Viscosity Ratio Research Articles

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.

Translational motion of a spheroidal drop in a viscous fluid

The problem of translational motion of a spheroidal drop along its axis of revolution in a viscous incompressible fluid is investigated semi-analytically. The flow fields in the exterior and interior of the drop are governed by the Stokes equations. Stream function formulation is adopted to solve the hydrodynamic equations in both regions. The general solution for the stream function in prolate and oblate spheroidal coordinates is expressed in an infinite-series form of semi-separation of variables. The leading order coefficients in the stream function are obtained using suitable boundary conditions. The hydrodynamic drag force experienced by the spheroidal drop is numerically evaluated with adequate convergence behavior for various values of the internal-to-external viscosity ratio and axial-to-radial aspect ratio of the drop. The numerical values of the drag force for the infinite and infinitesimal viscosity ratios agree with the available corresponding results for the slow translation of a slip spheroidal particle in the limiting conditions of no slip and full slip, respectively. At intermediate values of the viscosity ratio, the hydrodynamic force may not be a monotonic function of the aspect ratio. For a spheroidal drop with a fixed aspect ratio, its drag force increases monotonically with an increase in the viscosity ratio.

Study on two-phase displacement law considering mass transfer and diffusion

The influence of channeling on viscous fingering instability of CO2 miscible displacement is studied in the paper. Due to the viscous fingering not easily observed in porous media, channeling is used to simplify the viscous fingering instability. We adopted nonlinear simulation to investigate the development of viscous fingering instability during the displacement of Newtonian fluids in a channel by miscible fluids, and the influence of different Pe and different viscosity ratio R was studied. Under homogeneous conditions, when R is the same, the larger the Pe is, the more obvious the convection in the process of CO2 displacement is, the earlier the viscous fingering occurs, and the shorter the time for the finger to break through to the right boundary is. When Pe is the same, the larger the R is, the more unstable the contact area of miscible displacement becomes. More finger structures appear, and more complex fingering phenomena occur. The larger the R is, the earlier the fingering phenomenon appears, and the earlier it breaks through to the right boundary. In addition, we studied the change in Relative Mixing Length (RML) during the diffusion process quantitatively. Finally, our investigation delved into the impact of heterogeneity on viscous fingering. We observed that under significant heterogeneity, viscous fingering tends to manifest preferentially in the direction of increasing permeability.

Measurement of pressure gradients near the interface in the viscous fingering instability

The viscous fingering instability, which forms when a less-viscous fluid invades a more-viscous one within a confined geometry, is an iconic system for studying pattern formation. For both miscible and immiscible fluid pairs the growth dynamics change after the initial instability onset and the global structures, typical of late-time growth, are governed by the viscosity ratio. Here we introduce an experimental technique to measure flow throughout the inner and outer fluids. This probes the existence of a new length scale associated with the local pressure gradients around the interface and allows us to compare our results to the predictions of a previously proposed model for late-time finger growth. Published by the American Physical Society 2024

Ratio of viscosity to water content in solutions: A new indicator for designing of electrolytic polishing solutions for stainless steel

Leveraging a fresh comprehension of electrolytic polishing (EP) mechanisms, this study introduces a pivotal factor - viscosity/water content ratio (VWR) - for the first time, rooted in acidity ratio theory. The present study aligns with published works to affirm the validity of the VWR indicator and its correlation with surface roughness. A noteworthy contribution lies in the design of EP solutions that can serve as a guide for stainless steels. It strikes a balance between low cost, high efficiency, long service life and desirable surface roughness. This involves regulating the dissolution-ionization-deposition process at the metal/solution interface.

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.

Entropy generation and Arrhenius activation energy mechanisms in EMHD radiative Carreau nanofluid flow due to Brownian motion and thermophoresis with infinite shear rate viscosity: solar energy application and regression analysis

This research is devoted to analyzing the radiative electro-magnetohydrodynamic (EMHD) Carreau nanofluid flow, emphasising entropy generation and activation energy under unique conditions, specifically, with infinite shear rate viscosity and binary chemical reactions occurring over a nonlinear stretching sheet. Also, this innovative nanofluid model explicitly includes the vital role of Brownian motion and thermophoresis phenomenon, which are significant factors governing the movement and distribution of nanoparticles in the base fluid. A binary chemical reaction has also been taken in this study since it affects the mass transfer rates between different species present in the nanofluid. The ODEs were solved by using the bvp4c routine to effectively tackle momentum, temperature, and concentration equations. It is noted that velocity distribution increases with enhancement in the Weissenberg parameter, whereas the reverse trend is seen on the temperature profile. With an escalation of the viscosity ratio parameter, the velocity profile increases. Further, multiple linear regression has been utilised to statistically scrutinised the effect of pertinent parameters on skin friction coefficient, heat transfer rate, and Sherwood number by considering 64 sets of values of Nr in the range [0.3,0.6]. Nb & Nt in the range [0.1, 0.4] & [0.2, 0.3], respectively, to obtain the regression model.

