Hsu's classical nucleation model has long served as the foundational framework for predicting the onset of nucleate boiling (ONB). While the model's core thermodynamic criterion remains valid, its extension beyond pool boiling - to flow boiling more generally - has produced inconsistent results. Previous studies have attempted to adapt Hsu's framework to flow boiling by introducing simplifying or empirically based assumptions about the heat transfer coefficient or boundary layer behavior, but these modifications have not yielded a predictive model. The underlying issue is that Hsu's assumption of a quasi-static thermal boundary layer does not hold in flow boiling, where flow inertia reshapes the near-wall thermal field. These limitations are further amplified in microchannels, where scale effects introduce additional complexity. To investigate these effects systematically, we conducted experiments using FC-72 in machined copper microchannels with hydraulic diameters of 200 & micro;m, 400 & micro;m, and 600 & micro;m. High-speed visualization was employed to capture the nucleation dynamics and identify ONB. The results show that both ONB and active nucleation site density (Na) are strongly influenced by wall superheat, subcooling, channel size, and flow inertia. Accordingly, we developed a mechanistically guided predictive expression for the ONB heat flux, q(y)ONB, incorporating key non-dimensional parameters - including the Boiling number (Bo), Reynolds number (Re), confinement number (Co), and subcooled Stanton number (Stsub). The formulation captures how these parameters determine q(y)ONB, consistent with the heattransfer and thermal-boundary-layer considerations underlying Hsu's criteria.

Understanding the hydrodynamics of liquid films formed during microchannel flow boiling is essential for developing high-fidelity models that inform the design of high-performance heat sinks. To probe these dynamics, we performed two-phase adiabatic flow experiments spanning multiple channel sizes, fluids, and mass fluxes, enabling isolation of thin-film behavior and interrogation of instability mechanisms from a fluid-mechanics perspective. The experiments revealed two primary wave behaviors: solitary and periodic waves. Solitary waves, characterized by high velocity and amplitude, are driven by shear forces resulting from the velocity difference between the two phases. In contrast, periodic waves are slower, low-amplitude waves associated with inertial forces within the thin liquid film. Both wave types were found to be influenced by surface tension. A new long-wave evolution model, extending a previous wave growth model to incorporate inertia, successfully predicted the onset of periodic waves across various wavelengths. Additionally, an energy transfer model linked the growth of inertial and shear instabilities to the observed wave behaviors. These models demonstrated that unstable films grow due to both inertial and shear instabilities. New predictive metrics were developed based on force balance. For periodic waves, these metrics include the Weber (We) and Bond (Bo) numbers, while the Richardson (Ri) and Bo numbers are used for solitary waves. The study offers valuable insights into the interplay between inertia, shear forces, and surface tension in two-phase microchannel flow, providing improved analytical tools for predicting wave behaviors in liquid films.

Ramy H. Mohammed, Rohit Bhagwat, Michael Schmid, Paul Glanville, and Saeed Moghaddam

In this study, the application of electrodialysis for ion recovery as an active transport mechanism is evaluated where a low flow rate of deionized water containing 100 mM NaCl concentration, close to that of total blood plasma concentration, enters an electrodialysis cell including two inert graphite electrodes to apply electric field across an anion exchange membrane (AEM) and a cation exchange membranes (CEM) to separate the ions. A mathematical model of the cell is provided using Extended Nernst-Plank (ENP) equation, the resistance of the cell components are measured by a Luggin-Capillary device, Electro Impedance Spectroscopy (EIS) is used to study the ED cell behavior, and chronoamperometry is used to measure the clearance performance for various combinations of membranes. Results indicate that the electrodialysis cell with a single stack of AEM-CEM, effective area of 4×4 cm2, and intermembrane spacing of 1 mm at voltage of 4 V and volumetric flow rate of 30 ml/h can recover 40% of the ions with high current efficiency over 97%. A modular design using alternating AEM and CEM membranes in series and parallel will be able to process the desired volume of solution and achieve the required ion recovery rate. This study provides insight into the use of electrodialysis in the artificial kidney applications where a miniaturized electrodialysis cell can reduce the device size significantly and allow for the emergence of a long-awaited wearable devices to replace dialysis.

