Capillary Number Research Articles

Influence of a Pair of Unequal Rotational Fluxes on Entrained Gaseous Filament

Abstract Efforts are made to elucidate a comprehensive analysis of entrainment dynamics triggered by a couple of unequal rotational fluxes within a viscous pool. Cylindrical rollers are employed to establish the rotational field. The top drum is equally submerged in both phases and also it provides a constant rotational inertia. Concomitantly, the bottom roller is completely submerged in the viscous bath, and it provides an unequal rotational strength in reference to top roller. The average rotational strength of both rollers is measured using average Capillary number (Caavg). The entrainment phenomenon is strongly influenced by both Caavg and gap between the rollers (W/D). Characterization of entrained filament is elucidated by predicting the horizontal distance (L*), radial distance (r*), temporal vertical displacement (Y*), maximum vertical displacement (Ymax*), width (H*), and location of V-shaped diversion (Øs*). Characterization of liquid tip is performed by measuring the travel rate (γ*) along periphery of drum from receding to advancing junction. Air mass ejection from filament tip is analyzed by estimating the first bubble ejection time (t1st*), volume of accumulated of ejected gaseous masses (v*), and ejection frequency (f). Furthermore, the effect of gravitational pull (specified by Archimedes number, Ar) and viscous drag (measured by Morton number, Mo) on the pattern of entrained air filament is described. Lastly, an analytical framework is established to determine the width of the V-junction by balancing the important influencing forces, which are strongly affecting the filament. Analytical observations show a satisfactory agreement with numerical findings.

Correlation relationships between the levels of microRNA and mRNA involved in pathological angiogenesis in experimental liver cirrhosis

Objective. To identify the relationships between the levels of microRNA and mRNA during pathological angiogenesis under the conditions of experimental toxic liver cirrhosis.Materials and methods. Fibrosis and liver cirrhosis were induced in male Wistar rats using a freshly prepared solution of thioacetamide over 17 weeks. The dynamics of the process were studied at 9 time points. The areas of interlobular veins and interlobular arteries were measured in micrometers. The numbers of interlobular arteries, interlobular veins, and sinusoidal capillaries were counted. The expression levels of mRNA genes Ang, Vegfa, Tweak, Fn14, Notch1, Notch2, and microRNAs-195-5p, microRNAs-664-3p, microRNAs-489-3p, microRNAs-3085, microRNAs-3558-3p in the liver were determined by real-time polymerase chain reaction.Results. It was found that during progressive venous angiogenesis, as well as against the background of changes in the number of interlobular veins, sinusoidal capillaries, and the area of interlobular veins, the nature and strength of correlational interactions between the genes Ang, Vegfa, Tweak, Fn14, Notch1, Notch2, and microRNAs-195-5p, microRNAs-664-3p, microRNAs-489-3p, microRNAs-3085, microRNAs-3558-3p are associated with the stage of fibrosis and liver cirrhosis. Strong, moderate, and mild correlational links (p<0.01) were identified between the genes Ang, Vegfa, Tweak, Fn14, Notch1, Notch2 throughout the experiment.Conclusion. The obtained results indicate that the studied microRNAs - microRNAs-195-5p, microRNAs-664-3p, microRNAs-489-3p, microRNAs-3085, microRNAs-3558-3p - are involved in the processes of restructuring the intrahepatic vascular bed at different stages of experimental toxic fibrosis and liver cirrhosis. The results of the study not only reveal additional mechanisms of formation of the indicated conditions but also identify the biological role of the studied microRNAs in the progression of fibrosis and liver cirrhosis as potential targets for studying pathogenesis and developing treatment methods.

