Branch Level Research Articles

A new fractal permeability model for the dual-porous medium with a bundle of rough tree-like fracture networks

Shale gas reservoirs are typical dual-porous media where complex pore structures and fracture networks significantly impact gas transport. However, accurately predicting permeability in such media, especially complex fracture networks, remains challenging. The complex fracture network is modeled as of a bundle of rough tree-like fracture networks. The proposed permeability model comprehensively describes the structural characteristics of pores and fractures in shale gas reservoirs, including the fractal distribution of pore diameters and fracture apertures, the rough surface, and branching characteristics of fracture networks. Then, the model's accuracy is validated using reliable experimental permeability data. This model accurately predicts gas permeability and effectively describes gas transport characteristics in shale gas reservoirs with rough tree-like fracture networks. Each parameter has a clear physical meaning and avoids the use of empirical constants. Finally, sensitivity analyses are conducted to explore the effects of structural parameters on the permeability of dual-porous media. The results show that the permeability K of dual-porous media decreases exponentially with the increase in tortuosity fractal dimension Dtp of pores and surface fractal dimension Df of fractures, while it increases as a power function with increasing pore diameter fractal dimension Dp and fracture aperture fractal dimension Dh. The structural parameters of rough tree-like fracture networks significantly impact the permeability of dual-porous media. Increasing the aperture ratio γ, reducing the length ratio β, branching levels m, and the branching angles θ can significantly reduce gas flow resistance, decrease fluid kinetic energy loss, and increase the permeability of dual-porous media. This theoretical model is significant for enhancing permeability models of dual-porous media in shale gas reservoirs, offering reliable theoretical support for understanding gas migration and optimizing shale gas extraction.

Thermal Performance Enhancement of Ice Storage Capsule by Dandelion-Shaped Fins

Limited thermal conductivity of water hinders the performance of ice storage systems. This study proposes a novel approach to enhance ice storage performance using nature-inspired, dandelion-shaped fins with multi-level branches within spherical capsules. We aim to optimize the fin configuration to maximize the cooling energy storage capacity. Based on the enthalpy-porosity method, the solidification of water inside spherical ice storage capsules is investigated numerically. Compared to finless capsules, dandelion-shaped fins significantly improve heat transfer. Fins with two levels of branches outperform other fin types that averagely 34.64% increment in dimensionless cooling energy storage capacity per unit time is achieved with less than 6% loss in dimensionless cooling energy storage capacity per unit weight. Notably, a higher fractal dimension of length further enhances the performance of fins. Aluminum is identified as the optimal fin material due to its efficiency and cost-effectiveness. Finally, a normalized equation is proposed to predict the ice volume fraction under different cooling temperatures.

Tax illegality in the context of criminal and penal fiscalliability

Illegality is one of the conditions for a crime. This condition is the most important level of connections betweencriminal law and other branches of law. These relationships are weaker in terms of mala in se, which violates thebasic principles of interpersonal relations, while they are stronger in terms of mala prohibita, which violates detailednormative regulations. As a rule, this group includes tax crime, regardless of whether fiscal penal law orcommon criminal law is applied (the latter concerns VAT fraud and invoice forgery). In both cases, the basis forcriminal liability is a violation of tax law regulations (tax illegality). As a rule, tax law eludes the intuitive understandingof illegality (denial of legality). The main part of tax law provisions regarding the construction of taxesand the assessment of tax liability does not contain typical prohibitions or orders, but regulates the effects ofprivate law transactions, and the source of tax illegality will be the difference in views on the interpretation of theprovision between the taxpayer and the tax authority or administrative court. To the extent that the tax authoritydoes not issue a decision determining the tax liability (tax arrears), there is a presumption of the correctness ofthe tax declaration, which calls into question the authority of the criminal court to adjudicate a tax offense (to theextent that the statutory features of a prohibited act include incorrect declaration of tax).

