Capillary Number Research Articles

Use of microcirculatory parameters to evaluate foam sclerotherapy treatment of superficial chronic venous disease, associated or not with venotonic drug: randomized, double-blind trial.

Chronic venous disease (CVD) is a pathology with unfavorable outcome when treated and/or followed up incorrectly. In addition to macroscopic venous changes, CVD also causes changes in microcirculation. Based on these hypotheses, a non-invasive test to quantify the evolution of microangiopathy may be useful to assess the effects and benefits of treatment. Fifty female patients with varicose veins classified by clinical class C2 or C3 of the CEAP classification were selected and allocated randomly in two groups: foam sclerotherapy (FS) + micronized purified flavonoid fraction (MPFF) or FS + placebo, double-blind. Microcirculation was evaluated using Sidestream Dark Field techniques. The revised VCSS score was performed pre and post FS. It was found an improvement on VCSS and all microcirculation parameters, in both groups, except on the number of pathological capillaries. When comparing the results between groups, a greater reduction in the diameters of dermal papilla was observed in the MPFF group (P=0.053), which, despite not being statistically significant, had an effect size of 0.55 (-0.01-1.10). In addition, capillary bulk and capillary limb also had a higher decrease in the MPFF group. FS treatment of the trunk veins reduced distal venous hypertension, improving microcirculation in all patients, helping to control the venous disease. All patients got therapeutic success (total occlusion or partial occlusion with improvement in venous reflux or reduction in venous caliber).

Buckling of red blood cell membrane in narrow capillaries induces excessive wall shear stress.

Buckling of red blood cell membrane in narrow capillaries induces excessive wall shear stress.

Myostatin Knockout Mice Have Larger Muscle Fibers With Normal Function and Morphology.

We assessed whether muscle fibers in myostatin knockout (MSTN-/-) mice are just larger or also exhibit morphological, metabolic, and functional differences from MSTN+/+ mice. We compared single fiber contractile properties and histological fiber properties in muscles from MSTN-/- and MSTN+/+ mice. Even though in permeabilized muscle fibers from the extensor digitorum longus and soleus muscle maximal force was higher (p < 0.001) there were no significant differences in specific power (power per unit volume), specific tension (force per cross-sectional area), maximal shortening velocity, or curvature of the force-velocity relationship between MSTN-/- and MSTN+/+ mice. In histological sections of the soleus muscle, fibers were larger (p < 0.001), but the succinate dehydrogenase staining intensity and capillary density did not differ significantly between MSTN-/- and MSTN+/+ mice, which was explicable by the larger number of capillaries around a fiber (p < 0.001). A model showed no significant differences in soleus muscle oxygenation. The larger force-generating capacity of fibers from MSTN-/- mice is explicable by the larger fiber cross-sectional area. The data indicate that muscle fibers from MSTN-/- mice are quantitatively, but not qualitatively different from muscle fibers from MSTN+/+ mice. Myostatin inhibition may help increase muscle mass in conditions accompanied by muscle weakness without a detrimental impact on muscle quality, but systemic side effects need to be considered.

The Oil/Water Two-Phase Flow Behavior of Dual-Porosity Carbonates

Dual-porosity carbonates exhibit abundant macropores and micropores, yet the mechanisms governing oil/water flow at the dual-porosity scale remain inadequately understood. This study investigates the flow behavior in dual-porosity carbonates during forced imbibition. Initially, carbonate characteristics were extracted using a random field method to generate two types of porous media. Subsequently, the multiple-relaxation-time color-gradient lattice Boltzmann method, validated by experimental and analytical solutions, was employed to systematically evaluate the effects of wettability, capillary number, and oil/water viscosity ratio on oil displacement efficiency in dual-porosity carbonates during forced imbibition. The reliability of the simulated oil displacement efficiency was verified through core waterflooding experiments. The results reveal that under water-wet conditions, fluid flow paths in dual-porosity carbonates are strongly influenced by the blockage of micrite particles at low capillary numbers, while at high capillary numbers, the fragmentation of large continuous oil droplets interacting with micrite particles leads to more unstable interfaces. Under non-water-wet conditions, dominant capillary forces enhance oil displacement within macropores of dual-porosity carbonates. Under the same conditions, water-wet conditions are more favorable for improving oil displacement efficiency. As the capillary number increases, oil displacement efficiency exhibits a pronounced non-monotonic trend under non-water-wet conditions, attributed to the alternating dominance of viscous and capillary forces. Additionally, with an increase in oil/water viscosity ratio, the decline in oil displacement efficiency is less pronounced for dual-porosity carbonates compared to single-porosity carbonates, particularly under non-water-wet conditions at high capillary numbers.

