Low Reynolds number equi-bifurcation flow in a two-dimensional channel

The fluid flow in some physiological vessels such as the blood flow in blood vessels and the air flow through bronchi and bronchioles in the lungs undergoes a large number of bifurcations. The understanding of the bifurcation flow is of importance for a better comprehension of its effect in the blood and the air circulatory systems of the living body. The Reynolds number of flow in large blood vessels and bronchi is high and fluid inertia plays a dominant role in the bifurcation flow in such vessels. In small caliber blood vessels such as arterioles and capillaries, and bronchioles, the Reynolds number of flow is quite low and the effect of fluid inertia is negligible compared to the pressure and shear forces. In order to have a quantitative understanding of the bifurcation flow at low Reynolds numbers, the low Reynolds number equi-bifurcation flow in a two-dimensional channel at zero bifurcation angle is studied based on the Stokes approximation. The solution of the problem is posed as an infinite series, where the truncated version is used in numerical calculations. The results of this analysis is discussed in connection with the bifurcation flow of blood in small caliber blood vessels and that of the air in bronchioles in the lung.     

Numerical investigation of the non-Newtonian blood flow in a bifurcation model with a non-planar branch

The non-Newtonian fluid flow in a bifurcation model with a non-planar daughter branch is investigated by using finite element method to solve the three-dimensional Navier–Stokes equations coupled with a non-Newtonian constitutive model, in which the shear thinning behavior of the blood fluid is incorporated by the Carreau–Yasuda model. The objective of this study is to investigate the influence of the non-Newtonian property of fluid as well as of curvature and out-of-plane geometry in the non-planar daughter vessel on wall shear stress (WSS) and flow phenomena. In the non-planar daughter vessel, the flows are typified by the skewing of the velocity profile towards the outer wall, creating a relatively low WSS at the inner wall. In the downstream of the bifurcation, the velocity profiles are shifted towards the flow divider. The low WSS is found at the inner walls of the curvature and the lateral walls of the bifurcation. Secondary flow patterns that swirl fluid from the inner wall of curvature to the outer wall in the middle of the vessel are also well documented for the curved and bifurcating vessels. The numerical results for the non-Newtonian fluid and the Newtonian fluid with original Reynolds number and the corresponding rescaled Reynolds number are presented. Significant difference between the non-Newtonian flow and the Newtonian flow is revealed; however, reasonable agreement between the non-Newtonian flow and the rescaled Newtonian flow is found. Results of this study support the view that the non-planarity of blood vessels and the non-Newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube.

A numerical and experimental investigation of unsteady entry flow in a 90 degrees curved tube is presented to study the impact of the non-Newtonian properties of blood on the velocity distribution. The time-dependent flow rate for the Newtonian and the non-Newtonian blood analog fluid were identical. For the numerical computation, a Carreau-Yasuda model was employed to accommodate the shear thinning behavior of the Xanthan gum solution. The viscoelastic properties were not taken into account. The experimental results indicate that significant differences between the Newtonian and non-Newtonian fluid are present. The numerical results for both the Newtonian and the non-Newtonian fluid agree well with the experimental results. Since viscoelasticity was not included in the numerical code, shear thinning behavior of the blood analog fluid seems to be the dominant non-Newtonian property, even under unsteady flow conditions. Finally, a comparison between the non-Newtonian fluid model and a Newtonian fluid at a rescaled Reynolds number is presented. The rescaled Reynolds number, based on a characteristic rather than the high-shear rate viscosity of the Xanthan gum solution, was about three times as low as the original Reynolds number. Comparison reveals that the character of flow of the non-Newtonian fluid is simulated quite well by using the appropriate Reynolds number.     