Future data centers will employ large-area (greater than 25 mm x 25 mm), high-heat-flux (greater than 1 kW/cm2) central processing unit (CPU) and graphics processing unit (GPU) devices. Such devices, or chips, will necessitate aggressive cooling solutions, including two-phase cooling. In this work, we explore the potential of indium solder as a thermal interface material (TIM) for directly bonding cold plates to chips, providing a lowthermal-resistance pathway. By eliminating the need for multiple TIM layers, this approach enhances thermal efficiency while mitigating stresses by minimizing the coefficient of thermal expansion (CTE) and stiffness mismatch within the device stackup. We performed thermal-mechanical modeling of the device stack-up to analyze the temperature and stress maps. Our numerical results indicate that the highly viscoplastic and compliant nature of the indium solder TIM prevents excessive thermally induced built-in stress in the device after cooling postreflow. Furthermore, the numerical results clarify that the thickness of an additional copper-tungsten (CuW) layer, as a CTE alleviating component between the cold plate and device, can be minimized as its role is minor in preventing thermally induced stress, and in fact this layer increases package conductive thermal resistance. Thus, optimal thermal-mechanical performance for such large-area devices might be achieved through a minimal indium solder TIM thickness without such intermediary stress mitigation layers.

Microchannel flow boiling is becoming increasingly important in many applications, yet its modeling has remained a challenge due to a lack of mechanistic fluid flow models, particularly for thin liquid films. In a recent study, we determined the liquid film thickness and velocity in 300-mu m-wide microchannels and used the results to calculate the shear stress at the liquid-vapor interface. A graph of the shear stress versus the liquid film thickness delineated transition to wavy-annular flow regime. Here, we have extended our studies to different channel sizes and fluids, from low to high surface tension, using a combination of flow boiling and adiabatic test studies. The results show that the onset of films instability is a function of the shear stress at the liquid-vapor interface, consistent with the Kelvin-Helmholtz (K-H) instability. Various criteria for the onset of K-H instability are evaluated. The Richardson number (Ri) as an indicator of the onset of film instability is shown to decrease greatly for thin films in microchannels and is demonstrated to be dependent on surface tension such that Bond number, Bo/Ri for different fluids are relatively close. However, this criterion does not accurately predict the onset of instability of relatively thinner films. Further analysis suggests that Taitel and Dukler's (1976) criterion can accurately predict instability of adiabatic films. However, liquid films in boiling become unstable at a significantly lower interfacial shear stresses relative to Taitel and Dukler's prediction. Additional forces and perturbation mechanisms such as evaporative momentum effects, acoustics of nucleate boiling, and local temperature-induced surface tension variations could account for deviations relative to adiabatic films.

Efficient moisture removal from air without subcooling using liquid desiccants represents a major advancement in energy-efficient cooling, particularly through the separate sensible and latent cooling (SSLC) process. However, developing a high-performance, robust liquid desiccant dehumidification cycle remains challenging. Traditional open desiccant cycles rely on outdoor air to remove moisture from the desiccant solution in the regenerator, but this also extracts significant sensible heat, reducing overall efficiency. This study investigates a semi-open absorption cycle that eliminates the need for scavenging air, addressing a key inefficiency of conventional systems. An experimental system was tested under varying outdoor air conditions, demonstrating substantial performance improvements. The semi-open cycle significantly reduced sensible heat loss compared to traditional systems while maintaining strong moisture removal capabilities. Notably, it achieved a dehumidification coefficient of performance (COP) of up to 0.9, with peak latent cooling capacity observed at higher inlet air dew points. These findings underscore the semi-open cycle's potential for enhancing energy efficiency in dehumidification, particularly in regions with high latent loads.

