Effect of Membrane Permeance and System Parameters on the Removal of Protein-Bound Uremic Toxins in Hemodialysis.

Inadequate clearance of protein-bound uremic toxins (PBUTs) during dialysis is associated with morbidities in chronic kidney disease patients. The development of high-permeance membranes made from materials such as graphene raises the question whether they could enable the design of dialyzers with improved PBUT clearance. Here, we develop device-level and multi-compartment (body) system-level models that account for PBUT-albumin binding (specifically indoxyl sulfate and p-cresyl sulfate) and diffusive and convective transport of toxins to investigate how the overall membrane permeance (or area) and system parameters including flow rates and ultrafiltration affect PBUT clearance in hemodialysis. Our simulation results indicate that, in contrast to urea clearance, PBUT clearance in current dialyzers is mass-transfer limited: Assuming that the membrane resistance is dominant, raising PBUT permeance from 3 × 10-6 to 10-5 m s-1 (or equivalently, 3.3 × increase in membrane area from ~ 2 to ~ 6 m2) increases PBUT removal by 48% (from 22 to 33%, i.e., ~ 0.15 to ~ 0.22 g per session), whereas increasing dialysate flow rates or adding adsorptive species have no substantial impact on PBUT removal unless permeance is above ~ 10-5 m s-1. Our results guide the future development of membranes, dialyzers, and operational parameters that could enhance PBUT clearance and improve patient outcomes.

Capillary Condensation in 8 nm Deep Channels.

Condensation on the nanoscale is essential to understand many natural and synthetic systems relevant to water, air, and energy. Despite its importance, the underlying physics of condensation initiation and propagation remain largely unknown at sub-10 nm, mainly due to the challenges of controlling and probing such small systems. Here we study the condensation of n-propane down to 8 nm confinement in a nanofluidic system, distinct from previous studies at ∼100 nm. The condensation initiates significantly earlier in the 8 nm channels, and it initiates from the entrance, in contrast to channels just 10 times larger. The condensate propagation is observed to be governed by two liquid-vapor interfaces with an interplay between film and bridging effects. We model the experimental results using classical theories and find good agreement, demonstrating that this 8 nm nonpolar fluid system can be treated as a continuum from a thermodynamic perspective, despite having only 10-20 molecular layers.

Condensation in One-Dimensional Dead-End Nanochannels.

Phase change at the nanoscale is at the heart of many biological and geological phenomena. The recent emergence and global implications of unconventional oil and gas production from nanoporous shale further necessitate a higher understanding of phase behavior at these scales. Here, we directly observe condensation and condensate growth of a light hydrocarbon (propane) in discrete sub-100 nm (∼70 nm) channels. Two different condensation mechanisms at this nanoscale are distinguished, continuous growth and discontinuous growth due to liquid bridging ahead of the meniscus, both leading to similar net growth rates. The growth rates agree well with those predicted by a suitably defined thermofluid resistance model. In contrast to phase change at larger scales (∼220 and ∼1000 nm cases), the rate of liquid condensate growth in channels of sub-100 nm size is found to be limited mainly by vapor flow resistance (∼70% of the total resistance here), with interface resistance making up the difference. The condensation-induced vapor flow is in the transitional flow regime (Knudsen flow accounting for up to 13% of total resistance here). Collectively, these results demonstrate that with confinement at sub-100 nm scales, such as is commonly found in porous shale and other applications, condensation conditions deviate from the microscale and larger bulk conditions chiefly due to vapor flow and interface resistances.

Expressions for the Evaporation and Condensation Coefficients in the Hertz-Knudsen Relation.

Although the Hertz-Knudsen (HK) relation is often used to correlate evaporation data, the relation contains two empirical parameters (the evaporation and condensation coefficients) that have inexplicably been found to span 3 orders of magnitude. Explicit expressions for these coefficients have yet to be determined. This review will examine sources of error in the HK relation that have led to the coefficients' scatter. Through an examination of theoretical, experimental, and molecular dynamics simulation studies of evaporation, this review will show that the HK relation is incomplete, since it is missing an important physical concept: the coupling between the vapor and liquid phases during evaporation. The review also examines a modified HK relation, obtained from the quantum-mechanically based statistical rate theory (SRT) expression for the evaporation flux and applying a limit to it in which the thermal energy is dominant. Explicit expressions for the evaporation and condensation coefficients are defined in this limit, with the surprising result that the coefficients are not bounded by unity. An examination is made with 127 reported evaporation experiments of water and of ethanol, leading to a new physical interpretation of the coefficients. The review concludes by showing how seemingly small simplifications, such as assuming thermal equilibrium across the liquid-vapor interface during evaporation, can lead to the erroneous predictions from the HK relation that have been reported in the literature.

Source of temperature and pressure pulsations during sessile droplet evaporation into multicomponent atmospheres.

During sessile droplet evaporation, studies with IR thermography and shadowgraphs have indicated temperature pulsations. We confirm those observations with microthermocouples, but microthermocouples also indicate temperature pulsations in the atmosphere of the droplet. The pressure in this atmosphere pulsated as well and was correlated with the temperature pulsations in the droplet. Also, we find that if a droplet evaporates into its own vapor, there are no temperature or pressure pulsations. The pulsations occur only if the droplet evaporates into an atmosphere with a component having a heat of solution with the droplet when it adsorbs-absorbs. None of the currently proposed mechanisms for the temperature pulsations provide an explanation for the coupling between the temperature pulsations in the droplet and the vapor-phase pressure pulsations, and for the absence of the pulsations when the system is single-component. As a mechanism for the pulsations, we propose that when a droplet is exposed to an atmosphere containing a component that has a heat of solution with the droplet, energy will be released from adsorption-absorption. This energy will cause pulsations in the evaporation flux, and these pulsations could cause the observed temperature and pressure pulsations. We examine this mechanism by showing that, if the measured temperature pulsations in a water droplet exposed to a methanol atmosphere are used as the input to a theory of evaporation kinetics (statistical rate theory), the pressure pulsations of the water vapor in the methanol atmosphere are predicted and agree with those measured with a quadrupole mass analyzer. When the inputs and outputs are reversed in the theory, we find that the temperature pulsations in the droplet are correctly predicted from the measured water vapor pulsations in the atmosphere.