Newtonian Medium Research Articles

Response of monoflagellate pullers to a shearing flow: A simulation study of microswimmer guidance

Microscale swimming may be intuited to be dominated by background flows, sweeping away any untethered bodies with the prevalent flow direction. However, it has been observed that many microswimmers utilize ambient flows as guidance cues, in some cases resulting in net motion upstream, contrary to the dominant background fluid direction and our accompanying intuition. Thus the hydrodynamic response of small-scale motile organisms requires careful analysis of the complex interaction between swimmer and environment. Here we investigate the effects of a Newtonian shear flow on monoflagellated swimmers with specified body symmetry, representing, for instance, the Leishmania mexicana promastigote, a parasitic hydrodynamic puller that inhabits the microenvironment of a sandfly vector midgut and is the cause of a major and neglected human tropical disease. We observe that a lack of symmetry-breaking cellular geometry results in the periodic tumbling of swimmers in the bulk, with the rotations exhibiting a linear response to changes in shearing rate enabling analytic approximation. In order to draw comparisons with the better-studied pushers, we additionally consider virtual Leishmania promastigotes in a confined but typical geometry, that of a no-slip planar solid boundary, and note that in general stable guided taxis is not exhibited amongst the range of observed behaviors. However, a repulsive boundary gives rise to significant continued taxis in the presence of shearing flow, a phenomenon that may be of particular pertinence to the infective lifecycle stage of such swimmers subject to the assumption of a Newtonian medium. We finally propose a viable and general in vitro method of controlling microswimmer boundary accumulation using temporally evolving background shear flows, based on the analysis of phase-averaged dynamics and verified in silico.

Fluid-structure interaction (FSI) analysis of stent-graft for aortic endovascular aneurysm repair (EVAR): Material and structural considerations

The effect of hemodynamic load on various stent-graft designs used for endovascular aneurysm repair (EVAR) in cardiovascular treatments is studied using a numerical fluid-structure interaction (FSI) analysis that couples computational fluid dynamics (CFD) and finite element analysis (FEA). Radial displacements, mechanical stresses, wall shear stress and wall compliance quantities are evaluated for four stent materials and one graft material. The strut thickness is varied from 0.3 mm to 1 mm. The materials are assumed linearly elastic and isotropic while blood is assumed as a Newtonian and incompressible medium with a pulsatile and turbulent flow profile. Time dependent pressure conditions are assumed at the inlet and outlet. Results are benchmarked against a study taken from the literature and indicate that the stent material and the strut thickness greatly influence the mechanical behavior of the structure. This computational study will serve as an additional tool to vascular surgeons when assessing the choice of material and design for stent-graft recipients.

Heat or mass transport from drops in shearing flows. Part 1. The open-streamline regime

