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.     

Low Reynolds number turbulence modeling of blood flow in arterial stenoses.

Moderate and severe arterial stenoses can produce highly disturbed flow regions with transitional and or turbulent flow characteristics. Neither laminar flow modeling nor standard two-equation models such as the kappa-epsilon turbulence ones are suitable for this kind of blood flow. In order to analyze the transitional or turbulent flow distal to an arterial stenosis, authors of this study have used the Wilcox low-Re turbulence model. Flow simulations were carried out on stenoses with 50, 75 and 86% reductions in cross-sectional area over a range of physiologically relevant Reynolds numbers. The results obtained with this low-Re turbulence model were compared with experimental measurements and with the results obtained by the standard kappa-epsilon model in terms of velocity profile, vortex length, wall shear stress, wall static pressure, and turbulence intensity. The comparisons show that results predicted by the low-Re model are in good agreement with the experimental measurements. This model accurately predicts the critical Reynolds number at which blood flow becomes transitional or turbulent distal an arterial stenosis. Most interestingly, over the Re range of laminar flow, the vortex length calculated with the low-Re model also closely matches the vortex length predicted by laminar flow modeling. In conclusion, the study strongly suggests that the proposed model is suitable for blood flow studies in certain areas of the arterial tree where both laminar and transitional/turbulent flows coexist.     

Experimental investigation of branch flow ratio, angle, and Reynolds number effects on the pressure and flow fields in arterial branch models

An experimental investigation was carried out to acquire an understanding of local pressure changes and flow along the main lumen of arterial branch models similar to the femoral artery of man with three different branch angles (30, 60, and 90 deg) and side branch to the main lumen diameter ratio of 0.4. Effects of branch to main lumen flow rate ratios and physiological Reynolds numbers were found to be significant on the local pressure changes, while that of branch angle was also found to be important. The flow visualization study revealed that the flow separated in the main lumen near the branch junction when the pressure rise coefficient along the main lumen was above a critical value (i.e., 0.35 - 0.46), which was observed to be a function of the Reynolds number. The critical value of the branch to main lumen flow rate ratio was found to be about 0.38 - 0.44 also depending on the Reynolds number. Time averaged pressure distributions for pulsatile flow were similar in trend to steady flow values although they differed somewhat in detail in the main lumen in the branch region.     

Low Reynolds number steady state flow through a branching network of rigid vessels: I. A mixture theory

A mixture theory has been used to formulate a theory of blood perfusion. By means of a formal averaging procedure the discrete network of microvessels is transformed into a continuum. During this procedure, the distinction between arterioles, capillaries and venules is preserved by means of an arteriovenous parameter. In this paper, two equations are derived for the case of low Reynolds number steady-state flow through a rigid vessel network: the extended Darcy equation and the continuity equation. A verification of the theory is presented, on the basis of a network analysis.     

Using the Microcyte flow cytometer to monitor cell number, viability, and apoptosis in mammalian cell culture

The Microcyte is a novel, portable flow cytometer based on diode laser technology whose use has been established for yeast and bacterial analysis. We present data that demonstrate its suitability for routine mammalian cell counting and viability determination. To extend its range of applications in the field of animal cell culture biotechnology, a test to determine the number of apoptotic cells present has been developed for use with the instrument. Apoptosis was induced in hybridoma cell cultures by treatment with camptothecin. Apoptotic cells were labeled with biotinylated Annexin V and then visualized using a streptavidin-allophycocyanin conjugate. Their numbers were counted, and the cell size of the apoptotic cell population was determined using the Microcyte.     

Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish

The Scallop theorem states that reciprocal methods of locomotion, such as jet propulsion or paddling, will not work in Stokes flow (Reynolds number=0). In nature the effective limit of jet propulsion is still in the range where inertial forces are significant. It appears that almost all animals that use jet propulsion swim at Reynolds numbers (Re) of about 5 or more. Juvenile squid and octopods hatch from the egg already swimming in this inertial regime. Juvenile jellyfish, or ephyrae, break off from polyps swimming at Re greater than 5. Many other organisms, such as scallops, rarely swim at Re less than 100. The limitations of jet propulsion at intermediate Re is explored here using the immersed boundary method to solve the 2D Navier-Stokes equations coupled to the motion of a simplified jellyfish. The contraction and expansion kinematics are prescribed, but the forward and backward swimming motions of the idealized jellyfish are emergent properties determined by the resulting fluid dynamics. Simulations are performed for both an oblate bell shape using a paddling mode of swimming and a prolate bell shape using jet propulsion. Average forward velocities and work put into the system are calculated for Re between 1 and 320. The results show that forward velocities rapidly decay with decreasing Re for all bell shapes when Re<10. Similarly, the work required to generate the pulsing motion increases significantly for Re<10. When compared to actual organisms, the swimming velocities and vortex separation patterns for the model prolate agree with those observed in Nemopsis bachei. The forward swimming velocities of the model oblate jellyfish after two pulse cycles are comparable to those reported for Aurelia aurita, but discrepancies are observed in the vortex dynamics between when the 2D model oblate jellyfish and the organism. This discrepancy is likely due to a combination of the differences between the 3D reality of the jellyfish and the 2D simplification, as well as the rigidity of the time varying geometry imposed by the idealized model.     