Accurate identification of flow regime transitions is a foundational step toward developing high-fidelity predictive models for two-phase flow in microchannels. This study presents a comprehensive experimental investigation of the transition from bubbly to elongated bubbles flow regimes in machined metal microchannels. Recognizing that regime boundaries are governed by a combination of interfacial dynamics, vapor generation, and inertial transport, the objective of this work is to establish a generalized transition model applicable across various channel dimensions and working fluids. To contextualize the need for such a model, we conducted a critical evaluation of existing regime transition models and identified key gaps in their predictive capability. The influence of operating and geometric parameters - including heat flux, mass flux, channel size, and bubble coalescence dynamics - on flow regime transition was systematically examined. Key nondimensional parameters - Reynolds number (Re), Boiling number (Bo), Weber number (We), and Confinement number (Co) - were identified as governing variables. In addition, we introduce the Bubble Confinement Ratio (BCR = Db/Dh). This parameter exhibits a threshold beyond which the flow transitions from bubbly to elongated bubbles regime. A new empirical model was developed by correlating these parameters through a unified power-law expression, capable of predicting transition boundaries with accuracy across all tested conditions. These findings provide a foundation for a generalized transition framework that can be further refined through additional experiments and validations across a broader range of conditions.

Phosphonium-derived ionic liquids have emerged as a powerful class of thermoresponsive materials with sought after Lower Critical Solution Temperature (LCST) phase separation with applications across a broad range of fields. Herein, we report the spectroscopic examination of phosphonium salts bearing the general structure [X][P444n] wherein systematic structural variations were designed to gain a fundamental understanding behind the impact of alkyl chain length, anion size, and effective nuclear charge on their temperature-dependent phase separation behavior. Using variable temperature 1H, 31P, and 19F NMR, the bonding changes which drive LCST phase separation for the assembled thermoresponsive ILs were elucidated. For the first time, spectroscopic evidence revealed a delicate balance between the interdependence of alkyl chain length and anion size on phase separation that formed the basis of new LCST design principles.

This study introduces the scaled sigma potential of water (σr), a new metric using the COSMO-RS (Conductor like Screening Model for Real Solvents) framework, as a descriptor of upper and lower critical solution temperature (UCST and LCST) governed phase separation in aqueous ionic liquid (IL) solutions. The maximum and minimum values of σr correspond to the homogenous and phase separated states, at a given composition, for both UCST and LCST cases. Furthermore, the value of σr changes from positive to negative as the temperature increases in LCST exhibiting solutions, while as the temperature increases in UCST exhibiting solutions, the value of σr changes from negative to positive. Therefore, σr provides a less computationally intensive alternate to Gibbs free energy calculations and to the generation of phase diagrams for assessing UCST/LCST behavior in aqueous IL solutions.

Rising electronics power density has led to the adoption of immersion cooling as a thermal management strategy for next generation chips. However, immersion cooling is plagued by the critical heat flux (CHF) limit, which dictates the maximum heat transfer from a surface. Following its discovery in 1934 by Nukiyama, two explanations, namely the hydrodynamic instability theory introduced by Kutateladze in 1948 and established by Zuber in 1959, and the evaporation momentum theory conceptualized by Steinchen and Sefiane in 1996 and formalized by Kandlikar in 2001, have hitherto predicted a similar CHF limit (~ 100 W/cm 2 for water on a copper surface) despite hinging on contrasting physical phenomena. Here, we show through rigorous experimental and analytical investigation of boiling using liquids with diverse thermophysical properties and planar heater surfaces representing 44 unique experimental conditions, that the critical heat flux limit due to evaporation momentum (CHF EM ) is approximately four times higher than the hydrodynamic instability limit (CHF HI ) predicted by Zuber. Remarkably, this elevated CHF EM becomes manifest only when the hydrodynamics of liquid and vapor flow above the heater surface are fully stabilized. Our experiments demonstrate the existence of these two asymptotic limits governed by hydrodynamic and surface limitations, respectively, depending on hydrodynamic flow conditions above the heater surface such that the ratio CHF/CHF EM ranges from 0.2 to 1 across all examined fluids. Evaporation momentum theory encompasses the force balance on a bubble, which is evidenced in our experiments showing the presence of nucleating bubbles even as the surface heat flux approaches CHF. Further, a theoretical model is developed to predict CHF based on the single bubble assumption, and closely matches experimental data. Unlike previous assumptions, we find that the effect of gravity is negligible. This work could provide guidelines for development of surface topologies suitable for immersion cooling.