Rheological analysis of network structure of raw natural rubber prepared by different processing techniques

The performance of raw natural rubber (NR) is dominated by its network structure, particular the levels of long chain branching (LCB) and entanglement. Here, three type of raw rubbers were prepared using different processing methods for commercial grade NRs. Linear and nonlinear viscoelastic behaviors, as well as stress relaxation, were analyzed to access their network structures. The third relative harmonic, phase angle, and first to second quarter-period integral ratio of stress curve were utilized as indicators for the nonlinearity of samples. By combining these values with flow activation energy and characteristic times, it can be confirmed that naturally coagulated NR showed higher elasticity than acid-coagulated NR due to high levels of LCB and entanglement, and hot air drying could lead to chain degradation. These findings correlated with molecular weight parameters, gel content and Mooney viscosity results. This research establishes a method for monitoring raw NR quality and predicting its properties.

Role of pulse globulins and albumins in air-water interface and foam stabilization

Pulse protein isolates are promising substitutes for animal protein in foam preparation, but they typically are complex mixtures of multiple proteins, and the contribution of the individual proteins to the behavior of the mixture in air-water interface stabilization is largely unknown. The major protein fractions in isolates are the globulins and albumins, and this study systematically investigated the molecular properties, and interfacial and foaming properties of these two fractions for three different pulses: lentils, faba beans and chickpeas. The key parameters of these pulse proteins in air-water interface and foam stabilization were investigated by correlation analysis. Based on this, low denaturation enthalpy tends to result in both high foamability and foam stability, most likely due to a greater conformational flexibility that allows for a faster adsorption to the air-water interface, and higher degree of structural rearrangement at the interface, which increases interfacial network stiffness. For globulin-rich pulse protein fractions, vicilins and convicilins tend to introduce high surface hydrophobicity, which increases the affinity of the proteins for the interface, and increases protein-protein in-plane interactions through hydrophobic interactions, resulting in the enhancement of interfacial network connectivity and the level of network branching. These factors increase the interfacial resistance to large deformations and increase foam stability. Vicilins and convicilins also tend to have a high value of the surface charge and further promote foam stability by increasing electrostatic repulsion between air bubbles. Legumins tend to reduce foamability since they adsorb to the air-water interface slowly and tend to disrupt the interfacial network structure. These findings provide deeper insights in the role of pulse globulins and albumins in air-water interface and foam stabilization. The proposed key parameters will benefit the predictability of the interfacial and foaming behavior of pulse proteins.

Optimizing solar collector through constructal design of Y-shaped networks with power-law nanofluid flow

Solar energy is a plentiful and renewable resource; therefore, its use through clean energy technologies is necessary to reduce the consumption of fossil fuels and their consequent impact on the environment. Solar thermal energy can be harnessed to collect thermal energy through solar collectors for domestic or industrial use. In this work, a Y-shaped duct network was developed for a solar collector with a disc-shaped body. The shape and size of the network were defined using the constructal design method to harvest greater thermal energy from exposure to irradiance. For this purpose, the working fluid was a nanofluid composed of nanoparticles and a base fluid with non-Newtonian behavior, as described by the power-law model. The properties of the nanofluid were described using theoretical models that depend on the volume fraction of the nanoparticles in the base fluid. The aspect ratio of each element in the network was defined under the condition of minimum thermal resistance. For the shear-thinning nanofluid with a volume fraction of 0.04, the thermal resistance was reduced by 5.5% with an aspect ratio 5.8% lower than that of the pure base fluid. The minimum thermal resistance of the Y-shaped network arrangement occurs for shear-thinning fluids, whereas thermal resistance increases for shear-thickening fluids. This effect can be observed at different levels of branching and in pumping power. Results show that increasing the volume fraction of the nanofluid and base fluid with shear-thinning behavior aids in achieving minimal thermal resistance more easily with a smaller network. The above offers new design options for devices optimized to improve solar harvesting and thermal management, through shape, structure and rheological characteristics.

Breaking Down Silos in the Workplace: A Framework to Foster Collaboration.