We study the heat or mass transfer from a neutrally buoyant spherical drop embedded in an ambient Newtonian medium, undergoing a general shearing flow, in the strong convection limit. The latter limit corresponds to the drop Péclet number being large ($Pe\gg 1$). We consider two families of ambient linear flows: (i) planar linear flows with open streamlines (parametrized by $\unicode[STIX]{x1D6FC}$ with $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 1$, the extremal members being simple shear flow ($\unicode[STIX]{x1D6FC}=0$) and planar extension ($\unicode[STIX]{x1D6FC}=1$)) and (ii) three-dimensional extensional flows (parameterized by $\unicode[STIX]{x1D716}$, with $0\leqslant \unicode[STIX]{x1D716}\leqslant 1$, the extremal members being planar ($\unicode[STIX]{x1D716}=0$) and axisymmetric extension ($\unicode[STIX]{x1D716}=1$)). For the first family, an analysis of the exterior flow field in the inertialess limit (the drop Reynolds number, $Re$, being vanishingly small) shows that there exist two distinct streamline topologies separated by a critical drop-to-medium viscosity ratio ($\unicode[STIX]{x1D706}$) given by $\unicode[STIX]{x1D706}_{c}=2\unicode[STIX]{x1D6FC}/(1-\unicode[STIX]{x1D6FC})$. For $\unicode[STIX]{x1D706}<\unicode[STIX]{x1D706}_{c}$ all streamlines are open, while the near-field streamlines are closed for $\unicode[STIX]{x1D706}>\unicode[STIX]{x1D706}_{c}$. For the second family, the exterior streamlines remain open regardless of $\unicode[STIX]{x1D706}$. The two streamline topologies lead to qualitatively different mechanisms of transport for large $Pe$. The transport in the open streamline regime is enhanced in the usual manner via the formation of a boundary layer. In sharp contrast, the closed-streamline regime displays diffusion-limited transport, so there is only a finite enhancement even as $Pe\rightarrow \infty$. For $Re=0$, the drop surface streamlines in a planar linear flow may be regarded as generalized Jeffery orbits with a flow and viscosity dependent aspect ratio Jeffery orbits denote the aspect-ratio-dependent inertialess trajectories of a rigid axisymmetric particle in a simple shear flow; see Jeffery (Proc. R. Soc. Lond. A, vol. 102 (715), 1922, pp. 161–179). A Jeffery-orbit-based non-orthogonal coordinate system thus serves as a natural candidate to tackle the transport problem from a drop, in a planar linear flow, in the limit $Pe\gg 1$. Use of this system allows one to derive a closed-form expression for the dimensionless rate of transport (the Nusselt number $Nu$) from a drop in the open-streamline regime ($\unicode[STIX]{x1D706}<\unicode[STIX]{x1D706}_{c}$). Symmetry arguments point to a Jeffery-orbit-based coordinate system for any linear flow, and a variant of this coordinate system is therefore used to derive the Nusselt number for the family of three-dimensional extensional flows. For both classes of flows considered, the boundary-layer-enhanced transport implies that the Nusselt number takes the form $Nu={\mathcal{F}}(P,\unicode[STIX]{x1D706})Pe^{1/2}$, with the parameter $P$ being $\unicode[STIX]{x1D6FC}$ or $\unicode[STIX]{x1D716}$, and ${\mathcal{F}}(P,\unicode[STIX]{x1D706})$ given as a one and two-dimensional integral, respectively, which is readily evaluated numerically.

Computational fluid–structure interaction analysis of blood flow on patient-specific reconstructed aortic anatomy and aneurysm treatment with Dacron graft

We use the fluid–structure interaction (FSI) capability in Abaqus to evaluate radial displacements, von Mises stresses and wall shear stresses (WSS) on the human aorta in response to the blood flowing through it. Complications arise when aneurysm is detected and causes the wall to thinner so much that rupture may result. We use the Materialise suite, a specialty software to reconstruct a three-dimensional geometry of the aorta from two-dimensional computerized axial tomography (CAT) images. Results are compared to those obtained on a healthy individual. Blood is assumed to be a Newtonian and incompressible medium and the blood flow is taken as pulsatile, fully developed and turbulent. The model used for aorta is Holzapfel–Gasser–Ogden (HGO), a sophisticated hyperelastic model that can describe biological tissues. We also study the behavior of Dacron, a polyester fabric used as graft in aortic surgical repair. Here, Dacron is represented by a neo-Hookean (isotropic) hyperelastic model. Time-dependent pressure conditions are assumed at the inlet and outlet of the resulting structure. Results indicate that using a patient-specific geometry for the aorta yields additional insight on the state of the stresses applied on the aortic walls. In addition, stress contours on the Dacron are comparable to those obtained on a healthy patient and stresses evaluated at the interface of the biological tissues and the fabric, provide useful information regarding the suture strength needed during surgery. In the case of aneurysm, our simulation results agree well with experimental data taken from the literature particularly with regard to WSS which can be used to assess the seriousness of the aneurysm condition. If an idealized cylindrical shell is used in place of the reconstructed anatomy, the von Mises stress values do not differ much but it underestimates the values of WSS which could interpreted as the presence of an aneurysm when there is not. Among the novel contributions, the present FSI model has the ability to predict the Dacron’s response to realistic hemodynamic loading conditions.

Phospholipid Vesicles in Media for Tribological Studies against Live Cartilage.