R2 corrections on screening length

We study finite-coupling corrections on the screening length of a heavy quark-antiquark (QQ¯) pair moving in strongly coupled Super Yang-Mills plasma. We performed the analysis by computing the Wilson loop in a general AdS5 space with curvature-squared (R2) corrections and the Gauss-Bonnet (GB) background, respectively. For the general case, it is shown that the screening length with R2 corrections can be larger or smaller than that without R2 corrections depending on the correction coefficients, and these effects are more pronounced for the perpendicular case compared with parallel case. For the GB case, it turns out that increasing λGB (a dimensionless parameter in GB gravity) leads to decreasing the screening length thus reducing the binding energy of QQ¯ pair. In addition, we discuss how the screening length changes with the ratio of shear viscosity to entropy density at strong coupling under GB corrections.

Mixing ratio of nano hydroxyapatite and Epigallocatechin-3-gallate (EGCG) towards viscosity and antibacterial effect as a potential pulp capping Material: An experimental study

BackgroundFinding a new natural scaffold is challenging due to crucial impact on long-term treatment outcomes in pulp capping. In this context, nano hydroxyapatite (nano-HA) is a potential candidate having similar properties to bone tissue in the body. The compound is often synthesized with Epigallocatechin-3-gallate (EGCG) which offers anti-inflammatory and antibacterial properties. Therefore, this study aims to contribute novel insights into the development of effective pulp capping materials by determining the viscosity ratio of the combination of nano-HA and EGCG applied to the cavity according to standard pulp capping material, as well as proving the antibacterial effect against Lactobacillus acidophilus. MethodsThe combination of nano-HA – EGCG is divided into three treatment groups, (G1) 1:1 ratio, (G2) 1:1.5 ratio, (G3) 1:2 ratio, as well as control group G4 (Ca(OH)2 and aquadest) with a ratio of 1:1. Meanwhile, each group is tested for viscosity using a Brookfield viscometer. The well diffusion method is used to determine the antibacterial activity by measuring the diameter of the inhibition zone for each treatment, with C1 (Ca(OH)2 and aquadest) as control group at a ratio of 1:1, and three treatment groups (nano-HA – EGCG), (C2) 0.5:1 ratio, (C3) 1:1 ratio, and (C4) 2:1 ratio. ResultsThe results show that there is a difference in the viscosity of each group with G3 having a viscosity of 12.0183 cP, which is closest to control. Furthermore, significant differences are also reported in antibacterial activity between control and treatment groups. ConclusionThe ratio of 1:2 (G3) has a viscosity that closely matches the standard of pulp capping materials. The combinations of nano-HA and EGCG are proven to have antibacterial power against Lactobacillus acidophilus.

A computational study on transition mechanism of dripping to jetting flow in a flow‐focusing geometry

Abstract2D simulations have been performed to investigate flow regimes in a flow‐focusing geometry by changing the dispersed phase and continuous phase velocities. The dispersed phase is polydimethylsiloxane (PDMS), and the continuous phase is water. Simulations have been performed in a range of oil–water viscosity ratio from 3 to 50, and interfacial tension ranges from 0.0118 to 0.002 N/m. The walls of the microchannel are considered to be poly(methyl methacrylate) (PMMA) surfaces. The contact angle (θ) of an oil droplet in the presence of water wetting the PMMA surface is 140°. Our study observed two types of flow regimes, namely dripping and jetting, by changing the dispersed phase and continuous phase velocities. The sequential time steps of void fraction contour have been presented to explore the droplet formation mechanism. The droplet pinch‐off time and jet growth time have been calculated for the dripping and jetting regime, respectively. The outcomes are summarized in the form of a flow pattern map at a viscosity ratio of 12 and interfacial tension of 0.0118 N/m, which shows the transition boundary between dripping and jetting phenomena. The simulated transition boundary agrees well with the analytical solution available in the literature. The effect of oil–water viscosity ratio and interfacial tension on droplet size is also investigated. These findings will help understand different flow regimes and their transition in a flow focusing geometry and will directly apply to microfluidic platform‐based devices.