Flow-Driven Deformation in Granular Porous Media: Dimensionless Analysis

Fluid injection can induce mechanical deformation in granular porous media due to the elevation of internal pore fluid pressure. This gains more significance when more than two immiscible fluids are involved, attributable to capillary and viscous drag forces. Such a coupled hydromechanical behavior associated with immiscible fluid flows plays an important role in injection, storage, and recovery of fluids in deformable porous media. This study presents a dimensionless map with newly proposed dimensionless parameters to predict deformation occurrence due to an immiscible fluid flow in deformable porous media. A series of hydromechanically coupled pore network simulations are first performed while varying the capillary number, mobility ratio, medium stiffness, and effective confining stress over orders of magnitudes. The compilation of simulation results with previously published Hele–Shaw experiment results is analyzed with the dimensionless parameters, such as the capillary number, mobility ratio, particle-level force ratios, and particle-level pressure ratios. Particularly, the particle-level pressure ratios include the capillary pressure ratio, defined as the ratio of capillary pressure to fracture pressure, and the viscous drag pressure, defined as the ratio of viscous drag pressure to fracture pressure. The dimensionless map based on the particle-level pressure ratios, where the capillary pressure ratio and viscous drag pressure ratio are defined as the ratios of capillary pressure and viscous drag pressure to fracture pressure, effectively delineates four deformation regimes—no deformation, capillary-induced deformation, drag-driven deformation, and mixed-mode deformation. The results demonstrate that capillary-induced deformation occurs when the capillary pressure ratio is greater than 10−1, while drag-driven deformation is observed when the viscous drag pressure ratio exceeds 10−2. The presented dimensionless map and dimensionless parameters are expected to be applicable for geological subsurface processes, including geological storage of carbon dioxide and hydrogen, and enhanced oil recovery.

Study on Emulsification Effect of Crude Oil in Brine Emulsions by Automated Demulsibility Tester

The purpose of the surfactants used is to greatly reduce the interfacial tension between the crude oil and brine, thereby decreasing the capillary number. The resulting oil-in-water emulsions are often grouped according to the Winsor theory. Oil recovery aims to produce Winsor type-III emulsions because they have the lowest interfacial tension values and the most favorable flow properties. The sensitivity of oil–water–surfactant systems to environmental influences (e.g., mixing speed and equilibration time) increases close to the favorable environmental range (temperature, brine total salt concentration, pressure, etc.) of the Winsor III type, the middle microemulsion phase, which is favorable for crude oil recovery. The tests aimed to investigate the quality and quantity of emulsions prepared with surfactants used in enhanced oil recovery (EOR) using an automatic device to characterize and select surfactants for industrial petroleum applications. An essential method for surfactant selection is to study the emulsifying effect and phase behavior. Phase behavior tests and emulsifying effect tests were performed on surfactants and surfactant packages as a function of mixing parameters. The mixing speed and mixing time can influence the results of the phase behavior and emulsifying effect tests, although during the investigations, other parameters were unchanged.

Bubble-induced entrainment at viscoplastic–Newtonian interfaces

The passage of single air bubbles through the horizontal interface between viscoplastic and Newtonian fluids, considering various combinations of densities and viscosities for the fluid layers, is studied computationally. The primary focus is on the quantity of liquid transferred from the lower layer (viscoplastic fluid) to the upper layer (Newtonian fluid) as a result of the bubble's ascent, a factor with significant implications for the turbidity of methane-emitting lakes and water bodies. The entrainment characteristics are observed to vary considerably with the bubble shape, within the lower layer and as the bubble approaches the interface. The results show that at Bond number $(Bo)>1$ and moderate Archimedes ( $Ar$ ), prolate-shaped bubbles crossing the interface undergo elongation in the direction of their poles. This elongation is further accentuated when the viscosity of upper layer is less than the plastic viscosity of the lower layer. The bubble is found to break up when leaving the lower layer, of a critical capillary number, $Ca_c \approx 5$ . The results show a significant reduction in the volume of entrainment compared with the Newtonian counterpart. This suggests disturbances caused by the rising bubble at the interface dissipate over a smaller region. Four distinct entrainment regimes are identified, mainly indicating the height to which the entrained fluid can be transported away from the interface. In contrast to Newtonian fluids, the volume of entrainment increases by decreasing the viscosity of the upper layer. Interestingly, the heavy viscoplastic fluid that has been dragged up into the light Newtonian fluid does not recede with time.

