Capillary Number Research Articles

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<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.

Microdroplet formation of water and alumina nanofluid in a T-junction microchannel

A scarcity of studies about nanofluids’ utilization in droplet formation inside microdevices currently hovers in the literature although potential applications of nanoparticles in a microfluidic environment are foreseen. For this purpose, experimentally assessing both nanofluid and microdroplet characteristics is fundamental. This work reports a series of experimental tests on the microdroplet formation of distilled water (DIW) and DIW-based aluminum oxide (Al2O3) nanofluid in a microfluidic T-junction. While water and nanofluid are used as the dispersed phase, mineral oil is used as the continuous phase. Microdroplet formation in the squeezing, transitional, and dripping regimes is characterized and scaling laws for the non-dimensional droplet volumes are presented. The effects of flow rate, capillary number, microchannel aspect ratio, and nanoparticle concentration are investigated. The addition of Al2O3 nanoparticles to the water is observed to have a major impact in the transitional regime (up to 40% increase), whereas in the dripping regime its influence is lower, with less than 10% difference. This was attributed to the nanofluid's enhanced interfacial tension and viscosity compared to the DIW, as well as possible adsorption at the surface.

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

Understanding fingering, as a challenge to stable displacement during the immiscible flow, has become a crucial phenomenon for geological carbon sequestration, enhanced oil recovery, and groundwater protection. Typically governed by gravity, viscous and capillary forces, these factors lead invasive fluids to occupy pore space irregularly and incompletely. Previous studies have demonstrated capillary numbers, describing the viscous and capillary forces, to quantificationally induce evolution of invasion patterns. While the evolution mechanisms of invasive patterns have not been deeply elucidated under the constant capillary number and three variable parameters including velocity, viscosity, and interfacial tension. Our research employs two horizontal visualization systems and a two-phase laminar flow simulation to investigate the tendency of invasive pattern transition by various parameters at the pore scale. We showed that increasing invasive viscosity or reducing interfacial tension in a homogeneous pore space significantly enhanced sweep efficiency, under constant capillary number. Additionally, in the fingering crossover pattern, the region near the inlet was prone to capillary fingering with multi-directional invasion, while the viscous fingering with unidirectional invasion was more susceptible occurred in the region near the outlet. Furthermore, increasing invasive viscosity or decreasing invasive velocity and interfacial tension promoted the extension of viscous fingering from the outlet to the inlet, presenting that the subsequent invasive fluid flows toward the outlet. In the case of invasive trunk along a unidirectional path, the invasive flow increased exponentially closer to the outlet, resulting in a significant decrease in the width of the invasive interface. Our work holds promising applications for optimizing invasive patterns in heterogeneous porous media.

Detachment dynamics of sessile droplets triggered by interaction forces between oil and wall in a microchannel

Understanding the detachment dynamics of droplets adhered to reservoir walls holds significant importance for the residual oil displacement process in high water-cut oilfields. Existing studies demonstrated that increasing mainstream shear by adjusting displacement flow and weakening wall adhesion by increasing contact angle can enhance droplet detachment. However, the complex physical and chemical oil–wall interactions, a crucial reservoir feature, cannot be solely relied on the macroscopic representation through contact angle. A deviation in understanding the process of crude oil droplet detachment would be resulted due to the change of wall adhesion. Considering the intricate physical and chemical interactions between oil and walls, in this paper, we employed the extended Derjaguin–Landau–Verwey–Overbeek (EDLVO) theory to establish an oil–wall interaction forces system, and coupling computational fluid dynamics method to further explore the detachment dynamics of sessile oil droplets in a microchannel under varying EDLVO forces. The findings showed that (1) by increasing the Capillary number, the droplets gradually occur in four typical dynamic states: static, sliding, detachment, and pinch-off. (2) Static droplets are more prone to experience sliding behavior when influenced by EDLVO forces. (3) For droplets undergoing detachment and pinch-off, EDLVO forces inhibit entrainment behavior. These results contribute to an enhanced comprehension of droplet detachment dynamics in reservoirs, offering fresh insights for enhanced oil recovery strategies.

