based, standing-wave WTE was studied. The results highlight a remarkable trait of this system—a WTE is capable of producing a substantial flux of water vapor while exhibiting an operating hot-side temperature significantly lower than the boiling point. This “limiting temperature” is independent of the heat input to the system—theoretically predicted in systems that have no external “load” that consumes the acoustic power. In addition, the results suggest that the characteristics of the working gas play an important role in determining the device behavior. It was shown that in the tested range, a heavier, more complex-structured gas has significantly improved the steady-state performance of the engine. Specifically, a WTE working with SF6 as its working gas exhibited a vapor mass flux nearly three times greater than simple evaporation at the same heating power while maintaining a temperature as low as 57 °C. The link between gas characteristics and engine behavior is outlined. In conclusion, potential applications of the device and future research avenues are discussed.

Thermoacoustic instability – self-sustained pressure oscillations triggered by temperature gradients – has become an increasingly studied topic in the context of energy conversion. Generally, the process relies on conductive heat transfer between a solid and the fluid in which the generated pressure oscillations are sustained. In the present study, the thermoacoustic theory is extended to include mass transfer; specifically, the working fluid is modified so as to incorporate a ‘reactive’ gas, able to exchange phase with a solid/liquid boundary through a sorption process (or through evaporation/condensation), such that most heat is transferred in the form of latent heat rather than through conduction. A set of differential equations is derived, accounting for phase-exchange heat and mass transfer, and de-coupled via a small-amplitude asymptotic expansion. These equations are solved and subsequently manipulated into the form of a wave equation, representing the small perturbation on the pressure field, and used to derive expressions for the time-averaged, second-order heat and mass fluxes. A stability analysis is performed on the wave equation, from which the marginal stability curve is calculated in terms of the temperature difference, $\unicode[STIX]{x0394}T_{onset}$, required for initiation of self-sustained oscillations. Calculated stability curves are compared with published experimental results, showing good agreement. Effects of gas mixture composition are studied, indicating that a lower heat capacity of the inert component, combined with a low boiling temperature and high latent heat of the reactive component substantially lower $\unicode[STIX]{x0394}T_{onset}$. Furthermore, an increase in the average mole fraction of the reactive gas, $C_{m}$ strongly affects onset conditions, leading to $\unicode[STIX]{x0394}T_{onset}\sim 5\,^{\circ }\text{C}$ at the highest value of $C_{m}$ achievable under atmospheric pressure. An analysis of the system limit cycle is performed for a wide range of parameters, indicating a systematic decrease in the temperature difference capable of sustaining the limit cycle, as well as a significant distortion of the acoustic wave form as the phase-exchange mechanism becomes dominant. These findings, combined, reveal the underlying mechanisms by which a phase-exchange engine may produce more acoustic power than its counterpart ‘classical’ thermoacoustic system, while its temperature difference is substantially lower.

We develop a model for predicting the flow resulting from the relaxation of pre-strained, fluid-filled, elastic network structures. This model may be useful for understanding relaxation processes in various systems, e.g. deformable microfluidic systems or by-products from hydraulic fracturing operations. The analysis is aimed at elucidating features that may provide insight on the rate of fluid drainage from fracturing operations. The model structure is a bifurcating network made of fractures with uniform length and elastic modulus, which allows for general self-similar branching and variation in fracture length and rigidity between fractures along the flow path. A late-time $t<^>{-1/3}$ power law is attained and the physical behaviour can be classified into four distinct regimes that describe the late-time dynamics based on the location of the bulk of the fluid volume (which shifts away from the outlet as branching is increased) and pressure drop (which shifts away from the outlet as rigidity is increased upstream) along the network. We develop asymptotic solutions for each of the regimes, predicting the late-time flux and evolution of the pressure distribution. The effects of the various parameters on the outlet flux and the network's drainage efficiency are investigated and show that added branching and a decrease in rigidity upstream tend to increase drainage time.

Brackish water Reverse Osmosis (RO) and Nanofiltration (NF) are an attractive technology for potable water production and wastewater reclamation. However, scaling and fouling remain common problems that limit the optimal use of membranes, cause flux decline, increase energy demand and require periodic cleaning by chemical means. Herein, we consider the use of osmotic backwashing, already reported in the literature for seawater RO, as a cleaning method for brackish RO and NF. Three commercial membranes were used in a bench-scale system along with three draw solutions, NaCl, Na2SO4 and MgSO4, to assess the osmotic flux induced during a backwash cycle. The backwash flux was found to be in good agreement with calculations made using a computational model, which was then used to reveal the role of solution chemistry as well as membrane support properties in controlling the backwash intensity and duration. Specifically, sulphate-based solutions showed a good ability to maintain an osmotic flux, better than NaCl, for which lower membrane selectivity restricts use as a draw agent. While preliminary experiments demonstrated the ability of an osmotic backwash to remove CaPO4 scale, achieving nearly complete flux restoration for some cases, the process requires further optimization.