Mechanism of bone-conducted hearing: mathematical approach

For better understanding of bone-conducted (BC) hearing, a mechanical BC model is formulated using the Wentzel–Kramers–Brillouin (WKB) method. The BC hearing can be generally described by three main mechanisms: (1) cochlear fluid inertia, (2) in-phase motion of the outer bony shell, and (3) out-of-phase motion of the outer bony shell. Specifically, the second and third mechanisms can be identically explained by symmetric pressure compression–expansion and anti-symmetric compression–expansion, respectively. In this study, simulation results show that both the symmetric and anti-symmetric compression–expansion modes become significant at frequencies above 7 kHz while the fluid inertial mode is dominant at lower frequencies. The density difference between the scala fluid and soft cells of basilar membrane and the amplitude of the anti-symmetric compression–expansion input are identified as the difference between the air conduction and bone conduction. The natural frequency of the cochlear duct wall determines the magnitudes between the three mechanism and is approximated to be in the order of 10 MHz and above.     

An analysis of the squeeze-film lubrication mechanism for articular cartilage.

An asymptotic analysis of a lubrication problem is presented for a model of articular cartilage and synovial fluid under the squeeze-film condition. This model is based upon the following constitutive assumptions: (1) articular cartilage is a linear porous-permeable biphasic material filled with a linearly viscous fluid (i.e. Newtonian fluid); (2) synovial fluid is also a linearly viscous fluid. The geometry of the problem is defined by assuming that (1) cartilage is a uniform layer of thickness H; (2) synovial fluid is a very thin layer compared to H; (3) the radius R of the load-supporting area (or the effective radius of curvature of joint surface, Ri) is large compared to H. Squeeze-film action is generated in the lubricant by a step loading function applied onto the two bearing surfaces. The model assumptions and the material properties yield two small parameters in the mathematical formulation. Based on these two small parameters, two coupled nonlinear partial differential equations were derived from an asymptotic analysis of the problem: one for the lubricant (analogous to the Reynolds equation) and one for the cartilage. For known properties of normal cartilage, our calculations show: (1) the cartilage layer deforms to enlarge the load-supporting area; (2) cartilage deformation acts to reduce the lateral fluid speed in the lubricant, thus prolonging the squeeze-film time which ranges from 1 to 10 s; (3) lubricant fluid in the gap is forced from the central high-pressure region into cartilage, and expelled from the tissue at the low-pressure periphery of the load-bearing region; and (4) tensile hoop stress exists at the cartilage surface despite the compressive squeeze-film loading condition. This hoop stress results directly from the radial flow of the interstitial fluid in the cartilage layer.     

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.     

Subcritical flutter in collapsible tube flow: a model of expiratory flow in the trachea

Using an axisymmetric geometry that retains certain qualitative features of the trachea, we extend one-dimensional modeling of flow in collapsible tubes to include both curved shell effects and, for untethered tubes, wall inertia. A systematic scaling of the finite deformation membrane equations leads to an approximate set which is consistent with the one-dimensional fluid model; axial and normal wall variables are coupled elastically, but only axial inertia is retained. Transverse curvature causes elastic coupling that can give rise to axial wall motion and a flutter instability. The source of instability is the product of a nonzero reference axial curvature with axial tension variation due to axial stretching. The numerical results suggest that this mechanism may be significant even in processes which cannot be assumed one-dimensional.     

Numerical simulations of undulatory swimming at moderate Reynolds number

We perform numerical simulations of the swimming of a three-linkage articulated system in a moderately viscous regime. The computational methodology focuses on the creation, diffusion and transport of vorticity from the surface of the bodies into the fluid. The simulations are dynamically coupled, in that the motion of the three-linkage swimmer is computed simultaneously with the dynamics of the fluid. The novel coupling scheme presented in this work is the first to exploit the relationship between vorticity creation and body dynamics. The locomotion of the system, when subject to undulatory inputs of the hinges, is computed at Reynolds numbers of 200 and 1000. It is found that the forward swimming speed increases with the Reynolds number, and that in both cases the swimming is slower than in an inviscid medium. The vortex shedding is examined, and found to exhibit behavior consistent with experimental flow visualizations of fish.     