On the linear viscoelastic behavior of semidilute polydisperse bubble suspensions in Newtonian media

In this work, we investigated the linear viscoelasticity of semidilute polydisperse bubble suspensions via small amplitude oscillatory shear (SAOS) tests performed in a rheo-optical setup. For all tested suspensions, the measured viscoelastic moduli (G′, G″) aligned with the theoretical predictions of the Jeffreys model for average dynamic capillary numbers (⟨Cd⟩) greater than unity. But at lower ⟨Cd⟩ values, experimental G′ values exceeded theoretical predictions. To investigate this, we considered the effects of suspension polydispersity and various SAOS measurement artifacts, including bubble rise, coalescence, and changes in suspension microstructure over time. Polydispersity could not cause the observed deviation, because the viscoelastic trends deviate from those of classic single-mode relaxation only for bimodal bubble size distributions with equal volume fractions of very small and very large bubbles; in any other case, the polydisperse suspension behaves as monodisperse with a bubble radius equal to the volume-weighted mean radius. Furthermore, bubble rise proved to play a minor role, while SAOS rheo-optical experiments revealed that bubble size and organization varied negligibly during our measurements. The G′ deviation at low ⟨Cd⟩ values was linked to bubble fluid dynamic interactions induced by the bubble spatial distribution. Image analysis showed that at low bubble volume fractions, stronger and prolonged preshearing reduces these interactions by increasing the average interbubble distance. But this effect is negligible in denser suspensions, which show similar G′ trends for any applied preshearing. Finally, a multimode Jeffreys model fitted to the experimental data showed that bubble interactions complicate the relaxation process, introducing multiple relaxation modes.

Insight into evolution of invasive patterns on fingering phenomenon during immiscible two-phase flow through pore structure

Insight into evolution of invasive patterns on fingering phenomenon during immiscible two-phase flow through pore structure

Shexiang Tongxin Dropping Pill Promotes Angiogenesis through VEGF/eNOS Signaling Pathway on Diabetic Coronary Microcirculation Dysfunction.

To study the effect of Shexiang Tongxin Dropping Pill (STDP) on angiogenesis in diabetic cardiomyopathy mice with coronary microcirculation dysfunction (CMD). According to a random number table, 6 of 36 SPF male C57BL/6 mice were randomly selected as the control group, and the remaining 30 mice were injected with streptozotocin intraperitoneally to replicate the type 1 diabetes model. Mice successfully copied the diabetes model were randomly divided into the model group, STDP low-dose group [15 mg/(kg·d)], medium-dose group [30 mg/(kg·d)], high-dose group [60 mg/(kg·d)], and nicorandil group [15 mg/(kg·d)], 6 in each group. The drug was given by continuous gavage for 12 weeks. The cardiac function of mice in each group was detected at the end of the experiment, and coronary flow reserve (CFR) was detected by chest Doppler technique. Pathological changes of myocardium were observed by hematoxylin-eosin staining, collagen fiber deposition was detected by masson staining, the number of myocardial capillaries was detected by platelet endothelial cell adhesion molecule-1 staining, and the degree of myocardial hypertrophy was detected by wheat germ agglutinin staining. The expression of the vascular endothlial growth factor (VEGF)/endothelial nitric oxide synthase (eNOS) signaling pathway-related proteins in myocardial tissue was detected by Western blot. Compared with the model group, medium- and high-dose STDP significantly increased the left ventricular ejection fraction and left ventricular fraction shortening (P<0.01), obviously repaired the disordered cardiac muscle structure, reduced myocardial fibrosis, reduced myocardial cell area, increased capillary density, and increased CFR level (all P<0.01). Western blot showed that high-dose STDP could significantly increase the expression of VEGF and promote the phosphorylation of vascular endothelial growth factor receptor 2, phosphoinositide 3-kinase, protein kinase B, and eNOS (P<0.05 or P<0.01). STDP has a definite therapeutic effect on diabetic CMD, and its mechanism may be related to promoting angiogenesis through the VEGF/eNOS signaling pathway.