Dynamics of non-Newtonian agarose gel droplet formation in two-phase microfluidic systems

Droplet-based microfluidics is a valuable tool in interdisciplinary research fields like cell biology and diagnostics. Newtonian fluids, like aqueous-based solutions, are commonly used for droplet generation. However, non-Newtonian fluids, e.g., hydrogels, are becoming increasingly popular as the dispersed phase. In this study, we investigate the dynamics of non-Newtonian ultra-low-gelling agarose droplet formation under different conditions to evaluate stability, with an aim to better understand the underlying physics of droplet formation. We varied the agarose gel concentration, temperature (40, 50, and 60 °C), and the flow rate ratio (ϕ) between the continuous and dispersed phase and observed droplet formation dynamics in the squeezing regime (capillary number, Cac &amp;lt; 0.015) in a T-junction under different flow conditions. We experimentally investigated the droplet size (LD/w) as a function of those four parameters and found that LD/w depends strongly on ϕ, the agarose concentration, and temperature (which affects the viscosity ratio, λ), but is only weakly dependent on Cac. We then confirmed our experimental findings with numerical simulations, which showed good agreement across all conditions. We numerically showed that the agarose droplet formation process consists of five stages, namely, filling, necking, pinching, threading, and breakup, where threading is an additional stage with a non-Newtonian dispersed phase. Finally, with numerical simulation, we concluded that threading length (lthread) is directly proportional to ϕ and has a complex relation with agarose concentration, and temperature.

Marangoni interfacial instability induced by solute transfer across liquid-liquid interfaces

Marangoni interfacial instability induced by solute transfer across liquid-liquid interfaces

The Taylor flow characteristic and mass transfer in curved T-microchannels

Mass transfer processes in curved microchannels are challenging to measure due to the complex flow structures induced by curved geometries. This study systematically investigates Taylor flow and mass transfer mechanisms in curved T-microchannels using visualization experiments and numerical simulations. Three primary Taylor flow patterns—slug flow, long slug flow, and columnar flow—are observed. A slug length prediction model is developed based on the dispersed phase Reynolds number and the continuous phase capillary number. Comparisons of flow fields in different curved microchannels reveal that curvature effectively disrupts the symmetric internal circulation within the slug, shifting it toward the slug head and splitting it into multiple secondary circulations. This disruption enhances radial mixing and mass transfer within the slug. By introducing mixing efficiency and the Dean number, this study quantifies the influence of channel curvature radius, number of bends, and two-phase flow velocity on flow enhancement and mass transfer. Results indicate that smaller curvature radii, a greater number of bends, and higher dispersed phase volume fractions intensify secondary flow within the channel cross section, thereby promoting mass transfer. Additionally, pressure drop measurement demonstrates that microchannels with more bends and smaller curvature radii correspond to higher energy dissipation. Based on comprehensive numerical and experimental results, a broadly applicable and highly accurate mass transfer prediction model is established using the Dean number, two-phase Reynolds number, and dispersed phase capillary number. This study provides theoretical guidance for optimizing microchannel designs and furthering the application of microchannel reactors in fine chemical processes and related fields.

Low Capillary Elastic Flow Model Optimization Using the Lattice Boltzmann Method and Non-Dominated Sorting Genetic Algorithm

In simulations of elastic flow using the lattice Boltzmann method (LBM), the steady-state behavior of the flow at low capillary numbers is typically poor and prone to the formation of bubbles with inhomogeneous lengths. This phenomenon undermines the precise control of heat transfer, mass transfer, and reactions within microchannels and microreactors. This paper establishes an LBM multiphase flow model enhanced by machine learning. The hyperparameters of the machine learning model are optimized using the particle swarm algorithm. In contrast, the non-dominated sorting genetic algorithm (NSGA-II) is incorporated to optimize bubble lengths and stability. This results in a coupled multiphase flow numerical simulation model that integrates LBM, machine learning, and the particle swarm algorithm. Using this model, we investigate the influence of elastic flow parameters on bubble length and stability in a T-shaped microchannel. The simulation results demonstrate that the proposed LBM multiphase flow model can effectively predict bubble elongation rates under complex conditions. Furthermore, multi-objective optimization determines the optimal gas–liquid two-phase inlet flow rate relationship, significantly mitigating elastic flow instability at low capillary numbers. This approach enhances the controllability of the elastic flow process and improves the efficiency of mass and heat transfer.