Numerical investigation on the deformation and breakup of an elastoviscoplastic droplet in simple shear flow

In this paper, direct numerical simulations (DNSs) are performed to investigate the deformation and breakup of an elastoviscoplastic (EVP) droplet in a Newtonian matrix under simple shear flow. The two-phase interface is captured by the volume-of-fluid (VOF) method with adaptive mesh refinement technique. The Saramito model (Bingham model coupled exponential Phan-Thien–Tanner viscoelastic model) is used to characterize the rheological behavior of the droplet. The droplet deformation and conformational state are studied with different Capillary numbers Ca, Weissenberg numbers Wi, and Bingham numbers Bi, which represent the surface tension, elasticity, and yield stress of the droplet, respectively. Our results show that droplet deformation occurs at low Ca, while breakup occurs at high Ca. The droplet non-monotonically deforms with increasing Wi and Bi, while is elongated for higher Ca. In addition, three breakup modes (mid-point pinching, transitional breakup, and homogeneous breakup) are reported for EVP droplets, in which transitional breakup disappears due to the influence of high elasticity. The conformational state of the droplet intuitively demonstrates the change of breakup from horizontal shear to vertical breakup. In spite of the fact that the surface tension always inhibits the deformation of droplets, the present work indicates that Bi has little effect on the deformation with high Wi and high Ca, while the influence is obvious at low Wi and Ca. The observed elastic and plastic effects on droplet deformation and breakup are believed to have significant impacts, as yield stress fluids are widely encountered in industrial applications.

Determination of the vimentin marker in the placenta of cows in normal and delayed afterbirth

Modern dairy enterprises suffer financial losses due to the high morbidity of the dairy herd after calving. The current study presents the distribution of the extracellular matrix of the ratio of mesenchymal elements of the placenta in cows during physiological and complicated labor with retained placenta. Caruncle and cotyledon tissues were collected every 6 hours after spontaneous labor until the membranes were released. Depending on the time of release of membranes after birth, the samples were classified as follows: 1 - control group, in which the membranes were released within 6 hours after birth, considered complete, spontaneous and physiological (Partus normalis); 2 - experimental group, in which the membranes were released 9-12 hours after the fetus was delivered, the birth was considered pathological with retention of the placenta (Retenzio sekundarium). Identification of changes in the content of vimentin-containing elements involves the development of a system for express diagnostics of reproductive pathologies in dairy cattle during labor and after calving. Samples of placenta from cows undergoing physiological labor and placenta retention were subjected to standard histological procedures. Paraffin sections of the placenta, 5 µm thick, were mounted on glasses treated with poly-L-lysine (Menzel). Using immunohistochemical and immunofluorescence double staining, the immunolocalization of antibodies to vimentin was studied using clone EPR3776 (rabbit, monoclonal, Taiwan, GeneTex, Int. Corp). The localization of the content of intermediate filaments of the mesenchymal phenotype in the cow placenta was studied, in which the presence of a large number of small capillaries was revealed both in the villi of the cotyledons and in the caruncular crypts during normal pregnancy and childbirth, as well as the equilibrium ratio of mesenchymal structures in the placenta. In childbirth complicated by placenta retention, a decrease in the vascularization of chorionic villi in the cotyledons and degradation of filaments involved in the formation of cellular contacts between the cytotrophoblasts of the chorionic villi of the cotyledons of the fetal part of the placenta and endothelial and epithelial cells of the crypts of the caruncles of the maternal part of the placenta were demonstrated. Pronounced expression of vimentin was found in the cells lining the crypts of caruncles, as well as in the cytoplasmic membrane of villous cytotrophoblasts. A study of the ratio of mesenchymal elements using the immunofluorescent method of double staining of antibodies to vimentin showed that a significant decrease in them both in the cytotrophoblasts of cotyledons and in the epithelial cells of caruncles is observed in the placenta of cows with the development of a state of placental insufficiency, leading to a complication of labor by retention of the placenta. The present study provides the first evidence that vimentin is expressed in bovine placentomes during the gestational, prenatal, and parturient periods and suggests that this filament may, in combination with steriodogenic homones, mediate the separation of the fetal placenta from the maternal placenta.

