Outer Fluid Research Articles

Parametric study of the collision modes of compound droplets in simple shear flow

Compound droplet collision has been found in various industrial and academic applications. Such colliding phenomena of two droplets in simple shear flow are numerically resolved by a front-tracking technique. Initially, each compound droplet, assumed cylindrical, contains one concentric inner droplet. They are separated at the lateral and vertical intervals denoted by Δx0 and Δy0. Because of the shear flow, the compound droplets interact with each other and exhibit three collision modes: passing-over, merging (i.e. coalescence) and reversing. These modes and their transition are affected by many parameters including the Reynolds Re and Capillary Ca numbers (based on the properties of the outer fluid), the viscosity ratios μ13 and μ23, the interfacial tension ratio σ12 of the inner to outer interfaces, the ratio of the radii of the inner to outer droplets R12 and the initial distance between them (in terms of Δx0 and Δy0). It is found that from a merging mode, decreasing Re from 2.51 to a value less than or equal to 1.0 induces a transition to a reversing mode, whereas, increasing Ca from 0.005 to a value greater than or equal to 0.04 leads to a transition to a passing-over mode. A transition from the merging to passing-over modes also appears when varying μ23 in the range of 0.1–10.0 or varying R12 in the range of 0.2–0.8. A transition from a passing-over mode to a reversing one is available when increasing Δx0 or decreasing Δy0. Three modes of collision all occur when μ13 is varied in the range of 0.1–10.0. However, the variation of σ12 does not induce any transition between different modes. Several phase diagrams in terms of Re versus Ca, or Δx0 versus Δy0 are also proposed to show the transitions between these modes.

On demand coalescence in microchannel: Viscosity matters

Here, the coalescence of similar and dissimilar droplets has been investigated in microfluidics while varying the rheological and physical properties (e.g. viscosity, density) of the fluids.Our data indicate that in early regimes, the dynamics of coalescence depends on the properties of the inner fluid, which can generate a dominant viscous or inertial regime, while the outer fluid controls the activation or inhibition of the merging droplets. Besides, the models describing the mechanism in vacuum or in a very low viscous outer fluid become invalid when one of those conditions fails. An accurate modification resulted from accounting for the viscosity ratio of the inner and outer fluid. A phase diagram showing the crossovers into the different possible late-time dynamics identifies that, depending on the ratio of the viscosities of the inner and outer fluid, the coalescence develops by an inertial limited viscous, pure viscous or inertial regime.

Experimental and numerical study of wavy mechanical face seals operating under pressure inversions

This paper investigates the impact of the face waviness and pressure inversions on the leakage and on the outer fluid entry of mechanical face seals using a numerical model and an experimental setup. The numerical model couples a transient Reynolds equation, an analytical contact model, a force balance solver, and a solver for the thermo-mechanical deformations. The experimental tests on a face seal with low waviness and on a face seal with high waviness provide leakage and outer fluid entry data, which are reproduced by the model. Contrary to the face seal with low waviness, the face seal with high waviness has poor performance and the pressure inversions increase significantly the ingression of outer fluid. The parametric study shows a decrease of leakage with increasing spring force, and an increase of leakage and outer fluid entry with increasing values of waviness amplitude. The higher leakage observed for wavy seals is shown to be due to the higher average film thickness, and to some extent due to the mechanisms associated with waviness: hydrodynamic pressure generation, film squeeze and stretching.