Study of Charged Nanodroplet Deposition into Microcavity Through Many-Body Dissipative Particle Dynamics

For a near-eye display, a resolution of over 10,000 pixels per inch (PPI) for the display device is needed to eliminate the “screen door effect” and have better display quality. Electrohydrodynamic (EHD) printing techniques, which have the advantages of a high resolution, wide material applicability and flexibility in patterning, have been widely used in the printing of high-resolution structures. However, due to factors such as the extremely small size of the droplets, the electric charge, the electric field, and the unavoidable positioning error, various deposition defects can occur. For droplets at a nanoscale, the dynamic deposition process is hard to observe. The continuum hypothesis fails and the fluid cannot be described by the traditional Navier–Stokes equation. In this work, the behaviors of charged nanodroplet deposition into a microcavity in an electric field are studied. The many-body dissipative particle dynamics (MDPD) method is used to examine the deformation of the nanodroplet during the impact process at a mesoscale. The dynamic process of charged droplet deposition into a microcavity under an electric field is revealed. Strategies for failure-free printing are proposed by analyzing the influences of the impact speeds, positioning errors, charge levels and electric intensities on the out-of-pixel spread length. The relationship between the internal charge moves and the deformation of the charged droplet in the deposition process is first discussed. The spreading theory of charged droplet deposition into a microcavity with a positioning error is established by analyzing the Coulombic capillary number. Moreover, the printing parameter space that results in successful printing is acquired.

Absolute instability in the higher-generation airways: a pathway for airway closure

Absolute instability in the higher-generation airways: a pathway for airway closure

Optimizing and Regulating Electric-Induced Breakup of Salt-Containing Droplets through Magnetic Field Coupling: Insights from Molecular Dynamics Simulations.

Droplet electrodispersion is a fundamental phenomenon in various fields, such as electric demulsification, electrospray, and microfluidic manipulation. Electric-magnetic coupling technology, as an emerging noncontact method, shows substantial potential in modulating droplet electrohydrodynamics, yet the influence characteristics and mechanisms of coupled magnetic fields on droplet electrodispersion remain poorly understood. To address this gap, we conducted a detailed molecular dynamics simulation comparing the breakup dynamics of salt-containing droplets under a single electric field versus an electric-magnetic coupling field. Our results demonstrate that salty droplets in the electric-magnetic coupling field exhibit longer breakup response times and greater stretching deformation. This behavior is attributed to changes in ion migration speed and enrichment regions due to additional Lorentz forces. Furthermore, this effect of coupling field is observed only for ion numbers Nion > 0, with a marked attenuation at higher concentrations (Nion = 200), which is related to the hydration effect enhanced by magnetic field. When the electric capillary number Ca ranges from 0.88 to 3.91, the critical value triggering a shift in the breakup mode is enhanced in the coupling field. However, this effect diminishes as Ca approaches 8.8, at which point the coupled field no longer inhibits breakup. Additionally, as the dimensionless electric field frequency f* increases from 0.21 to 4.19, the ion migration trajectories become shorter and less able to accumulate at the interface, thereby limiting the effectiveness of the coupling field. Our study advances the fundamental understanding of salt-containing droplet breakup dynamics under an electric-magnetic coupling field and provides novel insights for controlling and suppressing electrodispersion in related technologies.

Pore-scale flow mechanism of immiscible gas-assisted gravity drainage in strongly heterogeneous glutenite reservoirs

Tight glutenite reservoirs are known for strong heterogeneity, complex wettability, and challenging development. Gas-Assisted Gravity Drainage (GAGD) technology has the potential to significantly improve recovery efficiency in glutenite reservoir. However, there is currently limited research on GAGD processes specifically designed for glutenite reservoirs, and there is a lack of relevant dimensionless numbers for predicting recovery efficiency. In this study, we developed a theoretical model based on the characteristics of glutenite reservoirs and used phase-field method to track the oil–gas interface for numerical simulations of dynamic GAGD processes. To explore the factors influencing gas-driven recovery, we simulated the effects of strong heterogeneity and dynamic wettability on the construction process under gravity assistance. Additionally, we introduced multiple dimensionless numbers (including capillary number, viscosity ratio, and Bond number) and conducted a series of numerical simulations. The results demonstrate that gravity enhances the stability of the oil–gas interface but causes unstable pressure fluctuations when passing through different-sized throat regions, particularly leading to front advancement in smaller throats. Although strong heterogeneity has negative impacts on GAGD, they can be mitigated by reducing injection velocity. Increasing oil-wettability promotes oil displacement by overcoming capillary forces, particularly in narrower pores, allowing residual oils to be expelled. Among the dimensionless numbers, the recovery efficiency is directly proportional to the Bond number and inversely proportional to the capillary number and viscosity ratio. Through sensitivity analysis of the dimensionless numbers’ impact on the recovery efficiency, a new dimensionless NGlu considering heterogeneity is proposed to accurately predict GAGD recovery of tight glutenite reservoirs.