Employees are often placed within an organization based on their respective roles or duties, which can lead to vertical and horizontal organizational silos. Organizational silos may restrict information, resources, and stymie progress and innovation. This analysis presents a framework to mitigate silos and overcome communication barriers within an organization by increasing collaboration. The project team examined results from the Centers for Disease Control and Prevention (CDC), the National Center for Chronic Disease Prevention and Health Promotion (NCCDPHP) 2020 Employee Viewpoint Survey Results and conducted 19 key informant discussions with NCCDPHP employees. Participants were asked to provide feedback on (1) understanding silos in the workplace and (2) best practices for reducing silos and fostering collaboration. A thematic analysis was conducted to understand organizational silos, the motivation to reduce silos, and identify best practices and strategies. Respondents felt that siloing exists at the division and branch levels; however, 95% of respondents were motivated to reduce silos. Fifty-eight percent of respondents identified that institutional factors such as the organizational structure (n=8) and red tape/bureaucracy (n=3) contribute to siloing. Additional behaviors and actions that perpetuate silos were identified, and efforts to reduce silos were categorized to propose a model: Framework to Foster Collaboration for improving organizational collaborative efforts. Key themes included inclusion, shared goals and vision, bi-directional communication, and relationship building and developing trust as critical elements for improving collaboration and creating synergy across teams in efforts to reduce silos in the workplace.

Obstructed Branching Networks: A Constructal Approach in Fluid Flow Investigation

Tree flow networks are common in both natural and manufactured systems. The organization of the flow hierarchy passes through the dimensional evolution of the form that is linked to the function. Thus, the objective of comparing bifurcated tube networks obtained by the constructal design method, where part of the structure is obstructed, aims to understand the effects on fluid flow and the prediction of evolutionary deviations in its function. This study compares designs of 3D tree networks with various homothety reduction factors for sizes, having tubes obstructed in some locals of the network. In this computational fluid dynamics study, the geometric constraint applied to these networks is the equal total volume of tubes at each branch level. The evaluation is based on the flow resistance of the networks. This study shows, among other things, that the performance of tree designs is highly dependent on geometric characteristics and the branching level where the obstructions are applied. The effect of the number and position of tubes obstructed in the network, as well as the alignment of the tubes across the network branching levels, on the asymmetry of fluid flow through the network is also studied. It is recommended that the results presented be considered when designing networks for engineering systems.

Discrepancies between Coronary Artery Calcium Score and Coronary Artery Disease Severity in Computed Tomography Angiography Studies.

The aim of this paper is to demonstrate the difference in usefulness of the coronary artery calcium score (CACS) and the full assessment of the severity of coronary artery disease in coronary computed tomography angiography (CCTA) studies. The difference between the population risk of coronary artery disease (CAD) assessed by the CACS and the severity of CAD was demonstrated in images from two CCTA studies. The first image is from a patient with a CACS of 0 and significant coronary artery stenosis. In the native phase of CCTA examination, no calcified changes were detected in the topography of the coronary arteries. In the middle section of the left descending artery (LAD), at the level of the second diagonal branch (Dg2), a large non-calcified atherosclerotic plaque was visible. Mid-LAD stenosis was estimated to be approximately 70%. The second image features a patient with a high CACS but no significant coronary artery stenosis. The calcium score of individual coronary arteries calculated using the Agatston method was as follows: left main (LM) 0, LAD 403, left circumflex (LCx) 207.7, right coronary artery (RCA) 12. CACS was 622.7, representing a significant population risk of significant CAD. In the proximal and middle sections of the LAD, numerous calcified and mixed atherosclerotic plaques with positive remodeling were visible, causing stenosis of 25-50%. Similarly, in the proximal and middle sections of the LCx, numerous calcified and mixed atherosclerotic plaques with positive remodeling were visualized, causing stenoses of 25-50%. Calcified atherosclerotic plaques were found in the RCA, causing stenosis <25%. The entire CCTA image met CAD-RADS 2 (coronary artery disease reporting and data system) criteria. In summary, CACS may be applicable in population-based studies to assess the risk of significant CAD. In the evaluation of individual patients, a comprehensive assessment of CAD severity based on the angiographic phase of the CCTA examination should be used.

Biomimetic fractal pillars for the thermal–hydraulic enhancement of a vapor chamber

Owing to their remarkable thermal–hydraulic performance, vapor chambers have diverse applications, especially for cooling electronic devices. However, the performances of circular and noncircular pillars throughout the entire vapor chamber under identical wick volume conditions have been compared in very few studies. In this study, a series of noncircular pillar arrays featuring biomimetic tree-like fractal networks is introduced. The incorporation of fractal pillars significantly enhances the thermal–hydraulic performance of the vapor chamber because the gas–liquid interface area is extended. Compared to a vapor chamber with circular pillars, the maximum condensation surface temperature difference, total thermal resistance, and liquid pressure drop of this vapor chamber with fractal pillars are reduced by up to 57.8 %, 13.8 %, and 10.9 %, respectively. In particular, with large branch levels and pillar diameters, the fractal structure is pivotal for boosting the overall performance. When the number of pillars is increased, the fractal structure's impact on the thermal performance reaches a limit, whereas its boosting effect on the flow performance weakens. This study is a pioneering exploration of the application of stretched geometries in pillar-type vapor chambers, with fractal pillars utilized in showcase demonstrations.