Deposition of shear‐thinning viscoelastic fluids by an elongated bubble in a circular channel regarding the weakly elastic regime

AbstractThin‐film deposition of fluids is ubiquitous in a wide range of engineering and biological applications, such as surface coating, polymer processing, and biomedical device fabrication. While the thin viscous film deposition in Newtonian fluids has been extensively investigated, the deposition dynamics in frequently encountered non‐Newtonian complex fluids remain elusive, with respect to predictive scaling laws for the film thickness. Here, we investigate the deposition of thin films of shear‐thinning viscoelastic fluids by the motion of a long bubble translating in a circular capillary tube. Considering the weakly elastic regime with a shear‐thinning viscosity, we provide a quantitative measurement of the film thickness with systematic experiments. We further harness the recently developed hydrodynamic lubrication theory to quantitatively rationalize our experimental observations considering the effective capillary number and the effective Weissenberg number , which describe the shear‐thinning and the viscoelastic effects on the film formation, respectively. The obtained scaling law agrees reasonably well with the experimentally measured film thickness for all test fluids. Our work may potentially advance the fundamental understanding of the thin‐film deposition in a confined geometry and provide valuable engineering guidance for processes that incorporate thin‐film flows and non‐Newtonian fluids.

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.

Numerical simulation study of bubble breakup mechanism in microchannels with V-shaped obstacle

Microfluidic gas-liquid two-phase flow in microchannels plays a crucial role in diverse applications, from electronics cooling to biomedical engineering. Precisely controlling microbubble formation and breakup is essential for industrial microfluidic processes. This study investigates microbubble breakup in microchannels with V-shaped obstacles. Four breakup patterns are identified: no breakup, breakup with permanent gaps, breakup with partly obstruction, and breakup with permanent obstruction. The bubble breakup with permanent obstruction could maintain a wider flow pattern range. The bubble breakup process is categorized into three stages: squeezing, transition, and pinch-off. We observe power-law relationships between bubble characteristics and dimensionless time in each stage, and the impact of the capillary number Ca and liquid phase viscosity μL on bubble properties. This research deepens our understanding of gas-liquid two-phase flow in microchannels with obstacle structures and is relevant to analytical chemistry and fine chemical engineering applications.

Dynamics of a viscoelastic droplet migrating in a ratchet microchannel under AC electric field

Droplet-based microfluidic devices can be powered or manipulated by applying an external electric field, and the ability to precisely control the flow in such devices is essential for various engineering and biomedical applications. In this numerical study, we investigate the deformation dynamics of a viscoelastic droplet in a ratchet microchannel under the influence of an AC electric field. We employ the leaky-dielectric electrohydrodynamic model for both the immiscible fluid phases coupled with the Oldroyd-B model for the droplet fluid. The effect of geometrical parameters such as the type of ratchet and the wavenumber of the ratchets along with the flow parameters such as the electrocapillary number, Weissenberg number and the capillary number significantly affect the droplet shape dynamics and the polymer chain extension. For the parameters considered in this work, the electric force tends to stretch the droplet in the streamwise direction and enhances the droplet deformation and polymer extension. Several interesting effects arise as a result of the coupling of the periodic hydrodynamic forcing of the ratchet walls and the electric field. Specifically, an exponential rise in the polymer chain extension for higher ratchet wavenumbers is observed, along with the cross-stream migration of the droplet for higher electrocapillary numbers when it reaches the outlet of the ratchet constriction.

Application of an artificial intelligence for quantitative analysis of endothelial capillary beds in vitro.

The use of endothelial cell cultures has become fundamental to study angiogenesis. Recent advances in artificial intelligences (AI) offer opportunities to develop automated assessment methods in medical research, analyzing larger datasets. The aim of this study was to compare the application of AI with a manual method to morphometrically quantify in vitro angiogenesis. Co-cultures of human microvascular endothelial cells and fibroblasts were incubated mimicking endothelial capillary-beds. An AI-software was trained for segmentation of endothelial capillaries on anti-CD31-labeled light microscope crops. Number of capillaries and branches and average capillary diameter were measured by the AI and manually on 115 crops. The crops were analyzed faster by the AI than manually (3 minutes vs 1 hour per crop). Using the AI, systematically more capillaries (mean 48/mm2 vs 27/mm2) and branches (mean 23/mm2 vs 11/mm2) were counted than manually. Both methods had a strong linear relationship in counting capillaries and branches (r-capillaries = 0.88, r-branches = 0.89). No correlation was found for measurements of the diameter (r-diameter = 0.15). The present AI reduces the time required for quantitative analysis of angiogenesis on large datasets, and correlates well with manual analysis.

