Channel Cross-sectional Geometry Research Articles

Whole-channel acoustic energy and acoustophoretic efficiency frequency spectrum by the in-flow focusing method

The in-flow focusing method, introduced herein, enables rapid and straightforward measurements of the whole-channel acoustic energy of acoustic flow-through devices. The method is applied to assess the whole-channel acoustic energy and acoustophoretic efficiency frequency spectra of a bottom-actuated silicon-glass and a side-actuated glass chip. The input variables are the time-independent geometrical shape of the particle trajectories along the manipulation chamber, the channel cross-section geometry, the physical properties of the reference particles and fluid, and the volumetric flowrate. The outputs are the total acoustic energy, the acoustophoretic efficiency, as well as the acoustic energy density distribution along the channel, which provide a comprehensive overview of the performance of acoustically driven lab-on-a-chip setups. The acoustophoretic efficiency is an important parameter that relates the energy dissipation, and therefore the heat development in the device, to the useful acoustic energy in the channel. Unlike the current state-of-the-art methods such as particle image velocimetry, particle tracking velocimetry, and optical trapping, which are typically limited to small channel areas and are time-consuming, the in-flow focusing method can be applied to long channels and enables rapid measurements of the whole-channel acoustic energy. Published by the American Physical Society 2024

Impact of the flow-field distribution channel cross-section geometry on PEM fuel cell performance: Stamped vs. milled channel

Polymer electrolyte membrane fuel cells (PEM FCs) represent an essential part of the emerging hydrogen economy. Metallic bipolar plates (BPs) allow high speed and capacity production using established industrial technologies, like mechanical stamping. Stamping, however, leads to different cross-sectional shapes of flow-field (FF) channels as compared to milled or compression-moulded bipolar plates. The impact of these changes on the resulting fuel cell performance is not yet fully understood. This study employs an experimentally validated three-dimensional, isothermal, steady-state, continuum-mechanics based mathematical model to gain a deeper insight into this issue and to identify optimal stamped BP channel cross-sectional shapes for parallel and serpentine FF. The uniformity of the local distribution of the physico-chemical quantities and the resulting load curves are analysed. The results obtained confirm that stamped BPs with channels of the trapezoidal cross-section are a viable alternative to the traditional milled or moulded BPs with channels of the rectangular cross-section. The observed differences in performance of FC with stamped and milled channels can be mitigated by optimization of the channel cross-section geometry parameters. As an optimal rib width 0.4 mm and an optimal channel ground width 1 mm for milled and 0.2 mm for stamped BPs are suggested.

Deep Learning-Based Automatic River Flow Estimation Using RADARSAT Imagery

Estimating river flow is a key parameter for effective water resource management, flood risk prevention, and hydroelectric facilities planning. Yet, traditional gauging methods are not reliable under very high flows or extreme events. Hydrometric network stations are often sparse, and their spatial distribution is not optimal. Therefore, many river sections cannot be monitored using traditional flow measurements and observations. In the last few decades, satellite sensors have been considered as complementary observation sources to traditional water level and flow measurements. This kind of approach has provided a way to maintain and expand the hydrometric observation network. Remote sensing data can be used to estimate flow from rating curves that relate instantaneous flow (Q) to channel cross-section geometry (effective width or depth of the water surface). Yet, remote sensing has limitations, notably its dependence on rating curves. Due to their empirical nature, rating curves are limited to specific river sections (reaches) and cannot be applied to other watercourses. Recently, deep-learning techniques have been successfully applied to hydrology. The primary goal of this study is to develop a deep-learning approach for estimating river flow in the Boreal Shield ecozone of Eastern Canada using RADARSAT-1 and -2 imagery and convolutional neural networks (CNN). Data from 39 hydrographic sites in this region were used in modeling. A new CNN architecture was developed to provide a straightforward estimation of the instantaneous river flow rate. Our results yielded a coefficient of determination (R2) and a Nash–Sutcliffe value of 0.91 and a root mean square error of 33 m3/s. Notably, the model performs exceptionally well for rivers wider than 40 m, reflecting its capability to adapt to varied hydrological contexts. These results underscore the potential of integrating advanced satellite imagery with deep learning to enhance hydrological monitoring across vast and remote areas.