Pre-clinical testing of hemiarthroplasty devices requires that the tribological conditions present in vivo with live cartilage be closely duplicated. A current limitation in the tribological testing of live cartilage involves the use of cell-culture media as lubricant. to develop and test a new hyaluronan-phospholipid based medium (HA-phospholipid medium) that combines the rheological and frictional properties of synovial fluid with the nourishing properties of culture media to keep cells alive. The HA-phospholipid medium consisted of culture medium with added phospholipid dipalmitoylphosphatidylcholine (0.3 mg/mL), and hyaluronic acid (2.42 mg/mL). A standard cell culture medium was used as the control. The rheology of each medium was determined using a flat plate configuration. Bovine calf cartilage was used to assess cell viability and friction in each medium. For friction measurements, a cobalt-chrome alloy ball was articulated against cartilage disks immersed in medium. Lipid vesicles 0.1 to 50 μm in diameter were identified in the HA-phospholipid medium. Cartilage cell viability was significantly higher in the HA-phospholipid medium (62% ± 8%, 95% CI) than in control medium (49.5% ± 5%) (p = 0.009). The HA-phospholipid medium exhibited strong shear-thinning behavior, similar to synovial fluid, with viscosities ~100-fold higher at 10 s-1 and 5-fold higher at 20,000 s-1 than the approximately Newtonian control medium. The HA-phospholipid medium also yielded 20% lower friction values than the control medium after one hour of testing. The rheological and friction results indicate that the HA-phospholipid medium is superior to the control cell culture medium in emulating the shear thinning and lubricative properties of natural synovial fluid, making it more clinically relevant for in vitro wear and friction testing with live cartilage.

Analytical solution of hydrodynamics and heat exchange problem in a porous rectangular channel for thermal boundary conditions of the second kind

In a three-dimensional formulation, an analytical solution of the Darcy-Brinkman equation is obtained together with the two-temperature Schumann model equations for the unidirectional flow of a Newtonian medium in a laminar regime through a horizontal porous channel of a constant rectangular cross-section with known thermal flows at the boundary for small Darcy numbers. The analysis of the specific structure of a compact porous heat exchanger is presented, where the possibilities of the obtained solution for justification its geometrical dimensions during the cooling process of the surface with a heat release of 100 W/cm2 are demonstrated.

Analysis of nano droplet dynamics with various sphericities using efficient computational techniques

Motion of a vertically falling nano droplet in incompressible Newtonian media with initial velocity is investigated. The instantaneous velocity and acceleration are carried out by using the variational iteration method (VIM) and homotopy perturbation method (HPM), which are analytical solution techniques. The obtained results are compared with Runge–Kutta method in order to verify the accuracy of the proposed methods. The results show that, the analytical solutions are in good agreement with each other and with the numerical solution. Also, the effects of sphericity (φ) on the velocity and acceleration profiles of the nano droplet are explained. Moreover, the results demonstrate that the VIM-Pade and HPM-Pade are very effective in generating analytical solutions for even highly nonlinear problems.

On-Chip Microparticle and Cell Washing Using Coflow of Viscoelastic Fluid and Newtonian Fluid.

This work investigates the on-chip washing process of microparticles and cells using coflow configuration of viscoelastic fluid and Newtonian fluid in a straight microchannel. By adding a small amount of biocompatible polymers into the particle medium or cell culture medium, the induced viscoelasticity can push particles and cells laterally from their original medium to the coflow Newtonian medium. This behavior can be used for particle or cell washing. First, we demonstrated on-chip particle washing by the size-dependent migration speed using coflow of viscoelastic fluid and Newtonian fluid. The critical particle size for efficient particle washing was determined. Second, we demonstrated continuous on-chip washing of Jurkat cells using coflow of viscoelastic fluid and Newtonian fluid. The lateral migration process of Jurkat cells along the channel length was investigated. In addition, the cell washing quality was verified by hemocytometry and flow cytometry with a recovery rate as high as 92.8%. Scanning spectrophotometric measurements of the media from the two inlets and the two outlets demonstrated that diffusion of the coflow was negligible, indicating efficient cell washing from culture medium to phosphate-buffered saline medium. This technique may be a safer, simpler, cheaper, and more efficient alternative to the tedious conventional centrifugation methods and may open up a wide range of biomedical applications.