Seasonality in embolism resistance and hydraulic capacitance jointly mediate hydraulic safety in branches and leaves of oriental cork oak (Quercus variabilis Bl.).

Seasonality in temperate regions is prominent during the era of increased climatic variability. A hydraulic trait that can adjust to seasonally changing climatic conditions is crucial for tree safety. However, little attention has been paid to the intraspecific seasonality of drought-related traits and hydraulic safety of keystone forest trees. We examined seasonal variations in the key morphological and physiological traits as well as multiple hydraulic safety margins (SMs) at the branch and leaf levels in oriental cork oak (Quercus variabilis Bl.), which is predominant in Chinese temperate forests. Pneumatic measurements indicated that, as seasons progressed, the water potential at which 50% of branch embolisms occur (P50_branch) decreased from -3.34 to -4.23MPa, with a coefficient of variation (CV) of 9.08%. Sapwood capacitance ranged from 48.19 to 248.08kgm-3MPa-1, peaking in autumn and reaching minimum in winter (CV 60.58%). Rehydration kinetics confirmed higher leaf embolism vulnerability (P50_leaf) in spring and autumn than those in summer, with values ranging from -1.06 to -3.02MPa (CV 39.85%). All leaf pressure-volume (PV) traits shifted with growth, with CVs ranging from 6.95% to 46.69%. Sapwood density had significant negative correlations with P50_branch and hydraulic capacitance for elastic water storage, whereas leaf mass per area was linearly associated with PV traits but not with P50_leaf. Furthermore, the branch typical SMs (difference between branch midday water potential and P50_branch) were consistently >1.84MPa, and vulnerability segmentation was prevalent throughout, implying a plausible hydraulic foundation for the dominance of Q. variabilis. Diverse hydraulic response patterns existed across seasons, leading to positive SMs mediated by the aforementioned physiological traits. Although Q. variabilis exhibits a high level of hydraulic safety, its susceptibility to sudden summer droughts may increase due to global climate change.

Study of vibration patterns and response transfer relationships in walnut tree trunks

Fruit tree trunk is the support structure of the whole tree, carrying the task of vibration transmission to all levels of branches, fruit tree trunk vibration response to the design and optimization of the vibration harvesting device to provide guiding value. In this paper, the vibration response and harvesting test was carried out for four walnut fruit trees with different morphology and size, and the vibration transmission relationship between the excitation device and the fruit tree as well as inside the fruit tree was analyzed and studied according to the acceleration response curves at each position point under different frequencies. At the same time, the theoretical vibration pattern of the fruit tree and the measured spatial three-dimensional vibration pattern were constructed, and the response transfer law between each point of the fruit tree was further analyzed in terms of the vibration pattern and direction of each position point on the tree. The results show that the excitation response acceleration is basically no attenuation inside the device, but there is some attenuation in the clamping part due to the presence of damping pads. The vibration response in the fruit tree trunk is greater in amplitude farther from the excitation point. The phase relationship between each position point is basically the same in the theoretical vibration mode and the measured vibration mode, but there is damping in the actual fruit tree, which leads to the accumulation of phase hysteresis in the transmission of excitation parameters. The actual response trajectory is a narrow ellipse, and the different position points show different rotational relationships along the ellipse trajectory due to the growth of the fruit tree.