Oscillations of a spherical particle in the presence of a flat interface separating two fluid phases

An analytical–numerical approach based on collocation techniques is introduced to examine the challenge of characterizing Stokes flow induced by a spherical particle in perpendicular motion to a plane interface that divides two semi-infinite, immiscible viscous fluid phases. The movement is examined under the conditions of low Reynolds and capillary numbers, where the interface undergoes negligible deformation. We contemplate both the rectilinear oscillations along and the rotational oscillation around an axis that is perpendicular to the interface. A comprehensive solution is formed by combining basic solutions in both cylindrical and spherical coordinate systems through superposition. Firstly, the boundary conditions at the fluid–fluid interface are fulfilled through Fourier–Bessel transforms, followed by addressing the conditions at the particle’s surface using a boundary collocation scheme. The drag force and torque coefficients, both in-phase and out-of-phase, acting on the particle are determined with satisfactory convergence across different geometric and physical parameter values. These results are illustrated through graphs and tables. We compare our results of drag force and torque coefficients with existing data in the literature, specifically for the limiting cases. The outcomes of this study highlight the substantial impact of the interface on both drag force and torque coefficients. This inquiry is driven by the necessity to enhance our comprehension of the fluid tapping mode in atomic force microscope devices, particularly when this mode involves an interface substrate with another fluid.

Direct numerical simulations of microlayer formation during heterogeneous bubble nucleation

In this article, we present direct numerical simulation results for the expansion of spherical cap bubbles attached to a rigid wall due to a sudden drop in the ambient pressure. The critical pressure drop beyond which the bubble growth becomes unstable is found to match well with the predictions from classical theory of heterogeneous nucleation imposing a quasi-static bubble evolution. When the pressure drop is significantly higher than the critical value, a liquid microlayer appears between the bubble and the wall. In this regime, the interface outside the microlayer grows at an asymptotic velocity that can be predicted from the Rayleigh–Plesset equation, while the contact line evolves with another asymptotic velocity that scales with a visco-capillary velocity that obeys the Cox–Voinov law. In general, three distinctive regions can be distinguished: the region very close to the contact line where dynamics is governed by visco-capillary effects, an intermediate region controlled by inertio-viscous effects away from the contact line yet inside the viscous boundary layer, and the region outside the boundary layer dominated by inertial effects. The microlayer forms in a regime where the capillary effects are confined in a region much smaller than the viscous boundary layer thickness. In this regime, the global capillary number takes values much larger then the critical capillary number for bubble nucleation, and the microlayer height is controlled by viscous effects and not surface tension.

A modified forcing approach in the Rothman–Keller method for simulations of flow phenomena at low capillary numbers

AbstractThe lattice‐Boltzmann method (LBM) is becoming increasingly popular for simulating multi‐phase flows on the microscale because of its advantages in terms of computational efficiency. Many applications of the method are restricted to relatively simple geometries. When a more complex geometry is considered—circular and inclined microchannels—some important physical phenomena may not be accurately captured, especially at low capillary numbers. A Y‐Y micro‐fluidic channel, widely used for a range of applications, is an example of a more complex geometry. This work aims to capture the various flow phenomena, with an emphasis on parallel flow and leakage, using the Rothman–Keller (RK) model of the LBM. To this purpose, we modify the forcing term to implement the surface tension for use at low capillary numbers. We compare the simulation results of the RK model with and without the force modification with experiments, Volume of Fluid and the phase field method and observe that the modified forcing term is an improvement over the current RK model at low capillary numbers, and it also captures parallel flow and leakage more accurately than the other simulation techniques.

Dynamics of meniscus-bound particle clusters in extensional flow

Capillary suspensions are three-phase mixtures containing a solid particulate phase, a continuous liquid phase, and a second immiscible liquid forming capillary bridges between particles. Capillary suspensions are encountered in a wide array of applications including 3D printing, porous materials, and food formulations, but despite recent progress, the micromechanics of particle clusters in flow is not fully understood. In this work, we study the dynamics of meniscus-bound particle clusters in planar extensional flow using a Stokes trap, which is an automated flow control technique that allows for precise manipulation of freely suspended particles or particle clusters in flow. Focusing on the case of a two-particle doublet, we use a combination of experiments and analytical modeling to understand how particle clusters rearrange, deform, and ultimately break up in extensional flow. The time required for cluster breakup is quantified as a function of capillary number Ca and meniscus volume V. Importantly, a critical capillary number Cacrit for cluster breakup is determined using a combination of experiments and modeling. Cluster relaxation experiments are also performed by deforming particle clusters in flow, followed by flow cessation prior to breakup and observing cluster relaxation dynamics under zero-flow conditions. In all cases, experiments are complemented by an analytical model that accounts for capillary forces, lubrication forces, hydrodynamic drag forces, and hydrodynamic interactions acting on the particles. Results from the analytical models are found to be in good agreement with experiments. Overall, this work provides a new quantitative understanding of the deformation dynamics of capillary clusters in extensional flow.