Theoretical investigation of dam-break waves in frictional channels with power-law sections

Both the hydraulic resistance and the channel cross-sectional geometry have significant effect on the propagation of the dam-break waves. Analytical models including either of them have been available. However, it is not feasible to assess the comprehensive influence using the existing solutions. The present study considers a resistance-dominated wave tip region followed by an ideal fluid flow region in a dry horizontal channel whose cross-sectional shape is controlled by a power-law index n. Laboratory experiments and numerical simulations are conducted to measure/predict the water surface profiles of the dam-break flows in five types of flumes. The water depth, location and celerities of the wave front predicted by the analytical model agree well with the experimental and numerical results. The quantitative effects of the bottom resistance and the channel cross-sectional shape on the wave properties are investigated. Results show that the spatio-temporal variation in the wave feature of the dam-break flows strongly depends on the channel cross-sectional geometry; while the retardation effect of the bottom resistance becomes more significant as n increases. Furthermore, the derived analytic solution as well as the experimental data can be used for evaluating numerical solutions considering the hydraulic resistance and cross-sectional geometry.

Numerical investigation of influence of cross-sectional dimensions of flow channels on PEM fuel cell performance

Proton exchange membrane fuel cell (PEMFC) has acquired increasing importance because of operating at higher efficiency and producing environmentally friendly power at low temperatures over the past decade. Flow channel as a vital part of PEMFC plays a critical role for augmenting the performance of PEMFC. In this paper, a single phase, 3-D model is generated to examine impact of the channel cross-section geometry on the cell performance. 15 different simulation cases were gained by altering the flow channel width and depth from 0.2 to 1.6 mm for the fixed depth and width of 1 mm, respectively. In the base case, the channel dimensions are 1.0 mm width and depth. The results revealed that decreasing depth and width of the channel enhanced the current density thanks to increasing gas velocity in the flow channels of the anode and cathode at the expense of increased pressure drop. The cases having the channel cross-sectional dimensions of 0.2 x 0.1 mm and 0.1 x 0.2 mm (channel width x depth) enhanced the current density about 57% and 45% at 0.4 V compared to the base case. Besides, oxygen consumption and water production in the cathode side are also remarkably increased in these cases. However, the channel cross-sectional size of 0.8 x 1 mm case which increases the current density 2.5% at 0.4 V in comparison with the base case can be best option by taking into consideration pressure drop into the flow channels.

PEM fuel cell cathode-side flow field design optimization based on multi-criteria analysis of liquid-slug dynamics

Since the Gas Diffusion Layer (GDL) clearance and the residence time of produced water in gas channels remarkably affect the proper operation of proton exchange membrane (PEM) Fuel Cells, the water management in this part plays a key role. To this end, the present study aims to introduce novel and optimized gas channels through geometrical modifications that act efficiently in terms of GDL clearance and liquid residence time. For this purpose, the VOF (Volume of Fluid) model was employed to numerically simulate two-phase flow by means of a finite volume method. Several decisive parameters including superficial gas velocity, channel surface wettability, and channel cross-section geometry were considered to find their effects on the liquid removal behavior. The liquid removal performance was analyzed by two-phase pressure drop, area coverage ratio (ACR), and liquid removal time. Results have been compared with previous works done on the conventional rectangular channels. Interestingly, it was found out that for the analyzed segment of the gas flow channels, the channel with triangle cross-section has superior performance in reducing ACR by 64% for inlet superficial air velocity of 0.5 ms and 8–24.45% reduction for higher velocities (1, 1.5 and 2.5 ms). Also, the transition from slug flow to film flow also stable two-phase pressure drop were only seen in this type of channel. The ranking of channels based on their residence time merit is as: hexagon>pentagon>rectangular>triangle. Increment of the contact angle of hydrophilic walls causes fluctuations in the two-phase pressure drop and decreases liquid water residence time. For triangle channel, surface with a contact angle of ∼120° and for the hexagon and pentagon channels 85–120° is suggested for the best fuel cell performance.

