scholarly journals The elements of fluid mechanics of bile flow through biliary drainage catheters

2019 ◽  
Vol 12 (1) ◽  
pp. 29-41
Author(s):  
Wenguang Li
Keyword(s):  
Reynolds Number ◽  
Obstructive Jaundice ◽  
Fluid Mechanics ◽  
Pressure Gradient ◽  
Friction Factor ◽  
Flow Rate ◽  
Bile Flow ◽  
Bile Flow Rate ◽  
Flow Through ◽  
Inner Diameter

Obstructive jaundice in the biliary tract can infect blood and result in mortality with a high rate. Percutaneous transhepatic biliary drainage (PTBD) with catheters is a useful solution discharging the obstructive jaundice. However, the elements of fluid mechanics showing clinical performance of a PTBD catheter have been documented little so far. In the article, empirical relationships between bile flow rate and pressure gradient in PTBD catheters were studied in terms of equivalent friction factor for the first time. Firstly, an equivalent friction factor in a catheter was raised and determined based on existing in vitro experimental data of bile flow through the catheters with different materials, various inner diameters and lengths under various pressure differences. Then, an empirical correlation of bile flow rate through a catheter was established based on pressure gradient, inner diameter and bile viscosity. The correlation was used to identify effects of catheter inner diameter and bile viscosity on the bile flow rate under the physiological bile pressure difference across obstructed common bile ducts. The feature of minor hydraulic losses in the catheters was clarified, too. The proposed equivalent friction factor was proportional to Reynolds number in a power of -0.654 in comparison with a power of -1 for the fully developed laminar flow in circular pipes. The bile flow rate through a catheter was proportional to inner diameter, kinematic viscosity, and pressure gradient in the powers of 3.2, -0.5 and 0.74, respectively. The minor hydraulic losses could be significant when Reynolds number was greater than 100.

Flow Through a Lens-Shaped Duct

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Flow Rate ◽  
Perturbation Methods ◽  
Flow Through ◽  
Better Than

The flow through a symmetric, lens-shaped duct is solved by accurate Ritz and perturbation methods. The flow rate (resistance) is found for various thickness ratios. The flow rate is much better than friction factor–Reynolds number product as an index for duct flows, especially for the lens duct studied in this paper. The results are also important for the torsion of lens-shaped bars.

Effect of Surface Roughness on Gaseous Flow Through Microchannels

2000 ◽  
Author(s):  
Stephen E. Turner ◽  
Hongwei Sun ◽  
Mohammad Faghri ◽  
Otto J. Gregory
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Friction Factor ◽  
Reynolds Numbers ◽  
Helium Flow ◽  
Local Pressure ◽  
Aspect Ratios ◽  
Corrugated Surfaces ◽  
Flow Through ◽  
Effect Of Surface

Abstract This paper presents an experimental investigation on nitrogen and helium flow through microchannels etched in silicon with hydraulic diameters between 10 and 40 microns, and Reynolds numbers ranging from 0.3 to 600. The objectives of this research are (1) to fabricate microchannels with uniform surface roughness and local pressure measurement; (2) to determine the friction factor within the locally fully developed region of the microchannel; and (3) to evaluate the effect of surface roughness on momentum transfer by comparison with smooth microchannels. The friction factor results are presented as the product of friction factor and Reynolds number plotted against Reynolds number. The following conclusions have been reached in the present investigation: (1) microchannels with uniform corrugated surfaces can be fabricated using standard photolithographic processes; and (2) surface features with low aspect ratios of height to width have little effect on the friction factor for laminar flow in microchannels.

Lateral-Flow Effect on Endwall Heat Transfer and Pressure Drop in a Pin-Fin Trapezoidal Duct of Various Pin Shapes

2000 ◽  
Vol 123 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Jenn-Jiang Hwang ◽  
Chau-Ching Lu
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Flow Rate ◽  
Lateral Flow ◽  
Transfer Enhancement ◽  
Pin Fin ◽  
Flow Reynolds Number ◽  
Outlet Flow ◽  
Flow Through