Direct numerical simulation of a supersonic turbulent boundary layer subject to adverse pressure gradient induced by external successive compression waves

A freestream Mach 2.9 flat-plate supersonic turbulent boundary layer subject to a “pure” adverse pressure gradient (APG) without the impact of wall curvatures is studied by direct numerical simulation and compared with a benchmark flow with zero pressure gradient. Due to APG, the streamwise velocity shows an increase in the near-wall region and a reduction in the outer boundary layer. The principal strain rate shows a sandwich distribution along the wall-normal direction. The mismatch between the temperature and velocity fluctuations in both the inner and the outer layer is observed. Enhanced LSMs (large-scale motions) and large velocity patches are the typical flow structures in the outer and inner boundary layer subject to APG, respectively. From the analysis of quadrant decomposition, the sweep events dominate in the near-wall region while ejection events dominate the rest of the boundary layer. It is found that the baroclinicity plays a significant role in the formation of the enhanced LSMs in the outer boundary layer and the near-wall velocity patches. The resulting amplified vorticity further drives the interactive motions of the outer fluid and inner fluid. The turbulent kinetic energy and turbulent Mach number profiles are amplified by APG and a second peak is observed in both profiles. Turbulent energy budget analysis demonstrates that both the production and viscous effects are strengthened in the near-wall region while in the outer layer, the production is significantly amplified and balanced by the increased convection and turbulent transport.

Effect of Magnetic Field on the Steady Viscous Fluid Flow Around a Semipermeable Spherical Particle

An analytical solution is presented for the steady axisymmetrical Stokes flow of an electrically conducting viscous incompressible fluid through a partially permeable sphere subjected to a uniform transverse magnetic field. The considered flow is divided into two regions, outer viscous fluid region and inner semipermeable region, which are governed by modified Stokes and Darcy’s law respectively due to the presence of magnetic field in the flow regions. The boundary conditions used at the interface are continuity of normal component of velocity, vanishing of tangential component of velocity and continuity of pressure at the surface in contact with the fluid and the semipermeable sphere. An expression for drag force acting on the semipermeable sphere in presence of magnetic field is obtained. Enhancement of drag force exerted on the particle is seen on application of magnetic field. The effect of Hartmann numbers, permeability parameter on the hydrodynamic drag force were discussed. Some renowned results are obtained as the limiting cases.

Dynamics of an electrified confined planar jet in a zero gravity environment

The present work deals with temporal electro-aerodynamics instability properties of an inviscid confined planar jet in a zero gravity environment and the existence of electric field. The considered system is composed of a horizontal liquid sheet surrounded by two identical moving layers of fluid. The electric field acts uniformly normal to the interfaces. The governing equations with the boundary conditions are solved for fluid dynamics and electric fields. The dispersion relation and the integrated solution for the model are obtained for both varicose and sinuous modes. The influence of different parameters governing the flow on instability behavior of the system such as the confinement, basic velocity ratio, and electric voltage is discussed in detail. We conclude that increasing the thickness of the outer fluids for small range of unstable wave numbers decreases the disturbance growth rate and increases the number of saddle points. In addition, when the basic velocity ratio is less than one the electric field has a stabilizing effects, but when it exceeds one it has a destabilizing effect.

Microfluidics-Based Fabrication of Cell-Laden Hydrogel Microfibers for Potential Applications in Tissue Engineering.

Fibrous hydrogel scaffolds have recently attracted increasing attention for tissue engineering applications. While a number of approaches have been proposed for fabricating microfibers, it remains difficult for current methods to produce materials that meet the essential requirements of being simple, flexible and bio-friendly. It is especially challenging to prepare cell-laden microfibers which have different structures to meet the needs of various applications using a simple device. In this study, we developed a facile two-flow microfluidic system, through which cell-laden hydrogel microfibers with various structures could be easily prepared in one step. Aiming to meet different tissue engineering needs, several types of microfibers with different structures, including single-layer, double-layer and hollow microfibers, have been prepared using an alginate-methacrylated gelatin composite hydrogel by merely changing the inner and outer fluids. Cell-laden single-layer microfibers were obtained by subsequently seeding mouse embryonic osteoblast precursor cells (MC3T3-E1) cells on the surface of the as-prepared microfibers. Cell-laden double-layer and hollow microfibers were prepared by directly encapsulating MC3T3-E1 cells or human umbilical vein endothelial cells (HUVECs) in the cores of microfibers upon their fabrication. Prominent proliferation of cells happened in all cell-laden single-layer, double-layer and hollow microfibers, implying potential applications for them in tissue engineering.