Intensity of microcarrier collisions in turbulent flow

A model is developed, allowing estimation of the share of inelastic interparticle collisions in total energy dissipation for stirred suspensions. The model is restricted to equal-sized, rigid, spherical particles of the same density as the surrounding Newtonian fluid. A number of simplifying assumptions had to be made in developing the model. According to the developed model, the share of collisions in energy dissipation is small.List of Symbols b parameter in velocity distribution function (Eq. (28)) - c _K factor in Kolmogoroff spectrum law (Eq. (20)) - D _t(r _p ) m²/s characteristic dispersivity at particle radius scale (Eq. (13)) - E(k, t) m³/s² energy spectrum as function of k and t (Eq. (16)) - E _K (k) m³/s² energy spectrum as function of k in Kolmogoroff-region (Eq. (20)) - E _p dimensionless mean kinetic energy of a colliding particle (Eq. (36)) - E _cp dimensionless kinetic energy exchange in a collision (Eq. (37)) - G(x, s) dimensionless energy spectrum as function of x and s (Eq. (16)) - G _B(x) dimensionless energy spectrum as function of x for boundary region (Eq. (29)) - G _K(x) dimensionless energy spectrum as function of x for Kolmogoroff-region (Eq. (21)) - g m/s² gravitational acceleration - I _cp dimensionless collision intensity per particle (Eq. (38)) - I _cv dimensionless volumetric collision intensity (Eq. (39)) - k l/m reciprocal of length scale of velocity fluctuations (Eq. (17)) - K dimensionless viscosity (Eq. (13)) - n(2) dimensionless particle collision rate (Eq. (12)) - n(r) l/s particle exchange rate as function of distance from observatory particle center (Eq. (7)) - r m vector describing position relative to observatory particle center (Eq. (2)) - r m scalar distance to observatory particle center (Eq. (3)) - r _pm particle radius (Eq. (1)) - s dimensionless time (Eq. (10)) - SC kg/ms³ Severity of collision (Eq. (1)) - t s time (Eq. (2)) - u(r, t) m/s velocity vector as function of position vector and time (Eq. (2)) - u(r, t) m/s magnitude of velocity vector as function of position vector and time (Eq. (3)) - u _r(r, t) m/s radial component of velocity vector as function of position vector and time (Eq. (3)) - u _r (r, t) m/s magnitude of radial component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of latitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u (r, t) m/s magnitude of longitudinal component of velocity vector as function of position vector and time (Eq. (3)) - u _gsm/s superficial gas velocity - u(r) m/s root mean square velocity as function of distance from observatory particle center (Eq. (3)) - u_r(r) m/s root mean square radial velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s root mean square latitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - u (r) m/s Root mean square longitudinal velocity component as function of distance from observatory particle center (Eq. (4)) - w(x) dimensionless root mean square velocity as function of dimensionless distance from observatory particle center (Eq. (11)) - V _pm³ particle volume (Eq. (36)) - w(2) dimensionless root mean square collision velocity (Eq. (34)) - w ^* parameter in boundary layer velocity equation (Eq. (24)) - x dimensionless distance to particle center (Eq. (9)) - x ^* value of x where G _Band G _K-curves touch (Eq. (32)) - x _K dimensionless micro-scale (Kolmogoroff-scale) of turbulence (Eq. (15)) - volumetric particle hold-up - m²/s³ energy dissipation per unit of mass - m²/s kinematic viscosity - kg/m³ density - (r) m³/s fluid-exchange rate as function of distance to observatory particle center - Latitudinal co-ordinate (Eq. (5)) - Longitudinal co-ordinate (Eq. (5))     

Laminar air flow versus barrier nursing in marrow transplant recipients

Forty-eight patients with acute leukaemia in relapse (n = 14), acute leukaemia in complete remission (n = 19), chronic myeloid leukaemia (n = 8) or severe aplastic anaemia (n = 7) received a marrow transplant. The first 26 patients were nursed in laminar-air-flow plastic isolators while the next 22 patients were treated in barrier nursing rooms. Gnotobiotic parameters and morbidity in the 2 groups are compared. Good decontamination of the gastro-intestinal tract was obtained using either of the 2 isolation techniques. The incidence of bacterial and mycotic infections, as well as the supportive care required by the patients was almost equal in both groups. Our results also suggest that the incidence of graft versus host disease may decrease with efficient decontamination of the patients.     

Number matters: control of mammalian mitochondrial DNA copy number

Regulation of mitochondrial biogenesis is essential for proper cellular functioning. Mitochondrial DNA （mtDNA） depletion and the resulting mitochondrial malfunction have been implicated in cancer, neurodegeneration, diabetes, aging, and many other human diseases. Although it is known that the dynamics of the mammalian mitochondrial genome are not linked with that of the nuclear genome, very little is known about the mechanism of mtDNA propagation. Nevertheless, our understanding of the mode of mtDNA replication has ad- vanced in recent years, though not without some controversies. This review summarizes our current knowledge of mtDNA copy number control in mammalian cells, while focusing on both mtDNA replication and turnover. Although mtDNA copy number is seemingly in excess, we reason that mtDNA copy number control is an important aspect of mitochondrial genetics and biogenesis and is essential for normal cellular function.     

Low Reynolds number steady state flow through a branching network of rigid vessels II. A finite element mixture model

This research aims at formulating and verifying a finite element mixture formulation for blood perfusion. The equations derived in a companion paper [3] are discretized according to the Galerkin method. A flow experiment in a rigid model of a vascular tree of about 500 vessels is performed in order to verify the finite element mixture formulation. Although the comparison of numerical results and experimental measurements is not conclusive as far as the validity of the theory is concerned, the results do suggest that the finite element model has predictive power in the case of low Reynolds number steady-state flow of a Newtonian fluid in a rigid vascular tree.