The effects of lateral-flow ejection 0<ε<1.0, pin shapes (square, diamond, and circular), and flow Reynolds number (6000<Re<40,000) on the endwall heat transfer and pressure drop for turbulent flow through a pin-fin trapezoidal duct are studied experimentally. A staggered pin array of five rows and five columns is inserted in the trapezoidal duct, with the same spacings between the pins in the streamwise and spanwise directions: Sx/d=Sy/d=2.5. Three different-shaped pins of length from 2.5<l/d<4.6 span the distance between two endwalls of the trapezoidal duct. Results reveal that the pin-fin trapezoidal duct with lateral-flow rate of ε=0.3-0.4 has a local minimum endwall-averaged Nusselt number and Euler number for all pin shapes investigated. The trapezoidal duct of lateral outlet flow only (ε=1.0) has the highest endwall heat transfer and pressure drop. Moreover, the square pin results in a better heat transfer enhancement than the diamond pin, and subsequently than the circular pin. Finally, taking account of the lateral-flow rate and the flow Reynolds number, the work develops correlations of the endwall-averaged heat transfer with three different pin shapes.

A theoretical study of viscous effects in peristaltic pumping

1994 ◽  
Vol 279 ◽  
pp. 177-195 ◽  
Author(s):  
Alden M. Provost ◽  
W. H. Schwarz
Keyword(s):  
Wave Propagation ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Mean Flow ◽  
Viscous Effects ◽  
Transverse Waves ◽  
Peristaltic Pumping ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Intuition and previous results suggest that a peristaltic wave tends to drive the mean flow in the direction of wave propagation. New theoretical results indicate that, when the viscosity of the transported fluid is shear-dependent, the direction of mean flow can oppose the direction of wave propagation even in the presence of a zero or favourable mean pressure gradient. The theory is based on an analysis of lubrication-type flow through an infinitely long, axisymmetric tube subjected to a periodic train of transverse waves. Sample calculations for a shear-thinning fluid illustrate that, for a given waveform, the sense of the mean flow can depend on the rheology of the fluid, and that the mean flow rate need not increase monotonically with wave speed and occlusion. We also show that, in the absence of a mean pressure gradient, positive mean flow is assured only for Newtonian fluids; any deviation from Newtonian behaviour allows one to find at least one non-trivial waveform for which the mean flow rate is zero or negative. Introduction of a class of waves dominated by long, straight sections facilitates the proof of this result and provides a simple tool for understanding viscous effects in peristaltic pumping.

Analytical Solution for Newtonian Laminar Flow Through the Concave and Convex Ducts

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
M. Firouzi ◽  
S. H. Hashemabadi
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Friction Factor ◽  
Cross Section ◽  
Cross Sections ◽  
Fully Developed Flow ◽  
Pipe Flows ◽  
Dimensionless Velocity ◽  
Flow Through ◽  
Fanning Friction Factor

In this paper, the motion equation for steady state, laminar, fully developed flow of Newtonian fluid through the concave and convex ducts has been solved both numerically and analytically. These cross sections can be formed due to the sedimentation of heavy components such as sand, wax, debris, and corrosion products in pipe flows. The influence of duct cross section on dimensionless velocity profile, dimensionless pressure drop, and friction factor has been reported. Finally based on the analytical solutions three new correlations have been proposed for the product of Reynolds number and Fanning friction factor (Cf Re) for these geometries.

Oscillatory forcing of flow through porous media. Part 2. Unsteady flow

2002 ◽  
Vol 465 ◽  
pp. 237-260 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Flow Through Porous Media ◽  
Mean Flow ◽  
Two Fluids ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Numerical computations are employed to study the phenomenon of oscillatory forcing of flow through porous media. The Galerkin finite element method is used to solve the time-dependent Navier–Stokes equations to determine the unsteady velocity field and the mean flow rate subject to the combined action of a mean pressure gradient and an oscillatory body force. With strong forcing in the form of sinusoidal oscillations, the mean flow rate may be reduced to 40% of its unforced steady-state value. The effectiveness of the oscillatory forcing is a strong function of the dimensionless forcing level, which is inversely proportional to the square of the fluid viscosity. For a porous medium occupied by two fluids with disparate viscosities, oscillatory forcing may be used to reduce the flow rate of the less viscous fluid, with negligible effect on the more viscous fluid. The temporal waveform of the oscillatory forcing function has a significant impact on the effectiveness of this technique. A spike/plateau waveform is found to be much more efficient than a simple sinusoidal profile. With strong forcing, the spike waveform can induce a mean axial flow in the absence of a mean pressure gradient. In the presence of a mean pressure gradient, the spike waveform may be employed to reverse the direction of flow and drive a fluid against the direction of the mean pressure gradient. Owing to the viscosity dependence of the dimensionless forcing level, this mechanism may be employed as an oscillatory filter to separate two fluids of different viscosities, driving them in opposite directions in the porous medium. Possible applications of these mechanisms in enhanced oil recovery processes are discussed.