MODELLING OF INTERNAL TRANSFORMATIONS OF GAS PHASE IN POROUS MEDIA

The paper presents the research of temperature change in the investigated medium during dynamic expansion of gas (CO2) generated in reservoir conditions, diffusion of carbon dioxide into the displacing fluid and their influence on the displacement process. In-situ gas generation can provide a way to control the nonequilibrium fractal state at the interface under displacement in a porous medium. The change from fractal growth to non-fractal growth can be characterised as a function of density and viscosity ratios. This effect is shown in the increase of hydrocarbon displacement coefficient due to the equalisation of densities of displacing and displaced agents as a consequence of the increase in gas saturation of the fluid.

Preparation, structure, and properties of biodegradable core‐sheath composite fibers derived from poly (butylene adipate‐co‐terephthalate) and polylactic acid

AbstractThe non‐biodegradability of Ethylene‐Propylene Side‐by‐Side (ES) fibers has led to significant environmental pollution from waste sanitary products, thereby posing a severe challenge to the environment. Replacing traditional non‐biodegradable materials with biodegradable polymeric materials is the most effective method to achieve a green environment. In this study, core‐sheath fibers composed of biodegradable poly (butylene adipate‐co‐terephthalate) (PBAT) as the sheath layer and polylactic acid (PLA) as the core layer were fabricated. The effects of different viscosity ratios and the composite ratios of sheath and core on the structure and performance of the resultant core‐sheath fibers were investigated in detail. The results showed that when the PBAT/PLA composite ratio is 50:50 and the viscosity ratio range from 0.8 to 1.43, the PBAT/PLA core‐sheath composite fibers exhibit good spinnability and a complete core‐sheath structure, with their tensile properties comparable to those of PP/PE core‐sheath composite fibers. Further research found that when the viscosity ratio was 1.00 and the PLA component content in the PBAT/PLA composite fibers increased from 40% to 60%, the fibers still maintained good spinnability and a complete core‐sheath structure. In addition, when the PBAT/PLA composite ratio was 60:40, after 120 days of biodegradation, its strength retention rate was only 35.2%.

Dynamics and active mixing of a droplet in a Stokes trap

Particle trapping and manipulation have a wide range of applications in biotechnology and engineering. Recently, a flow-based, particle-trapping device called the Stokes trap was developed for trapping and control of small particles in the intersection of multiple branches in a microfluidic channel. This device can also be used to perform rheological experiments to determine the viscoelastic response of an emulsion or suspension. We show that besides these applications, the various flow modes produced by the Stokes trap are able to manipulate drop shapes and induce active mixing inside droplets. To this end, we analyse the dynamics of a droplet in a Stokes trap through boundary-integral simulations. We also explore the dynamic response of drop shape with respect to distinct external flow modes, which allows us to perform numerical experiments such as step strain and oscillatory extension. A linear controller is used to manipulate drop position, and the drop deformation is characterized by a spherical-harmonic decomposition. For small drop deformations, we observe a linear superposition of harmonics, which, surprisingly, seems to hold even for moderate deformations. This result indicates that such a device can be used for shape control of droplets. We also investigate how the different flow modes may be combined to induce mixing inside the droplets. The transient combination of modes produces an effective chaotic mixing, which is characterized by a mixing number. The mixing inside the droplet can be further enhanced for lower viscosity ratios and low, but non-zero capillary number and flow frequencies.

A New Solution of Drag for Newtonian Fluid Droplets in a Power-Law Fluid

Understanding flow behaviors of multiple droplets in complex non-Newtonian fluids is crucial in many science and engineering applications. In this study, a new and improved analytical solution is developed based on the free surface cell model for the flow drag of swamp of Newtonian fluid drops through a power-law fluid. The developed solution is accurate and compares well to the numerical solutions. The improvement involves a new quantification of shear stress boundary condition at the interface and a more consistent approximation in linearizing the power-law fluid flow governing equation. The Newtonian fluid solutions can be reasonably used to linearize the flow governing equation. The approximation of the boundary conditions at the interface, however, has a major impact on the model prediction. The main improvement in the new solution is observed under the condition of comparable viscosities of the Newtonian drops and the outside power-law fluid when the results are sensitive to the interface boundary condition. Under the two extreme conditions of high viscosity ratio (approaching particles) and low ratio (approaching bubbles), the present and existing solutions converge.