Effect of uniform electric field on the drop deformation in simple shear flow and emulsion shear rheology

Electrohydrodynamic deformation and orientation of a neutrally buoyant, leaky dielectric, Newtonian drop suspended in another immiscible, leaky dielectric, Newtonian medium is analyzed under the combined influence of uniform electric field and simple shear flow. Application of uniform electric field, perpendicular to the direction of shear flow, not only deforms the drop but also modifies the rheological behavior of a dilute emulsion. In the creeping flow limit, an analytical solution for the deformed drop shape is obtained when the drop shape remains nearly spherical and the surface charge convection is weak. The effective shear rheology is obtained for a dilute emulsion of non-interacting drops by calculating the one-particle contribution to the emulsion stress. The results show that the combined influence of uniform electric field and shear flow is not a simple linear superposition of the independent contributions from electric field and shear flow. Application of uniform electric field always leads to larger drop deformation with drop inclination more towards the direction of velocity gradient for the particular case of perfectly dielectric drops. Presence of surface charge convection for a leaky dielectric drop can increase or decrease the drop deformation with the drop inclination more towards either the direction of shear flow or velocity gradient. The effective shear viscosity and normal stress differences are found to be independent of shear rate. These quantities are significantly affected by the surface charge convection and shape deformation. Shape deformation always increases the effective viscosity of a dilute emulsion composed of perfectly dielectric drops. Interestingly, for a dilute emulsion composed of leaky dielectric drops, results show that the combined influence of charge convection and shape deformation can augment or decrease the effective shear viscosity.

Theoretical and experimental study on the motion and shape of viscoelastic falling drops through Newtonian media

In this paper, creeping motion of a viscoelastic drop falling through a Newtonian fluid is investigated experimentally and analytically. A polymeric solution of 0.08 % xanthan gum in 80:20 glycerol/water and silicon oil is implemented as the viscoelastic drop and the bulk viscous fluids, respectively. The shape and motion of falling drops are visualized using a high speed camera. The perturbation technique is employed for both interior and exterior flows, and Deborah and capillary numbers are considered as perturbation parameters up to second order. The product of Deborah and capillary numbers is also used as a perturbation parameter to apply the boundary condition on the deformation on the interface of viscoelastic drop and viscous media. We used the Giesekus nonlinear constitutive equation for the drop phase for the first time. It is shown that the obtained analytical solution has better agreement with experimental observations than the previous analytical studies.

Effect of surface charge convection and shape deformation on the dielectrophoretic motion of a liquid drop.

The dielectrophoretic motion and shape deformation of a Newtonian liquid drop in an otherwise quiescent Newtonian liquid medium in the presence of an axisymmetric nonuniform dc electric field consisting of uniform and quadrupole components is investigated. The theory put forward by Feng [J. Q. Feng, Phys. Rev. E 54, 4438 (1996)10.1103/PhysRevE.54.4438] is generalized by incorporating the following two nonlinear effects-surface charge convection and shape deformation-towards determining the drop velocity. This two-way coupled moving boundary problem is solved analytically by considering small values of electric Reynolds number (ratio of charge relaxation time scale to the convection time scale) and electric capillary number (ratio of electrical stress to the surface tension) under the framework of the leaky dielectric model. We focus on investigating the effects of charge convection and shape deformation for different drop-medium combinations. A perfectly conducting drop suspended in a leaky (or perfectly) dielectric medium always deforms to a prolate shape and this kind of shape deformation always augments the dielectrophoretic drop velocity. For a perfectly dielectric drop suspended in a perfectly dielectric medium, the shape deformation leads to either increase (for prolate shape) or decrease (for oblate shape) in the dielectrophoretic drop velocity. Both surface charge convection and shape deformation affect the drop motion for leaky dielectric drops. The combined effect of these can significantly increase or decrease the dielectrophoretic drop velocity depending on the electrohydrodynamic properties of both the liquids and the relative strength of the electric Reynolds number and electric capillary number. Finally, comparison with the existing experiments reveals better agreement with the present theory.