A nonzero time-averaged mass flux is generated in oscillating flows due to phase-lags between the fluctuating velocity field and the diffusive transport. Herein, we demonstrate how, in addition, the acoustic phasing of a sound wave-the phase difference between pressure and velocity oscillations-interacts with material properties and geometry to affect the preferential transport of a reactive species undergoing reversible sorption. Experimental results illustrate how phasing affects the induced mass flux, its dependence on the diffusive and oscillation time-scales, and how they compare well with model calculations. The model is used to reveal the underlying mechanisms that generate the concentration gradient, vs those that dissipate it. This insight can assist the future development and design of acoustic gas separation processes.

Membrane-based treatment of oily wastewater remains a significant challenge, particularly under high salinity conditions. The main difficulty associated with this separation process is membrane fouling, mostly caused by wetting and coalescence of emulsified oil droplets on the membrane surface. In this study, electrically conducting carbon nanotube-based ultrafiltration membranes were used to treat an emulsified oil suspension at ionic strengths as high as 100 mM. By tuning the electrical potential applied to the membrane surface, we demonstrate how fouling can be dramatically reduced, even under high salinity conditions. Permeate water quality is shown to improve upon application of a negative potential. Using optical microscopy, we observed dramatic changes in the shape of oil droplets at the membrane/water interface in response to the applied electric potential; this change is associated with a redistribution of charged surfactant molecules at the oil/water interface in response to the external electric field. Specifically, using the membrane as a cathode repels surfactant molecules away from the oil/membrane interface, while anodic conditions lead to increased surfactant concentrations. We speculate that this change in surfactant molecule distribution is responsible for changes in the surface tension of oil droplets at the membrane/water interface, which results in a decrease in oil coalescence and subsequent fouling. The membranes used in this study offer an attractive treatment option when separating emulsified oil from water under high salinity conditions.

Low-temperature heat is abundant, accessible through solar collectors or as waste heat from a large variety of sources. Thermoacoustic engines convert heat to acoustic work, and are simple, robust devices, potentially containing no moving parts. Currently, such devices generally require high temperatures to operate efficiently and with high power densities. Here, we present a thermoacoustic engine that converts heat to acoustic work at temperature gradients as low as similar to 4-5 K/cm, corresponding with a hot-side temperature of similar to 50 degrees C. The system is based on a typical standing-wave design, but the working cycle is modified to include mass transfer, via evaporation and condensation, from a solid surface to the gas mixture sustaining the acoustic field. This introduces a mode of isothermal heat transfer with the potential of providing increased efficiencies - experiments demonstrate a significant reduction in the operating temperature difference, which may be as low as 30 K, and increased output - this 'wet' system produces up to 8 times more power than its dry equivalent. Furthermore, a simplified model is formulated and corresponds quite well with experimental observations and offering insight into the underlying mechanism as well as projections for the potential performance of other mixtures. Our results illustrate the potential of such devices for harvesting energy from low-temperature heat sources. The acoustic power may be converted to electricity or, in a reverse cycle, produce cooling - providing a potential path towards solar heat-driven air conditioners.

Composite membranes used for water purification are formed by interfacial polymerization (IP), where choices of chemistry, formulation and reaction conditions conspire to dictate the final membrane performance. Here, we report in-situ visualization experiments of IP, performed using a microfluidic platform, under several representative conditions. Calibrated, temperature-sensitive fluorescence intensity enabled mapping of microscopic fluorescent images into temperature fields. Specifically, the temperature at the interface was monitored and illustrated a two-stage time-evolution, increasing rapidly at early times and then tapering. Polymerization appears to proceed so long as monomers are supplied, suggesting that the process may not be truly self-limiting. Results further show that under conditions promoting fast mass transfer and supply of monomers, temperatures at the interface may reach the boiling point of some solvents. Such interfacial boiling or release of dissolved gasses may be responsible for the formation of voids recently shown to exist in polyamide thin films. Curiously, the morphologies formed in the microfluidic experiments resemble commercial membranes despite the disparate length-scales involved, suggesting a possible spatial similitude. Ultimately, extensions beyond our current device, adding the capability to measure transport properties of the film formed within the device, can lead to a microfluidic-based platform to be used for rapid prototyping of materials, using small samples and short time scales, and provide insight for better informed membrane design.

Electrostatic conversion devices operate through periodic modulation of capacitance. Such devices have a wide range of configurations, involving either changes in permittivity, electrode-plate spacing or wetting area. The presented study examines, theoretically, a potential configuration of an electric-double-layer capacitor (EDLC)-based transducer, as it converts concentration and temperature oscillations into an electric alternating current. A constant voltage applied at the EDLC electrodes results in the formation of two opposite-sign EDLs, and an electric current is generated when ionic charges pass from one EDL to the other. In the examined configuration, this ionic charge transfer is induced by boundary modulation of temperature and/or concentration. To capture the oscillating dynamics of the ion distribution and ion flux, we solve the full set of Poisson-Nernst-Planck (PNP) equations coupled with the energy equation. We find that the transducer's optimal conditions for conversion, for which the device's frequency response is maximized, are governed by three main factors: low irreversible Joule heating, confined geometry, where the capacitor thickness is a close as possible to the EDL's characteristic screening length, and, most importantly, 'tuning' the system to a resonance frequency dictated by the interplay between geometry and characteristic time scales for mass and heat diffusion.