Dynamics of deformable straight and curved prolate capsules in simple shear flow.

This work investigates the motion of neutrally-buoyant, slightly deformable straight and curved prolate fluid-filled capsules in unbounded simple shear flow at zero Reynolds number using direct simulations. The curved capsules serve as a model for the typical crescent-shaped sickle red blood cells in sickle cell disease (SCD). The effects of deformability and curvature on the dynamics are revealed. We show that with low deformability, straight prolate spheroidal capsules exhibit tumbling in the shear plane as their unique asymptotically stable orbit. This result contrasts with that for rigid spheroids, where infinitely many neutrally stable Jeffery orbits exist. The dynamics of curved prolate capsules are more complicated due to a combined effect of deformability and curvature. At short times, depending on the initial orientation, slightly deformable curved prolate capsules exhibit either a Jeffery-like motion such as tumbling or kayaking, or a non-Jeffery-like behavior in which the director (end-to-end vector) of the capsule crosses the shear-gradient plane back and forth. At long times, however, a Jeffery-like quasiperiodic orbit is taken regardless of the initial orientation. We further show that the average of the long-time trajectory can be well approximated using the analytical solution for Jeffery orbits with an effective orbit constant C eff and aspect ratio ℓ eff. These parameters are useful for characterizing the dynamics of curved capsules as a function of given deformability and curvature. As the capsule becomes more deformable or curved, C eff decreases, indicating a shift of the orbit towards log-rolling motion, while ℓ eff increases weakly as the degree of curvature increases but shows negligible dependency on deformability. These features are not changed substantially as the viscosity ratio between the inner and outer fluids is changed from 1 to 5. As cell deformability, cell shape, and cell-cell interactions are all pathologically altered in blood disorders such as SCD, these results will have clear implications on improving our understanding of the pathophysiology of hematologic disease.

Fabrication and flow characteristics of monodisperse bullet-shaped microparticles with controllable structures

The preparation of microparticles with non-spherical shapes has attracted increasing interest because the special physical properties of non-spherical microparticles can increase their performance in a wide variety of industrial applications and clinical pathologies. Here a simple and flexible approach is developed to fabricate monodisperse bullet-shaped microparticles with controlled structures from microfluidic droplet templates, which are deformed by both shear stress from outer fluid and spatial confinement from microchannel. The deformation of droplet templates can be simply controlled by varying the flow rate of outer fluid and the inner diameter of collection tube. By multiplying the microfluidic device, bullet-shaped microcapsules with different internal structures can be easily fabricated from deformed double emulsion droplets. The results of flow characteristics show that, the bullet-shaped microparticles have a higher velocity than the spherical microparticles with the same volume if they flow in the microchannel with smaller diameter than the length of the bullet-shaped microparticles; whereas their flowing velocity is slightly lower than that of spherical microparticles in the microchannel if the channel diameter is larger than the length of bullet-shaped microparticles. In microchannels of a model device, bullet-shaped microparticles show better embolization performance than spherical ones. The bullet-shaped microparticles and microcapsules are promising as materials candidates in the fields of embolization therapy, substance transfer and drug release systems. The proposed strategy in this study provides a facile route for fabricating bullet-shaped microparticles with controlled structures and presents intriguing possibilities for growing researches including non-spherical microparticles and micromachine systems.

Axisymmetric vortex breakdown: a barrier to mixing

In this paper, we investigate mixing in flows dominated by bubble-type vortex breakdown. Three-dimensional Navier–Stokes equations in cylindrical polar coordinates are solved to simulate flow in a cylindrical container. We have found that in steady regime of the flow, the vortex breakdown bubble is axisymmetric and apparent non-axisymmetric features observed in experiments are artifacts of imperfections in experimental set-ups. We also find that the heteroclinic manifold joining hyperbolic points of the vortex breakdown bubble is stable in the absence of any perturbation and no chaotic advection was found within vortex breakdown bubble. This makes the vortex breakdown bubble impermeable to outer fluid and hence, the vortex breakdown bubble inhibits mixing. We conclude that symmetry is a barrier to mixing.