Fluid entrapment during forced imbibition in a multidepth microfluidic chip with complex porous geometry

Understanding and controlling fluid entrapment during forced imbibition in porous media is crucial for many natural and industrial applications. However, the microscale physics and macroscopic consequences of fluid entrapment in these geometric-confined porous media remain poorly understood. Here, we introduce a novel multidepth microfluidic chip, which can mitigate the depth confinement of traditional two-dimensional (2-D) microfluidic chips and mimic the wide pore size distribution as natural-occurring three-dimensional (3-D) porous media. Based on microfluidic experiments and direct numerical simulations, we observe the fluid-entrapment scenarios and elucidate the underlying complex interaction between geometric confinement, capillary number and wettability. Increasing depth variation can promote fluid entrapment, whereas increasing capillary number and contact angle yield the opposite effect, which seemingly contradicts conventional expectations in traditional 2-D microfluidic chips. The fluid-entrapment scenario in depth-variable microfluidic chips stems from microscopic interfacial phenomena, classified as snap-off and bypass events. We provide theoretical analyses of these pore-scale events and validate corresponding phase diagrams numerically. It is shown that increasing depth variation triggers snap-off and bypass events. Conversely, a higher capillary number suppresses snap-off events under strong imbibition, and an increased contact angle inhibits bypass events under imbibition. These macroscopic imbibition patterns in microfluidic porous media can be linked with these pore-scale events by improved dynamic pore-network models. Our findings bridge the understanding of forced imbibition between 2-D and 3-D porous media and provide design principles for newly engineered porous media with respect to their desired imbibition behaviours.

Hydrodynamic efficiency limit on a Marangoni surfer

A Marangoni surfer is an object embedded in a gas–liquid interface, propelled by gradients in surface tension. We derive an analytical theorem for the lower bound on the viscous dissipation by a Marangoni surfer in the limit of small Reynolds and capillary numbers. The minimum dissipation can be expressed with the reciprocal difference between drag coefficients of two passive bodies of the same shape as the Marangoni surfer, one in a force-free interface and the other in an interface with surface incompressibility. The distribution of surface tension that gives the optimal propulsion is given by the surface tension of the solution for the incompressible surface and the flow is a superposition of both solutions. For a surfer taking the form of a thin circular disk, the minimum dissipation is $16\mu a V^2$ , giving a Lighthill efficiency of $1/3$ . This places the Marangoni surfers among the hydrodynamically most efficient microswimmers.

Transfer of a rational formulation and process development approach for 2D inks for pharmaceutical 2D and 3D printing

The field of pharmaceutical 3D printing is growing over the past year, with Spitam® as the first 3D printed dosage form on the market. Showing the suitability of a binder jetting process for dosage forms. Although the development of inks for pharmaceutical field is more trail and error based, focusing on the Z-number as key parameter to judge the printability of an ink. To generate a more knowledgeable based ink development an approach from electronics printing was transferred to the field of pharmaceutical binder jetting. Therefore, a dimensionless space was used to investigate the limits of printability for the used Spectra S Class SL-128 piezo print head using solvent based inks. The jettability of inks could now be judged based on the capillary and weber number. Addition of different polymers into the ink narrowed the printable space and showed, that the ink development purely based on Z-numbers is not suitable to predict printability. Two possible ink candidates were developed based on the droplet momentum which showed huge differences in process stability, indicating that the used polymer type and concentration has a high influence on printability and process stability. Based on the study a more knowledgeable based ink design for the field of pharmaceutical binder jetting is proposed, to shift the ink design to a more knowledgeable based and process-oriented approach.

Dynamics of hydrogen storage in subsurface saline aquifers: A computational and experimental pore-scale displacement study

Dynamics of hydrogen storage in subsurface saline aquifers: A computational and experimental pore-scale displacement study

A new methodology in evaluating nonlinear electrohydrodynamic azimuthal stability between two dusty viscous fluids

A new methodology in evaluating nonlinear electrohydrodynamic azimuthal stability between two dusty viscous fluids

In-situ particle analysis with heterogeneous background: a machine learning approach