How shearing affects air dissolution in fresh cement pastes under pressure

The air-void system of concrete is of paramount importance to ensure freeze–thaw durability. Pumping induces detrimental changes in the air-void system of concrete by dissolving the air bubbles in the surrounding water when pressure increases due to the pump action. This research work investigates the influence of shear rate and air-void size distribution on air dissolution with time of cement pastes under pressure. Steady-state shear rheology at different shear rates was applied on samples of different air-void size distributions but similar air contents. Due to the low capillary number of the mixtures, the application of pressure caused a decrease in viscosity. With increased applied shear rate and increased fineness of the air-void size distribution, the decrease in viscosity was more abrupt, indicating that the air dissolved almost immediately. Coarser air-void size distributions and lower shear rates caused a more gradual decrease in viscosity and thus a slower air dissolution. All experimental air dissolution times were lower than the calculated time needed for dissolution by pure diffusion. These results on the combined effect of pressure, duration, shear rate and air-void size distribution create the basis for a deeper understanding of the behavior of the air-void system of concrete during pumping.

Discussion on pore-to-field scale evolution of invasive pattern in immiscible two-phase flow with pseudoplastic behavior in porous media

The immiscible two-phase flow with non-Newtonian behavior presents many challenges for geoscience engineering applications. Due to the non-Darcy flow with pseudoplasticity in bitumen or heavy oil reservoir, the variable and velocity-affected viscous force leads to unstable and unpredictable evolution of invasive patterns in porous media. Primarily, drainage experiments, computational fluid dynamics, and analytical model analyses were conducted to track morphological variations of invasive interface, revealing the evolution mechanisms of invasive patterns with pseudoplasticity. Subsequently, the field-scale two-phase flow simulation, established by the blocked-centered finite difference method, quantitively investigates the impact of invasive patterns on the extraction of pseudoplastic oil. Ultimately, given previous methods for evaluation of invasive patterns, capillary number, and mobility ratio play a communicating role in the pore-scale and the field-scale study. Through the dual-scale framework, the capillary number and mobility ratio, serving as driving force and resistance, respectively, predictably improve the evolutionary diagram pore-scale invasive patterns and accurately evaluate the field-scale potential of pseudoplastic oil extraction. From both pore and field perspectives, our work holds promising application for optimizing invasive patterns by injection operation in the pseudoplastic oil reservoirs.

Transportation behaviors of double emulsion droplets under the influence of varied interfacial tensions

The transportation behaviors and dynamic characteristics of double emulsion droplets in a Y-junction are experimentally investigated to explore the influence of the interfacial tension. Based on the breakup behaviors, three flow patterns are identified: non-breakup (NB), once breakup of the outer droplet (OB), and twice breakup of the outer droplet (TB). Compared to the single emulsions, the inner droplet leads to new flow patterns for the double emulsions due to the coupling effect between interfaces. The flow pattern map can be built using the normalized droplet length and the capillary number. With the aid of the quantitative expression of the transition thresholds using a power law relation, the transitions are further found to rely on the junction structure and the physical properties of the double emulsion. It is indicated that the dynamic characteristics of double emulsions are shaped jointly by multiple controlling parameters, such as the droplet length, the capillary number, and the junction structure. A force model is proposed to estimate the quantitative evolutions of the working forces in different flow patterns. The evolution of the droplet morphology is consistent with the forces acting on it, and the prerequisite condition for the droplet breakup is confirmed to depend on the competition between the sum of the driving forces and the sum of the interfacial tensions. The variation of the transition thresholds in different liquid systems is further analyzed, which may provide useful methods to manipulate the double emulsions by changing the physical properties.