The vortex-entrainment sheet in an inviscid fluid: theory and separation at a sharp edge

In this paper a model for viscous boundary and shear layers in three dimensions is introduced and termed a vortex-entrainment sheet. The vorticity in the layer is accounted for by a conventional vortex sheet. The mass and momentum in the layer are represented by a two-dimensional surface having its own internal tangential flow. Namely, the sheet has a mass density per-unit-area making it dynamically distinct from the surrounding outer fluid and allowing the sheet to support a pressure jump. The mechanism of entrainment is represented by a discontinuity in the normal component of the velocity across the sheet. The velocity field induced by the vortex-entrainment sheet is given by a generalized Birkhoff–Rott equation with a complex sheet strength. The model was applied to the case of separation at a sharp edge. No supplementary Kutta condition in the form of a singularity removal is required as the flow remains bounded through an appropriate balance of normal momentum with the pressure jump across the sheet. A pressure jump at the edge results in the generation of new vorticity. The shedding angle is dictated by the normal impulse of the intrinsic flow inside the bound sheets as they merge to form the free sheet. When there is zero entrainment everywhere the model reduces to the conventional vortex sheet with no mass. Consequently, the pressure jump must be zero and the shedding angle must be tangential so that the sheet simply convects off the wedge face. Lastly, the vortex-entrainment sheet model is demonstrated on several example problems.

Fabrication and characterization of microcapsule encapsulating EOR surfactants by microfluidic technique

During the process of enhanced oil recovery (EOR), surfactants are injected underground in order to draw more oil from the reservoir. Surface active agent molecules, however, can be easily absorbed by the pore surface of the reservoir rock, causing a massive waste. This paper introduces a novel method for designing a type of microcapsule loading EOR surface activator to solve the absorption problem for surfactants injection. The approach employs microfluidic technique to generate O/W/O double emulsion templates that can be used to fabricate hollowed microcapsules coupled with free radical polymerization. Factors including emulsifier concentrations, flow rates, viscosities and densities of the inner, middle and outer fluids which can affect the formation and morphology of emulsions and microcapsules have been systematically investigated and optimized as well. Additionally, morphological analysis confirms that the as-prepared monodisperse microcapsule has the capacity of encapsulating surfactant molecules owing to its hollowed structure. Finally, the diffusion permeability of the prepared microcapsules is examined, indicating that permeability of the microcapsule membrane can be controlled by adjusting the thickness and cross-linking degree of the microcapsule membrane. Overall, this study provides controllable and versatile preparation for this kind of microcapsule with potential in the field of enhanced oil recovery. The results can also provide valuable guidance for further investigation regarding the “smart” controllable release of EOR surface active agent.

Cell encapsulation modes in a flow-focusing microchannel: effects of shell fluid viscosity

Flow-focusing microencapsulation is an important process to protect the cells in biomedical applications. This article characterizes different cell encapsulation modes and presents the droplet volume distribution, frequency of encapsulation and cell population in terms of inner and outer fluid capillary ratios and viscosity of the shell fluid. The desired mode of at least one cell in a droplet is determined for different capillary number ranges and each viscosity ratios. The droplet volume and frequency of droplet generation are normalized for a combined non-dimensional parameter to classify different patterns of compound droplet formation which helps us to improve single-cell encapsulation process. With increase in orifice radius, the droplet volume increases, and the success rate of cell encapsulation increases. Above a critical radius, the encapsulation mode transitions from one cell to multiple cells captured inside the droplet.