Theoretical study on sequential splitting of droplets flowing through fractal tree-shaped microchannel networks

A theoretical model for describing the sequential splitting of droplets flowing through the fractal tree-shaped microchannel network with arbitrary branch level is developed to explore the mechanisms underlying the hydraulic imbalance on the high-throughput droplets production. Accordingly, detailed droplet splitting characteristics are presented, including the droplet velocities in branches, droplet distribution coefficient, and monodispersity of droplets production. It is found that the uniformity of droplet mainly depends on two key dimensionless parameters, namely Λ1 and Λ2, where Λ1 is determined by the initial working condition involving the initial lengths and viscosity of the continuous and discrete phases, the width of the 0th level channel, and the initial capillary number, and Λ2 is concerned with the outlet pressure pout, [2n-1] and the pressure drops of the continuous and discrete phases at the 0th level channel. The monodispersity of droplets goes down with the decreasing Λ1 and the increasing Λ2. Based on the Λ1 and Λ2, the optimal design strategies contributing to enhancing the droplet generation uniformity are recommended, including increasing Ca, enlarging the length of continuous phase flow at the main channel, and increasing the lengths of each level channels. Furthermore, the tree-shaped microchannel networks with higher branch level (n) have stronger ability to resist asymmetric disturbances. In particular, in our work, the width fractal dimension Δ = 2 is adopted as a proper key structure parameter, so as to ensure sequential breakup of droplet at each T-junction under symmetric condition.

Neurovascular crossing patterns between leash of Henry and deep branch of radial nerve: implications for neurointervention and diagnostic imaging.

To detail the neurovascular crossing patterns between the leash of Henry (LoH) and the deep branch of the radial nerve (DBRN) in supination and pronation of the forearm, using imaging methods with anatomic correlation. This cross-sectional study was performed ex vivo with HRUS and MRI with anatomic correlation on 6 samples and in vivo with HRUS with Doppler on 55 participants scanned bilaterally. The in vivo participants were enrolled over a 6-month period. The crossing patterns between the LoH and DBRN were assessed ex vivo and in vivo. Additional morphological features of the DBRN, LoH, and fat plane were assessed in vivo only. Biometric features of the participants were recorded. Statistical analyses were performed using Shapiro-Wilk, parametric and non-parametric tests. The most common neurovascular crossing pattern was the ascending branch of the radial recurrent artery (RRAab) crossing below (ex vivo: 83.3%, in vivo: 85.3%) and the muscular branch crossing above (ex vivo: 100%, in vivo: 63.2% %) the DBRN. Both the deep and superficial surfaces of the DBRN exhibited an intimate relationship with the vessels of the LoH. A positive correlation between vessel diameter and anthropometric factors was observed. In addition, the muscular branch exhibited a significantly smaller diameter than the RRAab. Our study detailed the relationship between the LoH and the DBRN and highlighted the high incidence of vessel crossing above the DBRN at the level of the muscular branch. Knowledge of neurovascular crossings is crucial for understanding neurovascular entrapment syndromes and planning interventional procedures to reduce vascular complications.

The precision of technical aspects in the minimally invasive Broström–Gould procedure: a cadaveric anatomical study

BackgroundA comprehensive understanding of the anatomy of the anterolateral ankle joint and its interrelationships is essential for advancing the development of minimally invasive Broström–Gould procedure, thereby enhancing surgical efficacy and minimizing postoperative complications.MethodsTen fresh human ankle specimens were dissected to observe the shape and trajectory of the lateral bundle of the inferior extensor retinaculum (IER) and its relationship with the deep fascia. To observe the relationship between the ankle capsule and the anterior talofibular ligament (ATFL). The center of the insertion point of ATFL at the lateral malleolus was used as the reference point. The vertical distance from the reference point to the fibula tip, the horizontal distance from the reference point to the lateral branch of the superficial peroneal nerve, the shortest distance from the reference point to IER, the narrowest width of the IER, the angle between the line connecting the shortest distance from the reference point to the IER and the longitudinal axis of the fibula were measured. The tension and elasticity of ATFL was understood. To describe the minimally invasive Broström–Gould procedure according to the anatomical characteristics of the anterolateral ankle joint.ResultsAmong the 10 cases, 8 cases (80%) had double bundles of ATFL, 2 cases (20%) had single bundle of ATFL, and no outer superior oblique bundle was observed in IER. The vertical distance from the reference point to the fibula tip was 1.2 ± 0.3 (range 1.1–1.3) mm. The shortest distance from the reference point to the level of the superficial peroneal branch was 28.2 ± 4.3 (range 24.5–32.4) mm. The shortest distance from the reference point to IER was 12.5 ± 0.6 (range 12.1–12.9) mm, and the width of IER at this point was 7.2 ± 0.3 (range 7.0–7.6) mm. The angle between the line connecting the shortest distance from the reference point to the IER and the longitudinal axis of the fibula was about 60° ± 2.8° (range 58.1°–62.1°) mm. The space between the anterolateral deep fascia of the ankle joint and the ankle capsule is very small, and only a few fat granules are separated between them. The ATFL is largely fused to the ankle capsule. The ATFL exhibited high tension and poor elasticity after traction with the probe hook.ConclusionsThe results showed that in the minimally invasive Broström–Gould technique for lateral ankle stabilization, the Broström procedure actually sutured the insertion of the ATFL together with the ankle capsule to the anterior edge of the lateral malleolus. In the Gould procedure, the deep fascia was mostly reinforced with the ankle capsule. The minimum suture span was obtained when the Gould suture needle direction was at an Angle of 60° to the longitudinal axis of the fibula.