The bubble merger in rectangular microchannels during boiling processes based on conjugate heat transfer

In recent years, boiling heat transfer in microchannels has become an effective solution for managing high heat flux in electronic devices. Numerical simulations offer details on flow characteristics that experimental methods cannot capture, deepening our understanding of boiling mechanisms within microchannels. In this study, we developed a self-programmed solver, “interMultiRegionFoam,” based on the volume of fluid (VoF) method, phase-change mass transfer models, and conjugate heat transfer. Analyzing the force acting on individual bubbles, a model for two bubbles' merger was constructed, encompassing three stages: bubble bridging, bubble retraction, and bubble contraction. For isolated bubbles, during the restricted growth stage, the dry patch length increases by only 25% with an increase in the Capillary number, while in the elongation growth stage, it grows fivefold. Furthermore, the investigation into four typical bubble merger cases within microchannels demonstrated that the bubble merger model effectively describes the process. During the restricted and free growth stages, bubble merger was observed to enhance heat transfer, and the heat transfer coefficient in the bottom region of the macrolayer increased by a maximum of 16%. However, when bubbles merge in the elongation growth stage, the maximum increase in the heat transfer coefficient at the bottom of the macrolayer is only 7%. Several factors contribute to the enhanced heat transfer during bubble merger, including the evaporation and rewetting of macrolayer liquid, as well as the replenishment of the microlayer. Moreover, the disturbance caused by bubble merger and transient conduction arising from bubble retraction and contraction contributes to the enhancement in heat transfer. With an increase in the contact angle, the peak heat flux gradually decreases, with a maximum reduction of 27%. As the heat flux increases, the Nusselt number gradually increases, reaching a maximum peak increase of 52%. These studies provide theoretical guidance for the design of wall modifications and nucleation in microchannels.

Design and fabrication of a tellurite hollow-core anti-resonant fiber for mid-infrared applications

The hollow core anti-resonant fibers (HC-ARFs) based on soft glass are in high demand for 3-6 µm laser delivery. A HC-ARF based on tellurite glass with 6 touching capillaries as cladding was designed and fabricated for the first time, to the best of our knowledge. A relatively low loss of 3.75 dB/m at 4.45 µm was realized in it. The effects of capillary number, core diameter, wall thickness of capillary, and material absorption loss on the loss of the HC-ARF were analyzed by the numerically simulation. The output beam quality was measured and the influence of bending on the fiber loss was discussed. The results of numerical simulation suggested that the theoretical loss of the prepared fiber can be reduced to 0.1 dB/m, indicating that tellurite HC-ARFs have great potential for mid-infrared laser applications.

Viscoelasticity of suspension of red blood cells under oscillatory shear flow

We present a numerical analysis of the rheology of a suspension of red blood cells (RBCs) for different volume fractions in a wall-bounded, effectively inertialess, small amplitude oscillatory shear (SAOS) flow for a wide range of applied frequencies. The RBCs are modeled as biconcave capsules, whose membrane is an isotropic and hyperelastic material following the Skalak constitutive law. The frequency-dependent viscoelasticity in the bulk suspension is quantified by the complex viscosity, defined by the amplitude of the particle shear stress and the phase difference between the stress and shear. SAOS flow basically impedes the deformation of individual RBCs as well as the magnitude of fluid-membrane interactions, resulting in a lower specific viscosity and first and second normal stress differences than in steady shear flow. Although it is known that the RBC deformation alone is sufficient to give rise to shear-thinning, our results show that the complex viscosity weakly depends on the frequency-modulated deformations or orientations of individual RBCs but rather depends on combinations of the frequency-dependent amplitude and phase difference. The effect of the viscosity ratio between the cytoplasm and plasma and of the capillary number is also assessed.