Surface Fluctuations and Coalescence of Nucleolar Droplets in the Human Cell Nucleus

The nucleolus is a membraneless organelle embedded in chromatin solution inside the cell nucleus. It is a site of ribosomal biogenesis, plays a key role in cell cycle progression and stress response, and acts as an indicator in many human diseases and aging. However, the physical nature of the human nucleolus remains an open question. Elucidating nucleolar dynamics, such as their shape fluctuations and fusion, could not only help answer this question, but also provide insight into the material properties of the surrounding nucleoplasm. In this work, we analyze the surface dynamics and fusion kinetics of nucleoli in live human cells[1]. Nucleolar surface fluctuations inform on the nucleolus-nucleoplasm interface, while nucleolar fusion might resolve whether nucleoli aggregate like solid particles or coalesce like liquid droplets. We find that the surface exhibits subtle, but measurable, fluctuations and that the neck connecting two fusing nucleoli grows as r(t)∼t1/2. This is consistent with liquid droplets with low surface tension ∼10−6 Nm−1 coalescing in an outer fluid of higher viscosity ∼103 Pa s, i.e. chromatin solution. We hypothesize that the high viscosity of chromatin solution slows down the nucleolar coalescence kinetics to facilitate transcription inside nucleoli. Interestingly, we find the neck velocity, dr/dt, to be comparable to the velocity of chromatin solution[2]. Surprisingly, nucleolar coalescence occurs in an active fluid, yet can be described by coalescence theory for passive liquid droplets, suggesting that the measured viscosity and surface tension might be effective quantities. Our study presents a noninvasive approach of using natural probes, such as nucleoli, and their dynamics to investigate material properties of the cell and its constituents[1]. 1. Caragine CM et al., Phys. Rev. Lett., In Press, 2018. 2. Zidovska A et al., Proc. Natl. Acad. Sci., 110(39), 15555-60, 2013.

The Role of Downflows in Establishing Solar Near-surface Shear

Abstract The dynamical origins of the Sun’s tachocline and near-surface shear layer (NSSL) are still not well understood. We have attempted to self-consistently reproduce an NSSL in numerical simulations of a solar-like convection zone by increasing the density contrast across rotating 3D spherical shells. We explore the hypothesis that high density contrast leads to near-surface shear by creating a rotationally unconstrained layer of fast flows near the outer surface. Although our high-contrast models do have near-surface shear, it is confined primarily to low latitudes (between ±15°). Two distinct types of flow structures maintain the shear dynamically: rotationally constrained Busse columns aligned with the rotation axis and fast, rotationally unconstrained downflow plumes that deplete angular momentum from the outer fluid layers. The plumes form at all latitudes and, in fact, are more efficient at transporting angular momentum inward at high latitudes. The presence of Busse columns at low latitudes thus appears essential to creating near-surface shear in our models. We conclude that a solar-like NSSL is unobtainable from a rotationally unconstrained outer fluid layer alone. In numerical models, the shear is eliminated through the advection of angular momentum by the meridional circulation. Therefore, a detailed understanding of how the solar meridional circulation is dynamically achieved will be necessary to elucidate the origin of the Sun’s NSSL.

Semi-analytical solution of the time-dependent heat equation for three-dimensional anisotropic multi-layered media

In this paper, a semi-analytical solution of the time-dependent heat conduction equation is presented for laterally infinite, multi-layered media with anisotropic thermal conductivities, convective outer boundaries and perfect thermal contact between the layers. Space and time-dependent moving heat sources on the boundary as well as inside the medium are considered. In addition, the outer fluid temperature may also depend on space and time. The derived solutions are successfully compared to numerical solutions. A Python implementation of the solution is made freely available.