This study presents a facile method for assessing the effect of anion functional group substitution on the water affinity of phosphonium-acetate ionic liquids. By combining the same cation with three different α-substituted carboxylate anions, the effect of anion functional group substitution on the IL miscibility with water and hygroscopicity was experimentally evaluated and rationalized using COSMO-RS sigma profile analysis. Lower critical solution temperature (LCST) phase separation experiments and water vapor partial pressure measurements revealed that there is a stark α-substitution dependency on the affinity of water for acetate [AcO], pivalate [PivO], and trifluoroacetate [TFA] derived tributyl(octyl)phosphonium [P4448] ILs. It was found that the IL water affinities varied as: [P4448][AcO] > [P4448][PivO] > [P4448][TFA]. With the lowest water partial pressure and no LCST driven phase separation, [P4448][AcO] exhibited a high affinity for water. On the other hand, [P4448][PivO] and [P4448][TFA] exhibited LCST-driven phase separation and room temperature immiscibility, respectively, with higher water partial pressures, as a result of relatively weak water affinities. COSMO-RS sigma profile analysis revealed that the aliphatic carboxylate anions should incorporate apolar interactions commensurate with or greater than the polar hydrogen bond acceptor interactions for phase immiscibility of the corresponding IL with water. It was found that the relative magnitudes of apolar and polar interactions, assessed using the anion sigma profile peak intensity ratio (Ir), are directly correlated with the IL water affinity, and inversely correlated with the solution water activity coefficient. Therefore, it was concluded that Ir forms a quantitative link between the structural changes at the molecular level and the bulk water affinity exhibited by the ionic liquid as a whole.

The annular flow regime in microchannels is commonly described as the steady flow of a vapor core with a surrounding liquid film along the channel length. However, limited studies have suggested temporal disconti-nuity in the liquid film coverage of the microchannel wall. The lack of experimental tools to directly interrogate the liquid flow characteristics and the local surface heat flux has resulted in proliferation of different hypotheses concerning the physics of this process. Surface de-wetting due to high shear stresses at the vapor-liquid interface and liquid film instability and rupture due to perturbation growth at the vapor-liquid interface have been suggested as the underlaying causes of this phenomenon. In this study, a recently developed microsensor array capable of measuring the surface local heat flux and liquid film thickness and velocity is utilized to decipher thermohydraulic characteristics of the annular flow regime and intermittent dryout with unprecedented details. The studies are conducted in a 600 mu m square cross-section microchannel using FC-72 as the test fluid at 70-80% exit vapor quality. The results show that liquid film thinning because of evaporation rather than de-wetting and film rupture is responsible for intermittent surface dryout. Studies at different mass and heat fluxes suggest that for a given surface heat flux, there is a mass flux threshold above which intermittent surface dryout vanishes. Furthermore, the experimental liquid and vapor flow velocities and liquid film thickness are used to calculate the liquid-vapor interfacial shear stress. The results suggest that under the studied conditions, the liquid-vapor interfacial shear stress has little impact on the surface intermittent dryout. This study enhances predictable and reliable design and operation of two-phase heat sinks at high exit vapor qualities.

Microchannel heat exchangers play a critical role in development of more efficient and environmentally friendly energy systems. Thus, understanding the underlying physics that govern their heat transfer performance is of paramount importance. The most fundamental question is what is considered a microchannel, and what channel size, fluid properties, and flow conditions warrant use of a micro- versus macrochannel model. There have been extensive discussions in the literature regarding the appropriate definition of a microchannel; however, a clear, physics-based distinction of micro- from macrochannels has not emerged. This study analyzes this outstanding scientific question from the perspective of confinement effect on liquid films through investigating the effect of gravity on liquid films thickness. A set of experimental studies are conducted to determine the effect of gravitational force on liquid film asymmetry. The experimental findings are utilized to evaluate the existing criteria for transition from macro- to microchannels. Our analysis suggests that confinement numbers greater than 1.0 distinguish micro- from macrochannels in terms of liquid film symmetry. This analysis is supported by a force balance that shows gravitational force on liquid films exceeds the surface tension force in macrochannels.(c) 2022 Elsevier Ltd. All rights reserved.

