Narrow escape problem for Brownian particles in a microsphere with internal circulation

This paper considers the narrow escape problem of a Brownian particle within a two-dimensional domain with two escape windows and an internal circulation modeled by the flow within a Hill's vortex. To account for the spatially inhomogeneous flow within the domain, a Lagrangian study is undertaken using the complete equations of motion for a dense particle which is necessary to distinguish between the various regimes as the strength of the internal circulation is varied. For very low internal circulation the particle undergoes the conventional narrow escape problem, and agreement is good with the asymptotic expression. As the internal circulation is increased, regimes are identified with different scaling for the mean escape time. The potential application of this for drug delivery (were nanoparticles are encased in a microsphere) is discussed

Low-Reynolds-number flow past a cylinder with uniform blowing or sucking

We analyse the low-Reynolds-number flow generated by a cylinder (of radius a) in a stream (of velocity U∞) which has a uniform through-surface blowing component (of velocity Ub). The flow is characterized in terms of the Reynolds number Re (=2aU∞/ν, where ν is the kinematic viscosity of the fluid) and the dimensionless blow velocity Λ (=Ub/U∞). We seek the leading-order symmetric solution of the vorticity field which satisfies the near- and far-field boundary conditions. The drag coefficient is then determined from the vorticity field. For the no-blow case Lamb’s (Phil. Mag., vol. 21, 1911, pp. 112–121) expression is retrieved for Re→0. For the strong-sucking case, the asymptotic limit, CD≈−2πΛ, is confirmed. The blowing solution is valid for Λ<4/Re, after which the flow is unsymmetrical about θ=π/2. The analytical results are compared with full numerical solutions for the drag coefficient CD and the fraction of drag due to viscous stresses. The predictions show good agreement for Re=0.1 and Λ=−5,0,5

The effect of inertia and vertical confinement on the flow past a circular cylinder in a Hele-Shaw configuration

The Poiseuille flow (centreline velocity Uc ) of a fluid (kinematic viscosity ν ) past a circular cylinder (radius R ) in a Hele-Shaw cell (height 2h ) is traditionally characterised by a Stokes flow ( Λ=(UcR/ν)(h/R)2≪1 ) through a thin gap ( ϵ=h/R≪1 ). In this work we use asymptotic methods and direct numerical simulations to explore the parameter space Λ – ϵ when these conditions are not met. Starting with the Navier–Stokes equations and increasing Λ (which corresponds to increasing inertial effects), four successive regimes are identified, namely the linear regime, nonlinear regimes I and II in the boundary layer (the ‘ inner’ region) and a nonlinear regime III in both the inner and outer region. Flow phenomena are studied with extensive comparisons made between reduced calculations, direct numerical simulations and previous analytical work. For ϵ=0.01 , the limiting condition for a steady flow as Λ is increased is the instability of the Poiseuille flow. However, for larger ϵ , this limit is at a much higher Λ , resulting in a laminar separation bubble, of size O(h) , forming for a certain range of ϵ at the back of the cylinder, where the azimuthal location was dependent on ϵ . As ϵ is increased to approximately 0.5, the secondary flow becomes increasingly confined adjacent to the sidewalls. The results of the analysis and numerical simulations are summarised in a plot of the parameter space Λ – ϵ

Airfoil trailing-edge noise and drag reduction at a moderate Reynolds number using wavy geometries

This study utilizes a hybrid aeroacoustic model to investigate how airfoils with spanwise wavy geometries can be used to reduce trailing-edge noise alongside improving the aerodynamic performance. A smooth airfoil is compared to four variants, which have spanwise surface waves of different wavelengths, at a Reynolds number of Re = 64 000 and an angle-of-attack of 1°. The first three variants have a geometry modified by a single wavelength, whereas the fourth has a surface composed of two wavelengths, which creates a more irregular surface variation. The results show that modest noise reductions of around 4 dB are achieved for the first three variants, but a much larger reduction of 17.7 dB is achieved for the fourth variant. The mechanisms behind the noise reduction are explored, and it is shown that the geometry reduces the spanwise correlation of the pressure fluctuations and also modifies the boundary layer dynamics, which contributes to the large reduction. It is further shown that a wavy geometry can reduce the drag force by reducing the shear stress over parts of the airfoil surface and by limiting the flow separation on the suction side. The fourth variant is also assessed across a wider range of angles ([Formula: see text]) and is shown to produce less noise than the smooth wing across the entire range as well as a drag reduction for [Formula: see text]