Two-Fluid Model of Biofilm Disinfection

We consider a dynamic model of biofilm disinfection in two dimensions. The biofilm is treated as a viscous fluid immersed in a fluid of less viscosity. The bulk fluid moves due to an imposed external parabolic flow. The motion of the fluid is coupled to the biofilm inducing motion of the biofilm. Both the biofilm and the bulk fluid are dominated by viscous forces, hence the Reynolds number is negligible and the appropriate equations are Stokes equations. The governing partial differential equations are recast as boundary integral equations using a version of the Lorenz reciprocal relationship. This allows for robust treatment of the simplified fluid/biofilm motion. The transport of nutrients and antimicrobials, which depends directly on the velocities of the fluid and biofilm, is also included. Disinfection of the bacteria is considered under the assumption that the biofilm growth is overwhelmed by disinfection. Supported by NSF award DMS-0612467.     

Finger Flexor Force Influences Performance in Senior Male Air Pistol Olympic Shooting

The ability to stabilize the gun is crucial for performance in Olympic pistol shooting and is thought to be related to the shooters muscular strength. The present study examines the relation between performance and finger flexor force as well as shoulder abduction isometric force in senior male air pistol shooting. 46 Spanish national level shooters served as test subjects of the study. Two maximal force tests were carried out recording handgrip and deltoid force data under competition conditions, during the official training time at national Spanish championships. Performance was measured as the total score of 60 shots at competition. Linear regressions were calculated to examine the relations between performance and peak and average finger flexor forces, peak and average finger flexor forces relative to the BMI, peak and average shoulder abduction isometric forces, peak shoulder abduction isometric force relative to the BMI. The connection between performance and other variables such as age, weight, height, BMI, experience in years and training hours per week was also analyzed. Significant correlations were found between performance at competition and average and peak finger flexor forces. For the rest of the force variables no significant correlations were found. Significant correlations were also found between performance at competition and experience as well as training hours. No significant correlations were found between performance and age, weight, height or BMI. The study concludes that hand grip strength training programs are necessary for performance in air pistol shooting.     

Inertia Coupling Analysis of a Self-Decoupled Wheel Force Transducer under Multi-Axis Acceleration Fields

Wheel force transducer (WFT), which measures the three-axis forces and three-axis torques applied to the wheel, is an important instrument in the vehicle testing field and has been extremely promoted by researchers with great interests. The transducer, however, is typically mounted on the wheel of a moving vehicle, especially on a high speed car, when abruptly accelerating or braking, the mass/inertia of the transducer/wheel itself will have an extra effect on the sensor response so that the inertia/mass loads will also be detected and coupled into the signal outputs. The effect which is considered to be inertia coupling problem will decrease the sensor accuracy. In this paper, the inertia coupling of a universal WFT under multi-axis accelerations is investigated. According to the self-decoupling approach of the WFT, inertia load distribution is solved based on the principle of equivalent mass and rotary inertia, thus then inertia impact can be identified with the theoretical derivation. The verification is achieved by FEM simulation and experimental tests. Results show that strains in simulation agree well with the theoretical derivation. The relationship between the applied acceleration and inertia load for both wheel force and moment is the approximate linear, respectively. All the relative errors are less than 5% which are within acceptable and the inertia loads have the maximum impact on the signal output about 1.5% in the measurement range.     

The effects of slip velocity at a membrane surface on blood flow in the microcirculation

Closed-form solutions are presented for blood flow in the microcirculation by taking into account the influence of slip velocity at the membrane surface. In this study, the convective inertia force is neglected in comparison with that of blood viscosity on the basis of the smallness of the Reynolds number of the flow in microcirculation. The permeability property of the blood vessel is based on the well known Starling's hypothesis [11]. The effects of slip coefficient on the velocity and pressure fields are clearly depicted.     