Visualization study on solid-core encapsulation behaviors of double emulsion in a flow-focusing microchannel

A flow-focusing microfluidic chip based on assembled capillary method is developed and the solid-core encapsulation behaviors of double emulsion in a flow-focusing microchannel are visually observed via high-speed microscopic imaging system. The experimental results identify the encapsulation of single, double and triple cores in a flow-focusing microchannel arising from the competition among the inertial force of inner phase, the shear force of outer phase fluid, and the interfacial tension. In addition, the solid-core encapsulation of double emulsion in flow-focusing microchannel is either in the stable state or in the transition state, depending on the flow rates of inner and outer phase fluid. The stable microencapsulation includes the stable single-core, double-cores and triple-cores encapsulation states, while the transition microencapsulation includes the single-double-cores and double-triple-cores transition encapsulation state. Irrespective of encapsulation state, the solid-core encapsulation process can be classified into four stages, including entering, neck stretch, neck shrinking and breakup.

Numerical simulation of double emulsion formation in cross-junctional flow-focusing microfluidic device using Lattice Boltzmann method

This paper presents an analysis of double emulsion formation through a cross junctional flow-focusing microchannel which uses an improved color gradient lattice Boltzmann method. The model with the potential to simulate a ternary system of immiscible fluids was employed. Two double emulsion formation regimes, one-step and two-step, were simulated. The effect of the inner flow rate, as well as inner and outer flow viscosity was investigated on double emulsion formation. The inner flow rate had a significant influence on the inner liquid jet detachment point in the two-step process. However, the viscosity of the inner and outer fluid considerably affected the double jet detachment point in the one-step formation. The shell thickness of a double emulsion can be adjusted by altering the inner flow rate.

Experimental study of double emulsion formation behaviors in a one-step axisymmetric flow-focusing device

Formation behaviors of double emulsions in the one-step axisymmetric flow-focusing microfluidic device are studied experimentally based on a visualization system. Typical droplet formation regimes are examined and the effects of the flow rates on droplet sizes and morphologies are discussed. Especially, a comparative study of the performance between the flow-focusing and co-flowing device is conducted. The results indicate that the dripping and jetting regimes appear during the double emulsion formation under one-step flow-focusing, in which the dripping regime includes two distinct generation modes namely synchronized dripping and asynchronized dripping. Squeezing from the outer interface leads to the collapse of the inner interface in the synchronized dripping regime. The formation regime, droplet sizes as well as their polydispersities are determined by the flow rate of the outer fluid, while the shell thickness depends on the flow rate ratio between the middle fluid and the inner fluid. Compared with the co-flowing system, deformation of the interfaces is enhanced by the hydrodynamic focusing effect in the flow-focusing system where faster production of double emulsions with smaller sizes is achieved.

Analysis of critical fluid velocity and heat transfer in temperature-dependent nanocomposite pipes conveying nanofluid subjected to heat generation, conduction, convection and magnetic field

In this paper, analysis of critical fluid velocity and heat transfer in the nanocomposite pipes conveying nanofluid is presented. The pipe is reinforced by carbon nanotubes (CNTs) and the fluid is mixed by AL2O3 nanoparticles. The material properties of the nanocomposite pipe and nanofluid are considered temperature-dependent and the structure is subjected to magnetic field. The forces of fluid viscosity and turbulent pressure are obtained using momentum equations of fluid. Based on energy balance, the convection of inner and outer fluids, conduction of pipe and heat generation are considered. For mathematical modeling of the nanocomposite pipes, the first order shear deformation theory (FSDT) and energy method are used. Utilizing the Lagrange method, the coupled pipe-nanofluid motion equations are derived. Applying a semi-analytical method, the motion equations are solved for obtaining the critical fluid velocity and critical Reynolds and Nusselt numbers. The effects of CNTs volume percent, AL2O3 nanoparticles volume percent, length to radius ratio of the pipe and shell surface roughness were shown on the critical fluid velocity, critical Reynolds and Nusselt numbers. The results are validated with other published work which shows the accuracy of obtained results of this work. Numerical results indicate that for heat generation of Q = 10 MW/m3, adding 6% AL2O3 nanoparticles to the fluid increases 20% the critical fluid velocity and 15% the Nusselt number which can be useful for heat exchangers.