Production and characterization of a blood analogue based on alginate microparticles

This work addresses the need for a universal blood substitute by focusing on developing alginate-based microparticles engineered to replicate the mechanical properties of red blood cells (RBCs). Alginate, known for its biocompatibility and tunable mechanical properties, is used to create microparticles that closely resemble RBCs in size and shape. These alginate microparticles are produced through premix membrane emulsification (PME), ensuring a uniform size distribution. The viscosity ratio and the size of the filter pores influence the final size of the microparticles. Filters with pores of 20 µm were used to produce 5 wt% alginate microparticles with a diameter of 7.81 µm ± 0.77, and filters with pores of 30 µm were used to produce 0.5 wt% alginate microparticles with a diameter of 8.69 µm ± 3.30. The Deformability Index (DI) of the alginate microparticles follows the correlation that microparticles with higher elastic modulus exhibit lower DI values. The DI found for 0.5 wt% alginate microparticles solution is higher than the DI found for 5 wt% alginate microparticles. The DI of RBCs is higher than the ones found for the alginate microparticles, however the value is in the range of the experimental error. Rheological studies reveal that suspensions of 25–30 wt% alginate microparticles exhibit a shear-thinning behavior similar to human blood. The DI of the alginate microparticles shows little influence on the rheology of the suspensions. Furthermore, the Cell-Free Layer (CFL) of alginate microparticles is close to that of RBCs, reinforcing the potential of alginate as a suitable material for blood substitute development. The alginate microparticles produced in this work show a great potential to contribute to creating a blood-mimicking fluid for applications in medical treatments and research.

On development of lattice-Boltzmann method based multi phase flow solver

A numerical methodology based on lattice Boltzmann and level set function is presented to simulate the two-phase flows with stringent density and viscosity ratio. Two different strategies - single grid (SGLBLS) and dual grid (DGLBLS) are used. For accurate computation of interfacial forces in DGLBLS, the level set equations are solved on a uniform grid which is twice that for lattice-Boltzmann equations. The code validation and performance of SGLBLS and DGLBLS is carried on three different problems: Young’s Laplace law, 2D rising bubble and Rayleigh–Taylor instability. The results show that the representation of the interface is more accurate in DGLBLS with significantly less mass error - establishing it as an accurate method to handle stringent density and viscosity ratio. The comparison between DGLBLS and SGLBLS shows that the DGLBLS leads to a large improvement in the accuracy of the results with only slight increase in the computational cost.

Overstability of the 2:1 mean motion resonance: Exploring disc parameters with hydrodynamic simulations

Context. Resonant planetary migration in protoplanetary discs can lead to an interplay between the resonant interaction of planets and their disc torques called overstability. While theoretical predictions and N-body simulations hinted at its existence, there was no conclusive evidence until hydrodynamical simulations were performed. Aims. Our primary purpose is to find a hydrodynamic setup that induces overstability in a planetary system with two moderate-mass planets in a first-order 2:1 mean motion resonance. We also aim to analyse the impact of key disc parameters, namely the viscosity, surface density, and aspect ratio, on the occurrence of overstability in this planetary system when the masses of the planets are kept constant. Methods. We performed 2D locally isothermal hydrodynamical simulations of two planets, with masses of 5 and 10 $M_ oplus $, in a 2:1 resonance. Upon identifying the fiducial model in which the system exhibits overstability, we performed simulations with different disc parameters to explore the effects of the disc on the overstability of the system. Results. We observe an overstable planetary system in our hydrodynamic simulations. In the parameter study, we note that overstability occurs in discs characterised by low surface density and low viscosity. Increasing the surface density reduces the probability of overstability within the system. A limit cycle was observed in a specific viscous model with $ nu $. In almost all our models, planets create partial gaps in the disc, which affects both the migration timescale and structure of the planetary system. Conclusions. We demonstrate the existence of overstability using hydrodynamic simulations but find deviations from the analytic approximation and show that the main contribution to this deviation can be attributed to dynamic gap opening.