A study on thermohydraulic characteristics of fluid flow through microchannels

At present, miniaturization of the devices in order to make them for effective performance, reliability and ease at cost is the primary need of any nation. In this direction, the role of microchannels can play an important role in the further development of industrial growth. The increased demand of the microchips in the industrial areas has increased the number of transistors for the improved functionality which leads to the emission of the higher heat flux, which is already a big challenge in the electronic sector. In the present paper, a comprehensive review on microchannels has been done regarding single-phase and multi-phase studies. In the present paper, an intensive review of the thermal and hydraulic characteristics of fluid flow in microchannels at different hydraulic diameters and their effects on performance has been done. The effects of the various parameters such as the Reynolds number (Re), Nusselt number (Nu), friction factor (f), pressure drop (P), working fluid and cross-sectional geometry of duct, as well as the hydrodynamic and thermal aspects, has been also studied. It was concluded through the literature study that transition from laminar to turbulent is very much affected by channel cross-sectional geometry, aspect ratio, channel wall roughness and compressibility effects. Also, researchers only explored the laminar region for its pressure drop and heat transfer characteristics, while the turbulent flow regime is yet to be explored. It was observed that most of the correlation over-estimated the value of pressure drop in multi-phase flow.

Enhancement of power output in passive micro-direct methanol fuel cells with optimized methanol concentration and trapezoidal flow channels

This work presents design, fabrication and optimization of methanol concentration and flow channel cross-sectional geometry for enhanced power output in passive micro-direct methanol fuel cells. Passive micro-direct methanol fuel cells are fabricated with flow channels in silicon having both rectangular and trapezoidal cross-sectional geometry for flow of methanol at anode and air at cathode using microelectromechanical systems (MEMS) fabrication technique. The experiments are conducted at 25 °C by feeding methanol with a flow rate of 25 μl min−1 and supply of air at cathode by air-breathing method. Results show a peak in open circuit voltage and power density at 7 M methanol concentration for passive micro-direct methanol fuel cells having both rectangular and trapezoidal cross-sectional geometry. A study of influence of silicon flow channel cross-sectional geometry on passive micro-direct methanol fuel cell performance shows for the first time that the flow channels with trapezoidal cross-section enhance the power density (6.64 mW cm−2) nearly by a factor of two compared to that of flow channels with rectangular cross-section (3.9 mW cm−2) at 7 M methanol concentration. We believe that, though our results of significant enhancement of power density with trapezoidal fuel flow channels are obtained with micro-direct methanol fuel cells as a platform, they should also be applicable to other proton exchange membrane fuel cells with ethanol or humidified hydrogen as fuel.

Experimental and numerical study of elasto-inertial focusing in straight channels.

Elasto-inertial microfluidics has drawn significant attention in recent years due to its enhanced capabilities compared to pure inertial systems in control of small microparticles. Previous investigations have focused mainly on the applications of elasto-inertial sorting, rather than studying its fundamentals. This is because of the complexity of simulation and analysis, due to the presence of viscoelastic force. There have been some investigative efforts on the mechanisms of elasto-inertial focusing in straight channels; however, these studies were limited to simple rectangular channels and neglected the effects of geometry and flow rates on focusing positions. Herein, for the first time, we experimentally and numerically explore the effects of elasticity accompanying channel cross-sectional geometry and sample flow rates on the focusing phenomenon in elasto-inertial systems. The results reveal that increasing the aspect ratio weakens the elastic force more than inertial force, causing a transition from one focusing position to two. In addition, they show that increasing the angle of a channel corner causes the elastic force to push the particles more efficiently toward the center over a larger area of the channel cross section. Following on from this, we proposed a new complex straight channel which demonstrates a tighter focusing band compared to other channel geometries. Finally, we focused Saccharomyces cerevisiae cells (3-5 μm) in the complex channel to showcase its capability in focusing small-size particles. We believe that this research work improves the understanding of focusing mechanisms in viscoelastic solutions and provides useful insights into the design of elasto-inertial microfluidic devices.