On the flow past ellipses in a Hele-Shaw cell

n this work we investigate the effect of vertical confinement and inertia on the flow past thin ellipses in a Hele-Shaw cell (with centre line velocity Uc and height 2 h ) with different aspect ratios for symmetrical flows and at an angle of attack, using asymptotic methods and numerical simulations. A Stokes region is identified at the ellipse vertices which results in flow different to flow past bluff bodies. Comparison with asymptotic analysis indicates close agreement over the ‘flat’ portion of the ellipse, for δ=(b/a)=0.05 , where a and b are the semi-major and -minor ellipse axes, respectively. Two flow conditions are investigated for ellipses at an angle of attack of 10 ∘ for a fixed δ=0.05 . Firstly, for Λ=(Uca/ν)(h/a)2≪1 , the effect of increasing the vertical confinement of the Hele-Shaw cell results in the rear stagnation point (RSP) moving from close to the potential-flow prediction when ϵ=h/a is very small to the two-dimensional Stokes-flow prediction when ϵ is large. Secondly, for a fixed ϵ≪1 , when inertia is increased past Λ=O(ϵ) the RSP moves towards the trailing edge and is located there for Λ=O(1) . Under these conditions an attached exponentially decaying shear layer or ‘viscous tail’ is formed. A modified Bernoulli equation of the depth-averaged flow, together with the Kutta–Joukowski theorem is used to predict the drag and lift coefficients on the ellipse, which include a linear and a nonlinear contribution, corresponding to a Hele-Shaw and circulation component, respectively. Close agreement is found up to Λ=O(1)

Form, shape and function: segmented blood flow in the choriocapillaris

The development of fluid transport systems was a key event in the evolution of animals and plants. While within vertebrates branched geometries predominate, the choriocapillaris, which is the microvascular bed that is responsible for the maintenance of the outer retina, has evolved a planar topology. Here we examine the flow and mass transfer properties associated with this unusual geometry. We show that as a result of the form of the choriocapillaris, the blood flow is decomposed into a tessellation of functional vascular segments of various shapes delineated by separation surfaces across which there is no flow, and in the vicinity of which the transport of passive substances is diffusion-limited. The shape of each functional segment is determined by the distribution of arterioles and venules and their respective relative flow rates. We also show that, remarkably, the mass exchange with the outer retina is a function of the shape of each functional segment. In addition to introducing a novel framework in which the structure and function of the metabolite delivery system to the outer retina may be investigated in health and disease, the present work provides a general characterisation of the flow and transfers in multipole Hele-Shaw configurations

Stokes' and Lamb's viscous drag laws

Since Galileo used his pulse to measure the time period of a swinging chandelier in the 17th century, pendulums have fascinated scientists. It was not until Stokes' (1851 Camb. Phil. Soc. 9 8–106) (whose interest was spurred by the pendulur time pieces of the mid 19th century) treatise on viscous flow that a theoretical framework for the drag on a sphere at low Reynolds number was laid down. Stokes' famous drag law has been used to determine two fundamental physical constants—the charge on an electron and Avogadro's constant—and has been used in theories which have won three Nobel prizes. Considering its illustrious history it is then not surprising that the flow past a sphere and its two-dimensional analog, the flow past a cylinder, form the starting point of teaching flow past a rigid body in undergraduate level fluid mechanics courses. Usually starting with the two-dimensional potential flow past a cylinder, students progress to the three-dimensional potential flow past a sphere. However, when the viscous flow past rigid bodies is taught, the three-dimensional example of a sphere is first introduced, and followed by (but not often), the two-dimensional viscous flow past a cylinder. The reason why viscous flow past a cylinder is generally not taught is because it is usually explained from an asymptotic analysis perspective. In fact, this added mathematical complexity is why the drag on a cylinder was only solved in 1911, 60 years after the drag on a sphere. In this note, we show that the viscous flow past a cylinder can be explained without the need to introduce any asymptotic analysis while still capturing all the physical insight of this classic fluid mechanics problem