Capillary number effects on two-phase flow and residual oil morphology in water and supercritical CO₂ displacement: A microfluidic study

Capillary number effects on two-phase flow and residual oil morphology in water and supercritical CO₂ displacement: A microfluidic study

Polymer flooding characteristics in modified Hele–Shaw cells

In this study, numerical simulations are employed to investigate the displacement flow of oil by viscoelastic polymer solutions inside modified Hele–Shaw cells (HSCs). The flooding characteristics within converging and diverging geometrical configurations and various flow injection rates are explored by utilizing the White–Metzner model to capture the viscoelastic behavior of hydrolyzed polyacrylamide solutions at different concentrations. The simulations are conducted in OpenFOAM using the volume of fluid method to model the multiphase interface. Results demonstrate that higher elasticity numbers (El) and lower modified capillary numbers (Ca′) enhance the oil recovery to over 75% in terms of swept volume due to improved flow stability and reduced finger branching. Additionally, the diverging HSCs positively influence the flow patterns and facilitate an extra increase in sweeping efficiency (SE) by more than 12% via favorably alleviating the stability threshold in terms of Ca′–El relationship. In contrast, the opposite holds for the converging channel, decreasing SE by 16% and narrowing down the stability region. The findings indicate that adjusting polymer concentration and cell configuration can mitigate the adverse effects of finger instability, thereby improving the overall success of oil displacement processes. Moreover, a supervised machine learning study was carried out to predict the sweep efficiency based on the flow dimensionless numbers, where the multi-layered artificial neural network was exhibited as a high-accuracy model with an R2 value of 94.46%.

The onset of electrospray for droplet impact on hydrophilic/hydrophobic substrate

Droplet impact and ejection behavior under an electric field is common in droplet manipulation, power transmission lines, and inkjet printing. Here, the filamentous ejection of the droplet in a vertical electric field after impact was studied by visual experiment and numerical simulation with OpenFOAM. We experimentally investigated the effect of impact Weber number, advancing and receding angles on droplet impact in depth. We found that the threshold electric capillary number of filamentous ejection changes non-linearly with increasing of impact Weber number. The nonlinear change has not been reported before, and the mechanism is still unknown. In this study, we found that the sequence of droplet stretching and three-phase line retraction is the key to this nonlinear variation. Then, we presented geometric parameter prediction models for droplet stretching, obtained the distorted electric field at the top of the droplet, and developed a physical model for the threshold electric capillary number. Substrate characteristics, impact Weber number, electrode plate spacing, and liquid properties were proved to couple to affect ejection. Our physical model successfully involves these influences and is in good agreement with experiment.

Drop Dynamics during Condensation on Superhydrophobic Surfaces in Vapor Shear Flow.

Accurate models for predicting drop dynamics, such as maximum drop departure sizes, are crucial for estimating heat transfer rates during condensation on superhydrophobic (SH) surfaces. Previous studies have focused on examining the heat transfer rates for SH surfaces under the influence of gravity or vapor flowing over the surface. This study investigates the impact of surface solid fraction and texture scale on drop mobility in a condensing environment with a humid air flow. Experiments recorded condensation with varying surface feature sizes from micro- to nano scale under different flow rates. Video analysis detected the drop-size distribution and maximum drop departure sizes. Particle image velocimetry (PIV) provided accurate shear force representations. Results showed that the maximum drop departure sizes decreased with lower surface solid fractions and higher flow rates. A force balance analysis revealed that coalescence-induced drop jumping aids drop departure. Different drop behaviors due to coalescence were linked to surface characteristics. The study quantified drop jump distances under shear force during condensation on SH surfaces, and found that jump distances increased when coalescing drop sizes were similar. Based on these findings, a method for tuning SH surfaces to control drop size at coalescence and departure was suggested. Drop mobility was measured in terms of Bond and Capillary numbers, showing a dependence on surface solid fraction and pitch size. By combining these into surface slip length, it was shown that drop mobility increases with increasing slip length.

Research on the Parameter Configuration Law of Transfer of Ultramicro Liquid by Pipetting Needle Based on the Quasi-static State.

Microscale device surface encapsulation needs to use ultrafine liquid transfer technology. This technology can transfer a liquid from a donor surface to a receptor surface in a controlled manner. However, the requirement of microscale encapsulation for liquid transfer amounts is generally at the pL level. Controlling liquid transfer volume, ensuring consistency, and ensuring droplet position accuracy became more difficult at this level. In light of the existing pipetting needle transfer ultramicro liquid transfer technology and considering a slow stretching liquid bridge can maintain a constant liquid transfer ratio, we conducted in-depth research on the parameter configuration law of liquid transfer at the pL level. This study reveals the parameter configuration law under the condition of constant transfer ratio through the Young-Laplace equation and the Navier-Stokes equation. Research has shown that the initial distance and capillary number (Ca) affect the transfer ratio at a slow stretching speed. Through ultramicro liquid transfer experiments, with stretching speeds between 0.01 and 0.5 mm/s, the transfer ratio remained constant, the accuracy of the rheology-Cross model in predicting liquid transfer ratios was verified, and the absolute deviation rate between the actual and the predictive transfer ratio is 6.26%. This research plays a crucial role in enhancing the precision and success rate of microscale liquid transfer.