Plug Effect of Erythrocytes in Capillary Blood Vessels

As an idealized problem of the motion of blood in small capillary blood vessels, the low Reynolds number flow of plasma (a newtonian fluid) in a circular cylindrical tube involving a series of circular disks is studied. It is assumed in this study that the suspended disks are equally spaced along the axis of the tube, and that their centers remain on the axis of the tube and that their faces are perpendicular to the tube axis. The inertial force of the fluid due to the convective acceleration is neglected on the basis of the smallness of the Reynolds number. The solution of the problem is derived for a quasi-steady flow involving infinitesimally thin disks. The numerical calculation is carried out for a set of different combinations of the interdisk distance and the ratio of the disk radius to the tube radius. The ratio of the velocity of the disk to the average velocity of the fluid is calculated. The different rates of transport of red blood cells and of plasma in capillary blood vessels are discussed. The average pressure gradient along the axis of the tube is computed, and the dependence of the effective viscosity of the blood on the hematocrit and the diameter of the capillary vessel is discussed.     

Gas transfer characteristics of a novel membrane bioreactor

We show the design features of a membrane bioreactor based on pulsatile flow across dimpled membranes. Results show an enhanced mass transfer of air of at least five-fold magnitude as compared with flat membranes. An increased working volume form 20 mL to 120 mL reduced the k(L)A at a given Reynolds number because of axial mixing of fluid from the deoxygenated end chamber. The bioreactor was used to supply air to a hybridoma mammalian cell line, and the calculated oxygen uptake showed that high-density cultures could be maintained in a 20mL, single-dimpled cultures could be maintained in a 20 mL, single-dimpled membrane system. Indirect aeration of a 2 L continuous stirred tank reactor, by a double-membrane system, showed that air could be supplied to mammalian cells at cell densities of approximately 4 x 10(6) /mL.     

Pulsatile blood flow and oxygen transport past a circular cylinder

The fundamental study of blood flow past a circular cylinder filled with an oxygen source is investigated as a building block for an artificial lung. The Casson constitutive equation is used to describe the shear-thinning and yield stress properties of blood. The presence of hemoglobin is also considered. Far from the cylinder, a pulsatile blood flow in the x direction is prescribed, represented by a time periodic (sinusoidal) component superimposed on a steady velocity. The dimensionless parameters of interest for the characterization of the flow and transport are the steady Reynolds number (Re), Womersley parameter (alpha), pulsation amplitude (A), and the Schmidt number (Sc). The Hill equation is used to describe the saturation curve of hemoglobin with oxygen. Two different feed-gas mixtures were considered: pure O(2) and air. The flow and concentration fields were computed for Re=5, 10, and 40, 0< or =A< or =0.75, alpha=0.25, 0.4, and Schmidt number, Sc=1000. The Casson fluid properties result in reduced recirculations (when present) downstream of the cylinder as compared to a Newtonian fluid. These vortices oscillate in size and strength as A and alpha are varied. Hemoglobin enhances mass transport and is especially important for an air feed which is dominated by oxyhemoglobin dispersion near the cylinder. For a pure O(2) feed, oxygen transport in the plasma dominates near the cylinder. Maximum oxygen transport is achieved by operating near steady flow (small A) for both feed-gas mixtures. The time averaged Sherwood number, Sh, is found to be largely influenced by the steady Reynolds number, increasing as Re increases and decreasing with A. Little change is observed with varying alpha for the ranges investigated. The effect of pulsatility on Sh is greater at larger Re. Increasing Re aids transport, but yields a higher cylinder drag force and shear stresses on the cylinder surface which are potentially undesirable.     

A 3D thermal model to analyze the temperature changes of digits during cold stress and predict the danger of frostbite in human fingers

The existing computational models of frostbite injury are limited to one and two dimensional schemes. In this study, a coupled thermo-fluid model is applied to simulate a finger exposed to cold weather. The spatial variability of finger-tip temperature is compared to experimental ones to validate the model. A semi-realistic 3D model for tissue and blood vessels is used to analyze the transient heat transfer through the finger. The effect of heat conduction, metabolic heat generation, heat transport by blood perfusion, heat exchange between tissues and large vessels are considered in energy balance equations. The current model was then tested in different temperatures and air speeds to predict the danger of frostbite in humans for different gloves. Two prevalent gloves which are commonly used in cold climate are considered for investigation. The endurance time and the fraction of necrotic tissues are two main factors suggested for obtaining the response of digit tissues to different environmental conditions.     