Oscillating flows can generate nonzero, time-averaged fluxes despite the velocity averaging zero over an oscillation cycle. Here, we report such a flux, a nonlinear resultant of the interaction between oscillating velocity and concentration fields. Specifically, we study a gas mixture sustaining a standing acoustic wave, where an adsorbent coats the solid boundary in contact with the gas mixture. It is found that the sound wave produces a significant, time-averaged preferential flux of a "reactive" component that undergoes a reversible sorption process. This effect is measured experimentally for an air-water vapor mixture. An approximate model is shown to be in good agreement with the experimental observations, and further reveals the interplay between the sound-wave characteristics and the properties of the gas-solid sorbate-sorbent pair. The preferential flux generated by this mechanism may have potential in separation processes.

Thermoacoustic phenomena, that is, onset of self-sustained oscillations or time-averaged fluxes in a sound wave, may be harnessed as efficient and robust heat transfer devices. Specifically, miniaturization of such devices holds great promise for cooling of electronics. At the required small dimensions, it is expected that non-negligible slip effects exist at the solid surface of the “stack”-a porous matrix, which is used for maintaining the correct temporal phasing of the heat transfer between the solid and oscillating gas. Here, we develop theoretical models for thermoacoustic engines and heat pumps that account for slip, within the standing-wave approximation. Stability curves for engines with both no-slip and slip boundary conditions were calculated; the slip boundary condition curve exhibits a lower temperature difference compared with the no slip curve for resonance frequencies that characterize micro-scale devices. Maximum achievable temperature differences across the stack of a heat pump were also calculated. For this case, slip conditions are detrimental and such a heat pump would maintain a lower temperature difference compared to larger devices, where slip effects are negligible.

Cracks filled with fluid propagation when the pressurized fluid is injected into the crack. Subsequently, when the fluid inlet is exposed to a lower pressure, the fluid flows backwards (backflow) and the crack closes due to the elastic relaxation of the solid. Here we study the dynamics of the crack closure during the backflow. We find that the crack radius remains constant and the fluid volume in the crack decreases with time in a power-law manner at late times. The balance between the viscous stresses in the fluid and elastic stresses in the fluid and the elastic stresses in the solid yields a scaling law that agrees with the experimental results for different fluid viscosities, Young's moduli of the solid, and initial radii of the cracks. Furthermore, we visualize the time-dependent crack shapes, and the convergence to a universal dimensionless shape demonstrates the self-similarity of the crack shapes during the backflow process.

The mechanistic aspects of membrane fouling have been studied extensively using direct observation, but limited to early stages of particulate deposition. Herein, we describe a versatile method extending direct observation to organic fouling, facilitating real-time monitoring of fouling formation and detachment. A transparent gel-like fouling layer is visualized using epi-fluorescent microscopy with the aid of labeled marker beads, trapped at various distances from the membrane, enabling monitoring of variations within the deposit. Fouling and cleaning experiments were conducted, examining alginate deposition and detachment, and illustrating the utility of the proposed method for studying the kinetics of fouling processes.

The potential presence of voids in the fully-aromatic polyamide active layers of thin-film composite (TFC) membranes for water purification was studied in a selection of commercial membranes with a broad range of performance levels. The membranes were characterized for their potential void fractions using three independent methods: (i) analysis of transmission electron microscopy (TEM) images of membrane cross-sections, (ii) water uptake measurements by quartz crystal microbalance (QCM), and (iii) estimates of the effective refractive indices of active layers by spectroscopic ellipsometry. Results revealed that voids having tens of nanometers in diameter exist in the fully-aromatic polyamide active layers of TFC membranes, the voids fill up with water when immersed in it, and the voids account for a significant volume fraction of the active layers (i.e., 15–32% for the membranes studied). It was concluded that the voids in polyamide active layers do not form passageways connecting the feed and permeate sides, but rather are cavities disconnected from the feed side. In addition, it was also concluded that the globular features observable in TEM images of membrane cross sections that had been previously identified as voids or nodules are indeed voids, and not nodules. The finding that a significant volume fraction of fully-aromatic polyamide active layers corresponds to water-filled voids has deep implications on various aspects of TFC membrane science and technology. For example, we illustrate how the presence of voids can potentially increase the effective water permeability of the active layer by as much as a factor of ≈5 compared with the case of an equivalent active layer without any voids. The methods developed in this study to measure void volume fraction represent useful tools for future membrane characterization studies, and the void fractions measured can be used as input or calibration parameters in future modeling studies of active layer formation or water and solute transport.

A novel process is proposed for the pre-concentration of sugar-derived biofuels from an aqueous fermentation broth, using Engineered Osmosis, an emerging membrane technology. While in itself an interesting candidate for such applications, the outlined scheme is unique in that it utilizes an energy source inherent to such systems, namely the osmotic potential which exists between the stock solution (glucose) and the dilute fermentation product.