Two-phase displacements in microchannels of triangular cross-section

Varying microfluidic channel cross-sectional geometry can dramatically alter fluid flow behavior, particularly for capillary-driven flow. Most fabrication techniques, however, are planar and therefore incapable of providing depth-dependent variations in width. We introduce an ultrafast laser ablation technique that enables the fabrication of microchannels with arbitrary triangular cross sectional geometry. Triangular channels were fabricated with widths ranging from 45 to 116µm and aspect ratios between 0.7 and 1.9. This experimental platform was utilized to observe two-phase flow and evaluate the capillary pressures required to initiate flow within triangular capillaries. Applying Mayer, Stowe and Princen (MS-P) theory, critical drainage capillary pressures were predicted for varying cross sections and compared to experimental observations. Results indicate the capability to predict capillary pressures inside triangular channels with perfectly water wet surfaces, providing the first instance of experimental validation of the theory for arbitrary triangular cross sections. This work was extended to intermediate wet conditions, which provides an insight into the prediction of capillary pressure under more realistic conditions. The fabrication techniques and validation of predictive frameworks presented here provide an approach to microfluidic experimental design that will impact a wide range of fundamental and applied technology areas.

A single width–discharge regime relationship for individual threads of braided and meandering rivers from the Himalayan Foreland

We explore the existence of a single width–discharge regime relation for alluvial rivers of braided and meandering patterns. The study relies on the field measurement of a channel's cross section geometry (width, depth), discharge, and grain size of 98 individual threads of braided and meandering rivers from the Ganga–Brahmaputra plains of the Himalayan Foreland. Using this data set, we show that, irrespective of the diverse climatic and geologic setting along the strike, the braided and meandering threads share statistically indistinguishable regime relations and scale according to Lacey's law. To explain the observed trend in this empirical relationship, we use the threshold theory introduced by Glover and Florey (1951). Using this theory we detrend our data with respect to discharge to produce a statistically homogeneous ensemble of width measurements. The statistical distribution of the detrended width is similar for braided and meandering threads of the entire plains of the Foreland. This suggests that when we decompose a braided river into individual threads, each of these resemble single-thread meandering rivers. Based on this study, we conclude that the individual threads of braided and meandering rivers of the Himalayan Foreland are geometrically comparable and share a common width–discharge regime relation.

Shear work contribution to convective heat transfer of dilute gases in slip flow regime

In the literature some researchers highlighted that for a dilute gas in slip flow regime and in presence of a non negligible viscous heating, the analysis of the gas micro-convection has to be tackled by modifying the thermal boundary conditions to account for the shear work due to the slip at the wall. Although in the recent past a specific modified boundary condition has been proposed, theoretically justified and applied to investigate the effect of the shear work on the convective heat transfer in presence of dilute gases, in this paper is demonstrated that there is not a need of a modified boundary condition in order to take into account the effect of the shear work in the analysis of forced convection. In the present work by means of a comprehensive theoretical analysis is demonstrated that the modified boundary condition is useless for the analysis of the effect of shear work on the evaluation of the convective heat transfer coefficients in presence of a dilute gas with non-negligible viscous dissipation.Moreover, to evaluate the inaccuracy of the results obtained by using the modified boundary conditions the difference, in terms of Nusselt number, between the exact and the approximate solution has been numerically estimated for elliptical microchannels. The numerical outcomes point out that the adoption of the modified boundary condition leads to an underestimation or an overestimation of the Nusselt numbers depending on the values of Brinkman number and on the channel cross section geometry.

Comparative analysis of fabrication methods for achieving rounded microchannels in PDMS

Many microfluidic applications demand control over channel cross-sectional geometry. In particular, rounded microchannels are essential to the function of microfluidic valves, which have played an integral part in the success of microfluidics over the past fifteen years. Here we investigate the relative strengths and weaknesses of different strategies for fabricating rounded microchannels in PDMS, systematically examining five common strategies. We consider the appropriateness of the fabrication strategies for microchannels of differing sizes and aspect ratios, and evaluate these various strategies on a number of metrics ranging from microchannel resolution to fabrication difficulty. We discuss the merits of the different strategies for a range of applications, and make recommendations on which strategy to use based on the driving constraints of the device.