This paper presents the latest progress on characterization of our membrane assisted phase-change heat sinks at conditions suitable for implementation in data centers. Experiments are conducted using water as the working fluid at a saturation pressure of 16 kPa, corresponding to a saturation temperature of-55 degrees C. This temperature is sufficiently lower than the silicon junction temperature of-80 degrees C. As anticipated, the overall performance of the membrane-assisted heat sink at sub-atmospheric pressure is lower compared to analogous tests at atmospheric pressure. In agreement with previous studies on membrane-assisted heat sinks, the critical heat flux limit in-creases with enhancement of the heat transfer area ratio and liquid space pressure. We report a maximum heat flux of 670 W/cm2 on a surface with enhanced area ratio of 3.45, multiple times greater than the heat fluxes reported hitherto by comparable two-phase heat sinks in literature. Heat transfer coefficients as high as 890 kW/ m2-K are obtained. We compare the thermal performance of this device with other existing technologies including conventional microchannel heat sinks, thermosyphons, cold plates, jet impingement, and analyze its system level benefits.

The upper limit of heat transfer from a heated surface to a surrounding boiling liquid has been the subject of numerous studies ever since Nukiyama (1934) discovered this limit. The underlying physics governing this phenomenon, universally known as the critical heat flux (CHF) limit, has been extensively debated for nearly a century. Two prevailing hypotheses have emerged including hydrodynamic instability and evaporation momentum force thresholds proposed by Kutateladze (1948) and Steinchen and Sefiane (1996), respectively. Zuber (1959) and Kandlikar (2001) developed correlations based on these hypotheses that predict roughly similar CHF values i.e., similar to 100 W/cm 2 for water at 1 atm on a copper surface. Here, we present experimental and analytical studies conducted on liquids with a wide range of thermophysical properties on planar heater surfaces of different size (to stabilize the flow hydrodynamics) that show the evaporation momentum limit (CHF EM ) is roughly 4 times the Zuber's limit (CHF Zuber ). We show that CHF EM can only be observed when hydrodynamics of liquid and vapor above the surface is stabilized, delineating an ultimate limit governed by a force balance at the surface-fluid interface rather than the instability of liquid and vapor interface away from the surface. We find that CHF/CHF EM varies from 0.2 to 1 for all fluids, saturation temperatures, and heater geometries tested, representing 48 conditions. (c) 2022 Elsevier Ltd. All rights reserved.

Advancing the knowledge of surfaces and protein interactions is paramount to development of non‐fouling membranes for many applications, particularly continuous blood flow wearable and implantable devices. Here, highly controlled experiments to understand the effect of graphene oxide (GO) surface properties on its protein adsorption are presented. A newly developed self‐assembly process is implemented to build a GO membrane with an atomically smooth surface to eliminate the effect of surface roughness on protein adsorption. The GO oxidation level is varied to change the overall membrane hydrophilicity while the nanoplatelets size and edge area is maintained constant. The fouling characteristics of the membrane are examined through scanning electron microscope imaging and long‐term water flux measurements. These measurements unambiguously prove that proteins are primarily adsorbed on the basal areas of nanoplatelets, on the graphitic regions, away from the nanoplatelets edges. As a result, while decreasing the oxidation level reduced the overall surface hydrophilicity leading to more protein adsorption, the membrane mass flux is minimally impacted. Studies on a polymer membrane under similar conditions show expansion of protein agglomerates over time leading to formation of large biofilm domains, while the GO nanoplatelets edges function as a barrier to formation of an expansive biofilm.

This paper intends to propose a new mathematical framework for distribution expansion planning (DEP) based on which the uncertainties associated with electric demand and wind production are modeled through several plausible ellipsoidal uncertainty sets. In this regard, a hybrid model combining stochastic programming and robust optimization is constructed. Data related to the demand-wind scenarios are first divided into clusters of similar elements using an existing clustering technique. Then, an ellipsoidal uncertainty set is created corresponding to each of these generated clusters based on the theory of minimum volume covering ellipsoid (MVCE) using the Khachiyan algorithm (KA). The hybrid robust/stochastic scheme is formulated as a two-stage tri-level min-max-min optimization problem in which the convex conic relaxation of AC power flow is used to represent the electric distribution network. The multi-uncertainty-set-based model is then solved by employing the classic column-and-constraint-generation (C&CG) technique which guarantees the convergence to the optimal solution in a limited number of iterations. In this regard, a master problem and several subproblems related to each scenario will be solved, both of which are second-order cone programs. Numerical simulations reveal the superiority of the hybrid model compared to the existing ones.