AI-Based Forecasting of Polymer Properties for High-Temperature Butyl Acrylate Polymerizations.

High-temperature polymerizations involving self-initiation of the monomer are attractive because of high reaction rate, comparable lower viscosities, and no need for an additional initiator. However, the polymers obtained show a more complex microstructure, e.g., with specific branching levels or significant amounts of macromonomer. Simulations of the polymerization processes are powerful tools to gain a deeper understanding of the processes and the elemental reactions at the molecular level. However, simulations can be computationally demanding, requiring significant time and memory resources. Therefore, this study aims at applying AI-based forecasting of tailored polymer properties and using a kinetic Monte Carlo simulator for the generation of training and test data. The applied machine learning (ML) models (random forest and kernel density (KD) regression) predict monomer concentration, macromonomer content, and full molar mass distributions as a function of time, as well as the average branching level with an excellent performance (R 2 (coefficient of determination) > 0.99, MAE (mean absolute error) < 1% for kernel density regression). This study explores the number of training data needed for reliable and accurate predictions in ML models. Explainability methods reveal that the importance of input variables in ML models aligns with expert knowledge.

Classification of variant portal vein anatomy based on three-dimensional CT: surgical implications

PurposesThe purpose of this study was to develop a new and more comprehensive classification system for portal vein (PV) variations using three-dimensional visualization and evaluation (3DVE) and to discuss the prevalence rates and clinical implications of the variants.MethodsThe anatomies of PVs were tracked and analyzed by using three-dimensional visualization of CT images acquired between 2013 and 2022. Scans from 200 adults were evaluated and a total of 178 patients (N = 178) were included in the study. The new classification system, named BLB classification, was developed based on the level of the absent PV branch in each variant anatomy.ResultsUsing the BLB classification system, PVs were divided into thirteen subtypes. Only 82.6–84.8% of the portal veins of the 178 patients were depicted in Atri’s, Cheng’s or Covey’s classification, compared with 100% identified by the BLB classification. The BLB classification was validated against external data sets from previous studies, with 97.0-98.9% of patients classified by the BLB system.ConclusionVariant PV anatomies are more commonly seen based on 3DVE than in previous reports. The BLB classification covers almost all portal vein variants and may be used for planning liver surgery.

Scaling laws for optimal power-law fluid flow within converging–diverging dendritic networks of tubes and rectangular channels