Constructing river stage-discharge rating curves using remotely sensed river cross-sectional inundation areas and river bathymetry

Remote sensing from satellites and airborne platforms provides valuable data for monitoring and gauging river discharge. One effective approach first estimates river stage from satellite-measured inundation area based on the inundation area-river stage relationship (IARSR), and then the estimated river stage is used to compute river discharge based on the stage-discharge rating (SDR) curve. However, this approach is difficult to implement because of a lack of data for constructing the SDR curves. This study proposes a new method to construct the SDR curves using remotely sensed river cross-sectional inundation areas and river bathymetry. The proposed method was tested over a river reach between two USGS gauging stations, i.e., Kingston Mines (KM) and Copperas Creek (CC) along the Illinois River. First a polygon over each of two cross sections was defined. A complete IARSR curve was constructed inside each polygon using digital elevation model (DEM) and river bathymetric data. The constructed IARSR curves were then used to estimate 47 river water surface elevations at each cross section based on 47 river inundation areas estimated from Landsat TM images collected during 1994–2002. The estimated water surface elevations were substituted into an objective function formed by the Bernoulli equation of gradually varied open channel flow. A nonlinear global optimization scheme was applied to solve the Manning’s coefficient through minimizing the objective function value. Finally the SDR curve was constructed at the KM site using the solved Manning’s coefficient, channel cross sectional geometry and the Manning’s equation, and employed to estimate river discharges. The root mean square error (RMSE) in the estimated river discharges against the USGS measured river discharges is 112.4m3/s. To consider the variation of the Manning’s coefficient in the vertical direction, this study also suggested a power-law function to describe the vertical decline of the Manning’s coefficient with the water level from the channel bed lowest elevation to the bank-full level. The constructed SDR curve with the vertical variation of the Manning’s coefficient reduced the RMSE in the estimated river discharges to 83.9m3/s. These results indicate that the method developed and tested in this study is effective and robust, and has the potential for improving our ability of remote sensing of river discharge and providing data for water resources management, global water cycle study, and flood forecasting and prevention.

Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterisation, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash–Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ∼2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Residence time of water film and slug flow features in fuel cell gas channels and their effect on instantaneous area coverage ratio

Water in the gas channels of a Proton Exchange Membrane Fuel Cell is modeled as slugs and film, and removal mechanisms for these flow patterns are numerically investigated. The removal of excess liquid water is simulated using computational fluid dynamics (CFD) through the volume of fluid (VOF) model. The computational domain consists of a gas flow channel appropriate for commercial stacks for automotive applications. The effects of superficial air velocity, channel surface wettability, and channel cross-section geometry are investigated through quantitative comparison of two-phase pressure drop, area coverage ratio (ACR) over the gas diffusion layer (GDL) and liquid removal time. Top wall film flow was identified as a desirable feature since it did not cover the GDL and facilitated transport of oxygen to the reaction sites while removing the water. A range of hydrophilic channel walls in combination with a hydrophobic GDL is proposed to promote this behavior while reducing the fluctuations in two-phase pressure drop for different contact angles. Additional enhancements to liquid water removal were associated with the channel cross-section geometry. An alternative trapezoidal shape is suggested for improved top wall film flow while improving the manufacturability of the bipolar plates for mass production.

Abrasive waterjet micro-machining of channels in metals: Comparison between machining in air and submerged in water

Abrasive water jet technology can be used for micro-milling using recently developed miniaturized nozzles. Abrasive water jet (AWJ) machining is often used with both the nozzle tip and workpiece submerged in water to reduce noise and contain debris. This paper compares the performance of submerged and unsubmerged abrasive water jet micro-milling of channels in 316L stainless steel and 6061-T6 aluminum at various nozzle angles and standoff distances. The effect of submergence on the diameter and effective footprint of AWJ erosion footprints was measured and compared. It was found that the centerline erosion rate decreased with channel depth due to the spreading of the jet as the effective standoff distance increased, and because of the growing effect of stagnation as the channel became deeper. The erosive jet spread over a larger effective footprint in air than in water, since particles on the jet periphery were slowed much more quickly in water due to increased drag. As a result, the width of a channel machined in air was wider than that in water. Moreover, it was observed that the instantaneous erosion rate decreased with channel depth, and that this decrease was a function only of the channel cross-sectional geometry, being independent of the type of metal, the jet angle, the standoff distance, and regardless of whether the jet was submerged or in air, in either the forward or backward directions. It is shown that submerged AWJM results in narrower features than those produced while machining in air, without a decrease in centerline etch rate.