Transfer of Microparticles across Laminar Streams from Non-Newtonian to Newtonian Fluid

Engineering inertial lift forces and elastic lift forces is explored to transfer microparticles across laminar streams from non-Newtonian to Newtonian fluid. A co-stream of non-Newtonian flow loaded with microparticles (9.9 and 2.0 μm in diameter) and a Newtonian carrier medium flow in a straight rectangular conduit is devised. The elastic lift forces present in the non-Newtonian fluid, undeterred by particle-particle interaction, successfully pass most of the larger (9.9 μm) particles over to the Newtonian fluid. The Newtonian fluid takes over the larger particles and focus them on the equilibrium position, separating the larger particles from the smaller particles. This mechanism enabled processing of densely suspended particle samples. The method offers dilution-free (for number densities up to 10,000 μL(-1)), high throughput (6700 beads/s), and highly efficient (>99% recovery rate, >97% purity) particle separation operated over a wide range of flow rate (2 orders of magnitude).

Моделирование технологического процесса обработки почвы на склоновых агроландшафтах

The article is devoted to the development of a mathematical model of cultivation technological process on the slopes through the use of a deformable model of continuous Newtonian medium. We cited some results of numerical implementation of the model for the duckfoot cultivator, plow body and disk working unit.

Heterogeneity in the final stage of filament breakup of silicone oil/PMMA suspensions

We investigate the filament thinning behavior of the suspensions under extensional flow in the final stage of filament breakup process. Under the extensional flow, the particles dispersed in a Newtonian medium induce complex behaviors; in particular, the particles cause non-uniform filament thinning when the minimum neck diameter (W) of the filament becomes as thin as the length scale of the particle. We suspend 20 wt% of 10 μm poly(methyl methacrylate) (PMMA) particles in a silicone oil, and compare the filament thinning of the suspension with that of silicone oil having the same viscosity and surface tension. In this way, the effect of the particles on the thinning filament can be confirmed while eliminating differences in the rheological properties of the two fluids. The particles begin to affect filament shape when the filament becomes thinner than W = 10 D (D = 10 μm; particle diameter). The filament surface is rough and the shape of the filament is random for W < 2 D, which leads to a random pinch-off of the thinning filament, because the particles confined in the filament are distributed non-uniformly. The random distribution of the particles induces heterogeneity in the final stage of the filament thinning process, when the filament becomes as thin as the length scale of the particle.

Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Semicircular Cylinder

Laminar free convection heat transfer in Bingham plastic fluids from an isothermal semicircular cylinder has been studied numerically over the following ranges of conditions: Rayleigh number ; Prandtl number and Bingham number . New extensive results on the streamline and isotherm contours adjacent to the semicircular cylinder, yield surfaces separating the fluidlike and solidlike regions, drag coefficient, and local and surface average Nusselt number are discussed in detail, especially with reference to the corresponding behavior observed in ordinary Newtonian fluids. The extent of the unyielded regions progressively increases with Bingham number and/or with the decreasing value of the Rayleigh number. Naturally, conduction dominates heat transfer in the unyielded regions, and convection is relevant only to the yielded regions. In summary, for a given Bingham number, the Nusselt number bears a positive dependence on the Rayleigh number. On the other hand, as the value of the Bingham number is gradually increased, the average Nusselt number decreases from its maximum value in Newtonian media () to its conduction limit () when practically most of the fluid is frozen. Finally, the present numerical values of the average Nusselt number have been consolidated in terms of the modified Rayleigh number and Prandtl number , thereby enabling its prediction in a new application and/or for the intermediate values of the governing parameters.