Flows in dendritic–fractal networks have garnered extensive research attention, but most studies assume a constant tube or channel cross section. In many applications, the cross section of the tube or channel changes as the flow progresses through it, such as the blood flow through the arterial system, which is a prime example of a deformable or non-uniform tree-like network. Heating, ventilation, and air conditioning ductwork also exemplify a tree-like network with varying cross sections. This research investigates power-law fluid flows in the converging–diverging tubes and rectangular channels, prevalent in engineered microfluidic devices, many industrial processes, and heat transfer applications. Power-law fluid flows through linear, parabolic, hyperbolic, hyperbolic cosine, and sinusoidal converging–diverging dendritic networks of tubes and rectangular channels are studied. The flow is assumed to be steady, incompressible, two-dimensional planar, and axisymmetric laminar flow without considering network losses. A theoretical model has been derived to evaluate the flow conductance under network volume and surface-area constraints. The flow conductance is highly sensitive to network geometry. The effective conductance of all networks increases with increasing daughter-to-parent radius ratio before eventually declining. The maximum conductance occurs when a specific radius or channel-height daughter–parent ratio β* is achieved. This value depends on the constraint and vessel geometry, such as tubes or rectangular channels. The optimal flow conditions for maximum conductance in a constrained tube volume network, βmax*=βmin*=N−1/3, while for a constrained tube's surface-area network, βmax*=βmin*=N−(n+1)/(3n+2). This scaling applies to all converging–diverging tube network profiles. Here, βmax*, βmin* are the radius ratios of the daughter–parent pair at the maximum divergent or minimum convergent part of the vessel. N represents the number of branches splitting at each junction, and n is the power-law index of the fluid. Furthermore, the optimal flow scaling for the height ratio in the rectangular channel, βmax*=βmin*=N−1/2α−1/2 for constrained channel volume and βmax*=βmin*=N−1/2α−n/(2n+2) for constrained surface area for all converging–diverging channel networks, respectively, where α is the channel-width ratio between parent and daughter branches. Additionally, at optimal conditions in both the channels and tube network, pressure drops are equally partitioned across each branching level. The results in this work are validated with experiments and existing theories for limiting conditions. This research expands existing design principles for efficient flow systems, previously in the literature developed for uniform vessels, to encompass non-uniform converging–diverging vessels. Additionally, it provides a valuable framework for studying non-Newtonian flows within complex, non-uniform tree-like networks.

Balance regulation of heat transfer and flow performance in convective heat exchange process of microchannel plates

As high-performance computing devices continue to evolve toward miniaturization and integration, chip performance has increased significantly. However, chip dimensions are simultaneously shrinking. This trend has led to more challenging high heat flux density issues. Microchannel liquid cooling is an effective way to solve this issue, where the most critical aspect is the balance regulation of heat transfer performance and fluid dynamics. To address this challenge, this study initially divided a complete microchannel plate into two parts: an inlet distribution chamber (IDC) and an array structure. Subsequently, anentransy dissipation rate modeland apumping power consumption modelwere established for themicrochannel inlet diversion chamber, and an optimization design was carried out. This solved the problems of the optimal branch level and optimal channel size for designing the microchannel IDC within a given space. Next, themicrochannel array structurewas optimized to minimize boththermal resistanceandoverall flow resistance. This approach facilitated proactive optimization design for the microchannel array structure within the specified space. Finally, the independently optimizedinlet diversion chamberandarray structurewere combined into a complete optimized microchannel plate. Several comparative structures were also designed under the same constraints. Experimental research was conducted to validate the reasonableness of the optimization. The results indicated that, compared to randomly designed structures, the average overall performance of the optimized structure within the study scope hadincreased by at least 1.16 times, with the highest improvement reaching4.29 times. This study provides a theoretical reference for the active optimization design of microchannel plates in convective heat exchange process.

Enhancing colloidal stability of nanodiamond via surface modification with dendritic molecules for optical sensing in physiological environments

Pre-treatment of diamond surface in low-temperature plasma for oxygenation and in acids for carboxylation was hypothesized to promote the branching density of the hyperbranched glycidol polymer. This was expected to increase the homogeneity of the branching level and suppress interactions with proteins. As a result, composite nanodiamonds with reduced hydrodynamic diameters that are maintained in physiological environments were anticipated. Surfaces of 140-nm-sized nanodiamonds were functionalized with oxygen and carboxyl groups for grafting of hyperbranched dendritic polyglycerol via anionic ring-opening polymerization of glycidol. The modification was verified with Fourier-transform infrared spectroscopy and X-ray photoelectron spectroscopy. Dynamic light scattering investigated colloidal stability in pH-diverse (2–12) solutions, concentrated phosphate-buffered saline, and cell culture media. Thermogravimetric analysis of nanodiamonds-protein incubations examined non-specific binding. Fluorescence emission was tested across pH conditions. Molecular dynamics simulations modeled interparticle interactions in ionic solutions. The hyperbranched polyglycerol grafting increased colloidal stability of nanodiamonds across diverse pH, high ionic media like 10 × concentrated phosphate-buffered saline, and physiological media like serum and cell culture medium. The hyperbranched polyglycerol suppressed non-specific protein adsorption while maintaining intensive fluorescence of nanodiamonds regardless of pH. Molecular modelling indicated reduced interparticle interactions in ionic solutions correlating with the improved colloidal stability.