Phase inversion detection in immiscible binary polymer blends via zero‐shear viscosity measurements

AbstractIn the present work, we demonstrate that zero‐shear viscosity is a sensitive rheological function to detect phase inversion in immiscible binary polymer blends characterized by a viscosity ratio larger than one. The phase inversion of poly(propylene) (PP)/low‐density poly(ethylene) (LDPE) and poly(styrene) (PS)/LDPE, at various compositions, was assessed via our novel approach. For both blends, three distinctive regions could be determined through zero‐shear viscosity measurements; the LDPE matrix, the co‐continuous phase, and the PS or PP matrix. For PP/LDPE blends, the co‐continuous structure was between 50 and 75 wt.% PP, and for PS/LDPE blends the co‐continuous structure was between 45 and 75 wt.% PS, in agreement with scanning electron microscopy analysis, empirical model predictions, and literature data.Highlights Phase inversion revealed via viscosity measurements. Limitations of linear viscoelastic models for immiscible blends assessed.

Preparation and characterization of thermo-processable poly(benzimidazole imide)s with soluble and high heat-resistance containing N-phenyl-benzimidazole

In this paper, we present a synthetic strategy for N-phenyl substituted benzimidazole-derived diamines, including 2-(4-(4-aminophenoxy) phenyl)-1-phenyl-1H-benzo[d]imidazole-5-amine (para-diamine) and 2-(3-(4-aminophenoxy) phenyl)-1-phenyl-1H-benzo[d]imidazole-5-amine (meta-diamine). Two distinct series of N-phenyl substituted poly (benzimidazole imide)s (PBIPIs) were synthesized via reaction with different aromatic dianhydrides. The simulation reveals distinct amine reaction activities of two diamine monomers. The obtained PBIPIs exhibit exceptional heat resistance attributed to N-phenyl substituted benzimidazole (BI). The temperature at which weight loss of 5 % (T5%) is in the range of 491–595 °C under N2 environment, while the glass transition temperature is 237–329 °C. The PBIPIs exhibit specific solubility characteristics due to the flexible ether linkage groups' non-coplanarity and bulky pendant benzene groups. The PBIPIs possess tensile strength between 108 and 142 MPa, a tensile modulus of 4.0–5.9 GPa, and an elongation at a break of 4.2–26.4 %, indicating excellent mechanical properties. Additionally, the PBIPI with controlled molecular weight generated from BPADA incorporating 2-(3-(4-aminophenoxy) phenyl)-1-phenyl-1H-benzo[d]imidazole-5-amine (B-BPADA-PA) demonstrates exceptional melt processability. B-BPADA-PA possesses remarkable melt stability since its minimum complex viscosity is only 2100 Pa⋅s at 400 °C, and its melt viscosity ratio is 1.34 at 380 °C.

MRI turbulence in vertically stratified accretion discs at large magnetic Prandtl numbers

ABSTRACT The discovery of the first binary neutron star merger, GW170817, has spawned a plethora of global numerical relativity simulations. These simulations are often ideal (with dissipation determined by the grid) and/or axisymmetric (invoking ad hoc mean-field dynamos). However, binary neutron star mergers (similar to X-ray binaries and active galactic nuclei inner discs) are characterized by large magnetic Prandtl numbers, $\rm Pm$, (the ratio of viscosity to resistivity). $\rm Pm$ is a key parameter determining dynamo action and dissipation but it is ill-defined (and likely of order unity) in ideal simulations. To bridge this gap, we investigate the magnetorotational instability (MRI) and associated dynamo at large magnetic Prandtl numbers using fully compressible, three-dimensional, vertically stratified, isothermal simulations of a local patch of a disc. We find that, within the bulk of the disc (z ≲ 2H, where H is the scale-height), the turbulent intensity (parametrized by the stress-to-thermal-pressure ratio α), and the saturated magnetic field energy density, Emag, produced by the MRI dynamo, both scale as a power with Pm at moderate Pm (4 ≲ Pm ≲ 32): Emag ∼ Pm0.74 and α ∼ Pm0.71, respectively. At larger Pm (≳ 32), we find deviations from power-law scaling and the onset of a plateau. Compared to our recent unstratified study, this scaling with Pm becomes weaker further away from the disc mid-plane, where the Parker instability dominates. We perform a thorough spectral analysis to understand the underlying dynamics of small-scale MRI-driven turbulence in the mid-plane and of large-scale Parker-unstable structures in the atmosphere.