The effect of a uniform through-surface flow on a cylinder and sphere

The effect of a uniform through-surface flow (velocity ) on a rigid and stationary cylinder and sphere (radius ) fixed in a free stream (velocity ) is analysed analytically and numerically. The flow is characterised by a dimensionless blow velocity and Reynolds number , where is the kinematic viscosity). High resolution numerical calculations are compared against theoretical predictions over the range and for planar flow past a cylinder and axisymmetric flow past a sphere. For , the flow is viscously dominated in a thin boundary layer of thickness adjacent to the rigid surface which develops in a time ; the surface vorticity scales as for a cylinder and sphere. A boundary layer analysis is developed to analyse the unsteady viscous forces. Numerical results show that the surface pressure and vorticity distribution within the boundary layer agrees with a steady state analysis. The flow downstream of the body is irrotational so the wake volume flux, , is zero and the drag force is , where is the density of the fluid and is the normal flux through the body surface. The drag coefficient is therefore or for a cylinder or sphere, respectively. A dissipation argument is applied to analyse the drag force; the rate of working of the drag force is balanced by viscous dissipation, flux of stagnation pressure and rate of work by viscous stresses due to sucking. At large , the drag force is largely determined by viscous dissipation for a cylinder, with a weak contribution by the normal viscous stresses, while for a sphere, only of the drag force is determined by viscous dissipation with the remaining due to the flux of stagnation pressure through the sphere surface. When , the boundary layer thickness initially grows linearly with time as vorticity is blown away from the rigid surface. The vorticity in the boundary layer is weakly dependent on viscous effects and scales as or for a cylinder and sphere, respectively. For large blow velocity, the vorticity is swept into two well-separated shear layers and the maximum vorticity decreases due to diffusion. The drag force is related to the vorticity distribution on the body surface and an approximate expression can be derived by considering the first term of a Fourier expansion in the surface vorticity. It is found that the drag coefficient for a cylinder (corrected for flow boundedness) is weakly dependent on while for a sphere, decreases with

Absence of Detectable Influenza RNA Transmitted via Aerosol during Various Human Respiratory Activities – Experiments from Singapore and Hong Kong

Two independent studies by two separate research teams (from Hong Kong and Singapore) failed to detect any influenza RNA landing on, or inhaled by, a life-like, human manikin target, after exposure to naturally influenza-infected volunteers. For the Hong Kong experiments, 9 influenza-infected volunteers were recruited to breathe, talk/count and cough, from 0.1 m and 0.5 m distance, onto a mouth-breathing manikin. Aerosolised droplets exhaled from the volunteers and entering the manikin’s mouth were collected with PTFE filters and an aerosol sampler, in separate experiments. Virus detection was performed using an in-house influenza RNA reverse-transcription polymerase chain reaction (RT-PCR) assay. No influenza RNA was detected from any of the PTFE filters or air samples. For the Singapore experiments, 6 influenza-infected volunteers were asked to breathe (nasal/mouth breathing), talk (counting in English/second language), cough (from 1 m/0.1 m away) and laugh, onto a thermal, breathing manikin. The manikin’s face was swabbed at specific points (around both eyes, the nostrils and the mouth) before and after exposure to each of these respiratory activities, and was cleaned between each activity with medical grade alcohol swabs. Shadowgraph imaging was used to record the generation of these respiratory aerosols from the infected volunteers and their impact onto the target manikin. No influenza RNA was detected from any of these swabs with either team’s in-house diagnostic influenza assays. All the influenza-infected volunteers had diagnostic swabs taken at recruitment that confirmed influenza (A/H1, A/H3 or B) infection with high viral loads, ranging from 105-108 copies/mL (Hong Kong volunteers/assay) and 104–107 copies/mL influenza viral RNA (Singapore volunteers/assay). These findings suggest that influenza RNA may not be readily transmitted from naturally-infected human source to susceptible recipients via these natural respiratory activities, within these exposure time-frames. Various reasons are discussed in an attempt to explain these findings.published_or_final_versio

Coaction of Spheroid-Derived Stem-Like Cells and Endothelial Progenitor Cells Promotes Development of Colon Cancer

Although some studies described the characteristics of colon cancer stem cells (CSCs) and the role of endothelial progenitor cells (EPCs) in neovascularization, it is still controversial whether an interaction exists or not between CSCs and EPCs. In the present study, HCT116 and HT29 sphere models, which are known to be the cells enriching CSCs, were established to investigate the roles of this interaction in development and metastasis of colon cancer. Compared with their parental counterparts, spheroid cells demonstrated higher capacity of invasion, higher tumorigenic and metastatic potential. Then the in vitro and in vivo relationship between CSCs and EPCs were studied by using capillary tube formation assay and xenograft models. Our results showed that spheroid cells could promote the proliferation, migration and tube formation of EPCs through secretion of vascular endothelial growth factor (VEGF). Meanwhile, the EPCs could increase tumorigenic capacity of spheroid cells through angiogenesis. Furthermore, higher microvessel density was detected in the area enriching cancer stem cells in human colon cancer tissue. Our findings indicate that spheroid cells possess the characteristics of cancer stem cells, and the coaction of CSCs and EPCs may play an important role in the development of colon cancer