Filament thinning of silicone oil/poly(methyl methacrylate) suspensions under extensional flow

We investigate the effect of particles dispersed in a Newtonian medium on the filament breakup of suspensions under extensional flow. In particular, we focus on the final stage of the breakup process: 10 μm poly(methyl methacrylate) (PMMA) particles with 0∼20 wt% are dispersed in silicone oil and the effects of the added particles on the thinning dynamics of the filament are observed with time-dependent changes in the minimum neck diameter (W). The particles decelerate the breakup process until the minimum thickness (W) of the filament becomes 5 d (d = 10 μm: particle diameter), and then they accelerate the process rapidly until the pinch-off. When the thinning dynamics and filament shape of the 20 wt% PMMA suspension are compared with those of a silicone oil with the same viscosity and surface tension, the particles affect the thinning dynamics by changing the breakup velocity under W∼35 d compared with the viscosity-matched silicone oil. When the filament becomes thinner than W∼10 d, the particles induce different surface shapes compared with those of the viscosity-matched silicone oil. When the filament becomes thinner than W∼5 d, the roughness of the filament surface increases. Thus, the effect of the particles in the final stage of filament breakup is more complicated than that in the initial stage, and we demonstrate that the particles dispersed in a Newtonian medium induce complex behaviors in the final stage of filament breakup.

Non-spherical particles sedimentation in an incompressible Newtonian medium by Padé approximation

The settling behavior of solid particles is of fundamental importance in natural and artificial applications. In this paper, the unsteady motion of a vertically falling non-spherical particle in incompressible Newtonian media was investigated. The velocity and acceleration were carried out by using the differential transformation method (DTM) and a Padé approximate which are an analytical solution technique. The velocity and acceleration are shown for different values of the embedding parameters. The analytical results indicate that the velocity of the gold particle is higher than the copper and aluminum particles. Furthermore, the velocity and acceleration increases with an increase in the sphericity. Comparison of the results illustrates that the analytical method and numerical data are in a good agreement with each other.

Double Stratification Effects on Mixed Convection along a Vertical Plate in a Non-darcy Porous Medium

This article presents non-similarity solutions to study the influence of thermal and mass stratification on mixed convection over a vertical flat plate immersed in a Newtonian fluid saturated non-Darcy porous medium. The model for the flow in the porous medium is characterized by the Darcy-Forchheimer model. The governing equations are first transformed into a dimensionless form by the non-similar transformation and then solved numerically using the Keller-box method. The significance of thermal, mass stratification parameters and mixed convection parameter on dimensionless velocity, temperature, concentration, heat and mass transfer rates are presented graphically.

The study of spermatozoa and sorting in relation to human reproduction

In this review article, we seek to provide a link between our understanding of the spermatozoa on the physical aspects and applications involving assisted reproduction, so that future research in this field can be better poised for improving current procedures. A brief discussion is included regarding the difference in the fluid mechanics of a Newtonian and viscoelastic fluid medium. A review is then done on the current microfluidic sorting techniques applicable to spermatozoa, which includes the albumin gradient separation, fluorescence activated flow cytometry, electrophoresis, dielectrophoresis, countercurrent distribution, movement of motile sperms, accumulation at walls, and optical trapping. Common preparation methods for spermatozoa used in assisted reproduction are also introduced. A number of other general particle manipulation methods which could potentially be incorporated for sperm sorting are also discussed.

Coating formation during drying of β-lactoglobulin: gradual and sudden changes.

The drying dynamics of protein coatings is of importance for many applications. The main focus of research so far was to investigate macroscopic properties of protein coatings, leaving drying dynamics virtually unexplored. A unique combination of techniques is used to monitor drying of a coating containing the protein β-lactoglobulin. The techniques used cover both macroscopic and microscopic aspects of the drying process. For all water fractions amenable to diffusing wave spectroscopy analysis (xw > 0.2 w/w), the tracer particles diffuse in the coating as in a Newtonian viscous medium. Magnetic resonance imaging shows both protein and water are distributed homogeneously over the coating during drying, up to water fractions above 0.2 w/w. When drying continues to lower water fractions, sudden transitions in drying behavior are observed by both dynamic vapor sorption and IR spectroscopy, which we suggest are due to changes in molecular interactions caused by dehydration of the protein backbone.