We propose a novel framework that combines state-of-the-art deep learning approaches with pre- and post-processing algorithms for particle detection in complex/heterogeneous backgrounds common in the manufacturing domain. Traditional methods, like size analyzers and those based on dilution, image processing, or deep learning, typically excel with homogeneous backgrounds. Yet, they often fall short in accurately detecting particles against the intricate and varied backgrounds characteristic of heterogeneous particle–substrate (HPS) interfaces in manufacturing. To address this, we've developed a flexible framework designed to detect particles in diverse environments and input types. Our modular framework hinges on model selection and AI-guided particle detection as its core, with preprocessing and postprocessing as integral components, creating a four-step process. This system is versatile, allowing for various preprocessing, AI model selections, and post-processing strategies. We demonstrate this with an entrainment-based particle delivery method, transferring various particles onto substrates that mimic the HPS interface. By altering particle and substrate properties (e.g., material type, size, roughness, shape) and process parameters (e.g., capillary number) during particle entrainment, we capture images under different ambient lighting conditions, introducing a range of HPS background complexities. In the preprocessing phase, we apply image enhancement and sharpening techniques to improve detection accuracy. Specifically, image enhancement adjusts the dynamic range and histogram, while sharpening increases contrast by combining the high pass filter output with the base image. We introduce an image classifier model (based on the type of heterogeneity), employing Transfer Learning with MobileNet as a Model Selector, to identify the most appropriate AI model (i.e., YOLO model) for analyzing each specific image, thereby enhancing detection accuracy across particle–substrate variations. Following image classification based on heterogeneity, the relevant YOLO model is employed for particle identification, with a distinct YOLO model generated for each heterogeneity type, improving overall classification performance. In the post-processing phase, domain knowledge is used to minimize false positives. Our analysis indicates that the AI-guided framework maintains consistent precision and recall across various HPS conditions, with the harmonic mean of these metrics comparable to those of individual AI model outcomes. This tool shows potential for advancing in-situ process monitoring across multiple manufacturing operations, including high-density powder-based 3D printing, powder metallurgy, extreme environment coatings, particle categorization, and semiconductor manufacturing.

Study of droplet formation in parallel flow focusing microchannel under electrostatic field control

Study of droplet formation in parallel flow focusing microchannel under electrostatic field control

Geometric influence of width ratio and contraction ratio on droplet dynamics in microchannel using a 3D numerical simulation

AbstractMicrochannel geometry is an important factor in determining droplet dynamics in droplet‐based microfluidic systems, much like fluid properties and flow conditions. In this context, two important geometric parameters—the contraction ratio () and the width ratio ()—that are limited to particular value ranges are taken into consideration for evaluation. These parameters interact with the capillary number () and viscosity ratio () to affect different aspects of droplet migration and manipulation, such as trap and squeeze regimes. A theoretical model is proposed, and a three‐dimensional numerical simulation method is used in this work. This model predicts the change from trap to squeeze, which is caused by the interaction of the previously mentioned variables. Interestingly, an inverse correlation exists between the width ratio and the critical capillary number for this transition, which is determined as . Furthermore, the investigation explores the droplet elongation and velocity ratio during their passage through the microchannel. By matching input parameters with microchannel geometry, this information may be useful for the design of microfluidic systems, which would facilitate the careful control and manipulation of droplets.

Estrogen stimulates fetal vascular endothelial growth factor expression and microvascularization.

We recently showed that the ratio of capillaries to myofibers in skeletal muscle, which accounts for 80% of insulin-directed glucose uptake and metabolism, was reduced in baboon fetuses in which estrogen was suppressed by maternal letrozole administration. Since vascular endothelial growth factor (VEGF) promotes angiogenesis, the present study determined the impact of estrogen deprivation on fetal skeletal muscle VEGF expression, capillary development, and long-term vascular and metabolic function in 4- to 8-year-old adult offspring. Maternal baboons were untreated or treated with letrozole or letrozole plus estradiol on days 100-164 of gestation (term = 184 days). Skeletal muscle VEGF protein expression was suppressed by 45% (P < 0.05) and correlated (P = 0.01) with a 47% reduction (P < 0.05) in the number of capillaries per myofiber area in fetuses of baboons in which serum estradiol levels were suppressed 95% (P < 0.01) by letrozole administration. The reduction in fetal skeletal muscle microvascularization was associated with a 52% decline (P = 0.02) in acetylcholine-induced brachial artery dilation and a 23% increase (P = 0.01) in mean arterial blood pressure in adult progeny of letrozole-treated baboons, which was restored to normal by letrozole plus estradiol. The present study indicates that estrogen upregulates skeletal muscle VEGF expression and systemic microvessel development within the fetus as an essential programming event critical for ontogenesis of systemic vascular function and insulin sensitivity/glucose homeostasis after birth in primate offspring.