Pressure-driven flow past spheres moving in a circular tube

2007 ◽  
Vol 592 ◽  
pp. 233-262 ◽  
Author(s):  
G. J. SHEARD ◽  
K. RYAN
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Axial Force ◽  
Flow Rate ◽  
Circular Tube ◽  
Reynolds Numbers ◽  
Diameter Ratio ◽  
Tube Diameter ◽  
Flow Past ◽  
Pressure Driven Flow

A computational investigation, supported by a theoretical analysis, is performed to investigate a pressure-driven flow around a line of equispaced spheres moving at a prescribed velocity along the axis of a circular tube. This fundamental study underpins a range of applications including physiological circulation research. A spectral-element formulation in cylindrical coordinates is employed to solve for the incompressible fluid flow past the spheres, and the flows are computed in the reference frame of the translating spheres.Both the volume flow rate relative to the spheres and the forces acting on each sphere are computed for specific sphere-to-tube diameter ratios and sphere spacing ratios. Conditions at which zero axial force on the spheres are identified, and a region of unsteady flow is detected at higher Reynolds numbers (based on tube diameter and sphere velocity). A regular perturbation analysis and the reciprocal theorem are employed to predict flow rate and drag coefficient trends at low Reynolds numbers. Importantly, the zero drag condition is well-described by theory, and states that at this condition, the sphere velocity is proportional to the applied pressure gradient. This result was verified for a range of spacing and diameter ratios. Theoretical approximations agree with computational results for Reynolds numbers up toO(100).The geometry dependence of the zero axial force condition is examined, and for a particular choice of the applied dimensionless pressure gradient, it is found that this condition occurs at increasing Reynolds numbers with increasing diameter ratio, and decreasing Reynolds number with increasing sphere spacing.Three-dimensional simulations and predictions of a Floquet linear stability analysis independently elucidate the bifurcation scenario with increasing Reynolds number for a specific diameter ratio and sphere spacing. The steady axisymmetric flow first experiences a small region of time-dependent non-axisymmetric instability, before undergoing a regular bifurcation to a steady non-axisymmetric state with azimuthal symmetrym= 1. Landau modelling verifies that both the regular non-axisymmetric mode and the axisymmetric Hopf transition occur through a supercritical (non-hysteretic) bifurcation.

Resveratrol reduces matrix metalloproteinases and alleviates intrahepatic cholestasis of pregnancy in rats

2016 ◽  
Vol 94 (4) ◽  
pp. 402-407 ◽  
Author(s):  
Zhong Chen ◽  
Lingqing Hu ◽  
Mudan Lu ◽  
Zongji Shen
Keyword(s):  
Ursodeoxycholic Acid ◽  
Flow Rate ◽  
Intrahepatic Cholestasis ◽  
Bile Flow ◽  
Liver Disorder ◽  
Enzymatic Activities ◽  
Intrahepatic Cholestasis Of Pregnancy ◽  
Resveratrol Treatment ◽  
Bile Flow Rate ◽  
Cholestasis Of Pregnancy

Intrahepatic cholestasis of pregnancy (ICP) is a severe liver disorder occurring specifically in pregnancy, and matrix metalloproteinase (MMP)-2 and MMP-9 were found to be elevated in ICP patients. Using ethinylestradiol-induced ICP rats as the model, we examined the effect of resveratrol on ICP symptoms such as bile flow rate, serum enzymatic activities, and TBA concentration, as well as MMP levels, and compared with the known ICP drug ursodeoxycholic acid. Both MMP-2 and MMP-9 were upregulated in ICP rats, and resveratrol treatment could inhibit the elevation of both MMPs, whereas ursodeoxycholic acid did not exhibit any effect. Although ursodeoxycholic acid alleviated ICP symptoms, resveratrol treatment in general exhibited better outcome in restoring bile flow rate, serum enzymatic activities, and TBA concentration. Our results for the first instance strongly supported the potential of RE as a new therapeutic agent in treating ICP, possibly through inhibiting MMP-2 and MMP-9.

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