The fluid property dependency on micro-fluidic characteristics in the deposition process for microfabrication

The droplet impingement into a cavity at micrometer-scale is one of important fluidic issues for microfabrications, e.g. the inkjet deposition process in the PLED display manufacturing. The related micro-fluidic behaviors in the deposition process should be carefully treated to ensure the desired quality of microfabrication. The droplets generally dispensing from an inkjet head, which contains an array of nozzles, have a volume in several picoliters, while each nozzle responds very quickly and jets the droplets into cavities on substrates with micrometer size. The nature of droplet impingement depends on the fluid properties, the initial state of droplet, the impact parameters and the surface characteristics. The commonly chosen non-dimensional numbers to describe this process are the Weber number, the Reynolds number, the Ohnesorge number, and the Bond number. This paper discusses the influences of fluid properties of a Newtonian fluid, such as surface tension and fluid viscosity, on micro-fluidic characteristics for a certain jetting speed in the deposition process via a numerical approach, which indicates the impingement process consists of four different phases. In the first phase, the droplet stretching outwards rapidly, where inertia force is dominated. In the second phase, the recoiling of droplet is observed, where surface tension becomes the most important force. In the third phase, the gravitational force pulls the droplet surface towards cavity walls. The fourth phase begins when the droplet surface touches cavity walls and ends when the droplet obtains a stable shape. If the fluid viscosity is relatively small, the droplet surface touches cavity walls in the second phase. A stable fluid layer would not form if the viscosity is relatively small.     

Coordination of contact forces during multifinger static prehension

This study investigated the effects of modifying contact finger forces in one direction-normal or tangential-on the entire set of the contact forces, while statically holding an object. Subjects grasped a handle instrumented with finger force-moment sensors, maintained it at rest in the air, and then slowly: (1) increased the grasping force, (2) tried to spread fingers apart, and (3) tried to squeeze fingers together. Analysis was mostly performed at the virtual finger (VF) level (the VF is an imaginable finger that generates the same force and moment as the four fingers combined). For all three tasks there were statistically significant changes in the VF normal and tangential forces. For finger spreading/squeezing the tangential force neutral point was located between the index and middle fingers. We conclude that the internal forces are regulated as a whole, including adjustments in both normal and tangential force, instead of only a subset of forces (normal or tangential). The effects of such factors as EFFORT and TORQUE were additive; their interaction was not statistically significant, thus supporting the principle of superposition in human prehension.     

Viscous flow through slowly expanding or contracting porous walls with low seepage Reynolds number: a model for transport of biological fluids through vessels

In this article, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, is investigated. The governing non-linear equations and their associated boundary conditions are transformed into a highly non-linear ordinary differential equation. The series solution of the problem is obtained by utilising the homotopy perturbation method. Graphical results are presented to investigate the influence of the non-dimensional wall dilation rate and seepage Reynolds number (Re) on the velocity, normal pressure distribution and wall shear stress. Since the transport of biological fluids through contracting or expanding vessels is characterised by low seepage Res, the current study focuses on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls.     

The effect of air velocity on the wingstroke frequency of the blowflyCalliphora erythrocephala

Summary The effect of air velocity and pressure on the wingstroke frequency ofCalliphora erythrocephala, flying in a windtunnel, was studied. The results can be understood by considering the flight mechanism as a mechanical oscillator with an inertia, that depends on air velocity and pressure, without any need for nervous control.The effect of changes in air velocity on the wingstroke frequency was calculated, taking the inertia of a steady two-dimensional boundary layer around the wings as the variable part of the inertia of the flight mechanism. The calculated effect was ten times smaller than that observed experimentally. The reason for this discrepancy is discussed.