Dynamic simulation of immiscible displacement in fractured porous media

Investigating immiscible displacement in fractured porous media is essential for understanding the two-phase flow behavior within pores and fractures. In this work, a three-dimensional pore-fracture network model was developed to address the influence of fracture on flow patterns and to characterize fracture-matrix crossflow under different flow conditions. Sensitivity studies at a wide range of viscosity ratios and capillary numbers underscored that fracture significantly influenced flow patterns in the capillary fingering zone. Fracture with an advantageous path effect in the displacement direction caused a shift in the boundary of capillary fingering zone toward an increase in capillary numbers. As fracture aperture decreased and aspect ratio increased, there was a discernible decline in the crossflow rate. When fracture aperture equaled average matrix throat diameter, fracture lose advantageous path effect in compact displacement zone but retained it in viscous fingering and capillary fingering zones. Distinct matrix-fracture crossflow development processes were observed in different zones: in cross zone, following displacement breakthrough, the crossflow underwent a “long-term” process to attain stability. Viscous fingering zone promptly achieved stability post-breakthrough, whereas both capillary fingering and compact displacement zones had already reached a stable state before breakthrough. Nonlinear variations in breakthrough saturation were observed in the cross zone between compact displacement and capillary fingering zones. The control process of immiscible displacement exhibited variability under different flow conditions: compact displacement zone was characterized by matrix dominance, viscous fingering zone was jointly controlled by matrix displacement and fracture-matrix crossflow, and capillary fingering zone was primarily governed by fracture-matrix crossflow. These findings enhance scholarly comprehension of immiscible displacement behavior in fractured porous media.

Droplet migration through deformable stenosed microchannel: Dynamics and blockage

Understanding droplet migration in stenosed microchannels is crucial for various applications. This study explores how droplet properties (viscosity, surface tension, density, and diameter) and channel characteristics (stenosis degree and wall elasticity) affect droplet movement and blockage in deformable stenosed microchannels. Higher viscosities lead to lubrication film formation between droplet and wall, reducing viscous resistance, while increased surface tension enhances wall adherence, amplifying Laplace pressure. Droplet entry is primarily influenced by viscosity, while passage is governed by surface tension and curvature effects at the droplet–wall interface. Surface tension dominates pressure generation in the channel and within the droplet, influencing wall deformation and hydrodynamic resistance. The study examines the relationship among droplet viscosity, density, surface tension, channel wall elasticity, and the maximum capillary number (Camax) on the lubrication film thickness between the droplet and the channel wall. A lubrication film exists for Camax≥0.095, reducing blockage chances. A critical range of the modified Ohnesorge number Oh*×1000≤132 and the capillary number (Camax&amp;lt;0.095) indicates higher chances of droplet blockage. The blockage prediction method based on the modified Ohnesorge exhibits a sensitivity of 100%, specificity of 92.6%, and accuracy of 95.9%. Additionally, the study explores the impact of channel wall elasticity on droplet entry, transit, and hydrodynamic resistance. Higher wall elasticity facilitates faster entry but introduces curvature during passage, increasing frictional resistance and blockage likelihood as the wall softens.

Understanding droplet formation in T-shaped channels with magnetic field influence: A computational investigation

This study investigates the production of ferrofluid droplets in a T-junction geometry using the level set method and magnetic force manipulation in the three-dimensional. The analysis reveals key insights into droplet formation processes in four stages: entering, blocking, necking, and detachment. The results show that increasing the Capillary number leads to a significant decrease in volume for non-ferrofluid droplets. Application of a magnetic force enhances the balance of forces during droplet formation, directly impacting droplet volume. Moreover, increasing the magnetic Bond number substantially increases droplet volume, with a more pronounced effect at lower Capillary numbers. Modifying magnetic properties influences droplet volume, with doubling the magnetization results in a significant volume increase. Overall, magnetic forces emerge as a crucial control parameter for droplet volume in ferrofluid systems, offering potential applications in droplet-based technologies and microfluidic devices.