Prediction of zonal and total discharges in smooth straight prismatic compound channels using regression modeling

Experimental results are presented concerning the zonal and total discharge distribution and characteristics in a compound channel cross-section comprising one rectangular main channel and two symmetrical floodplains. The discharges in the main channel, floodplains, and total compound channel are found to be highly correlated to several dimensionless parameters defined using the compound channel cross-section geometry. Multi-variable regression analysis was utilized for developing predictive models that can estimate the main channel, floodplains and total discharges as a function of four different dimensionless parameters. The developed models to predict the zonal and total discharges in compound channels are found to be highly significant according to several major statistics including the model standard error, coefficient of determination (R2), and F-statistic. The developed multi-variable regression-based models are also tested for validity using available experimental data. Several statistical tests applicable to the analysis of residuals have indicated the effectiveness of the developed predictive models.

Sensitivity of a hydraulic model to channel erosion uncertainty during extreme flooding

Recent research into flood modelling has primarily concentrated on the simulation of inundation flow without considering the influences of channel morphology. River channels are often represented by a simplified geometry that is implicitly assumed to remain unchanged during flood simulations. However, field evidence demonstrates that significant morphological changes can occur during floods to mobilize the boundary sediments. Despite this, the effect of channel morphology on model results has been largely unexplored. To address this issue, the impact of channel cross-section geometry and channel long-profile variability on flood dynamics is examined using an ensemble of a 1D–2D hydraulic model (LISFLOOD-FP) of the ~1 : 2000 year recurrence interval floods in Cockermouth, UK, within an uncertainty framework. A series of simulated scenarios of channel erosional changes were constructed on the basis of a simple velocity-based model of critical entrainment. A Monte-Carlo simulation framework was used to quantify the effects of this channel morphology together with variations in the channel and floodplain roughness coefficients, grain size characteristics and critical shear stress on measures of flood inundation. The results showed that the bed elevation modifications generated by the simplistic equations reflected an approximation of the observed patterns of spatial erosion that enveloped observed erosion depths. The effect of uncertainty on channel long-profile variability only affected the local flood dynamics and did not significantly affect the friction sensitivity and flood inundation mapping. The results imply that hydraulic models generally do not need to account for within event morphodynamic changes of the type and magnitude of event modelled, as these have a negligible impact that is smaller than other uncertainties, e.g. boundary conditions. Instead, morphodynamic change needs to happen over a series of events to become large enough to change the hydrodynamics of floods in supply limited gravel-bed rivers such as the one used in this research.

Single bubble geometry evolution in micro-scale space

Two types of single vapour bubble growth in micro-scale space are experimentally investigated. Degassed pentane and FC-72 are used to study the bubble confined between superheated parallel plates without liquid flow. Liquid properties which are influential on bubble growth are discussed. Effects of plate superheating and plate gap on bubble growth rate are examined. Bubble growth during flow boiling in high aspect ratio micro-channels is also examined to extensively investigate the single bubble growth in a dynamic configuration. The hydraulic diameters of the tested channel are 571 μm, 762 μm and 1454 μm, with an aspect ratio of 20, 20 and 10 respectively. Transparent heating technique is utilised to provide heating power while ensuring sufficient transparency for visualisation. A three-stage bubble growth mode is presented. Moreover, bubble geometry evolution is found to be strongly related to channel cross-sectional geometry but slightly affected by heat flux or mass flux. Bubble growth critical time is defined. Bubble equivalent radius, bubble aspect ratio and width versus length trends are also discussed.