Laminar Flow Theory Research Articles

Electro-Viscous Effects on Liquid Flow in Microchannels

The presence of the electrical double layer near a solid-liquid interface results in the electro-viscous effect on pressure-driven liquid flow through microchannels. The objective of this paper is to examine the magnitude of the additional flow resistance caused by the electrokinetic effect in microchannels. Deionized ultrafiltered water, 10−4 and 10−2 M aqueous KCl solutions, 10−4 M AlCl3 solution, and 10−4 M LiCl solution were used as the testing liquids. Carefully designed flow measurements were conducted in three silicon microchannels with a height of 14.1, 28.2, and 40.5 μm, respectively. The measured dP/dx for the pure water, the 10−4 M KCl solution, and the 10−4 M LiCl solution was found to be significantly higher than the prediction of the conventional laminar flow theory at the same Reynolds number. Such a high flow resistance and the resulting high apparent viscosity strongly depend on the channel's height, the ionic valence, and the concentration of the liquids. The zeta potentials for the liquid-solid systems were calculated by using the measured streaming potential data. The experimentally determined dP/dx∼Re relationships were compared with the predictions of a theoretical electro-viscous flow model, and a good agreement was found for pure water, 10−4 M KCl solution, and 10−4 MAlCl3 solution systems. The present electrokinetic flow model cannot interpret the flow characteristics of the LiCl solution.

Pressure-driven water flows in trapezoidal silicon microchannels

Experiments were conducted to investigate flow characteristics of water through trapezoidal silicon microchannels with a hydraulic diameter ranging from 51 to 169 μm. In the experiments, the flow rate and pressure drop across the microchannels were measured at steady states. The experimental results were compared with the predictions from the conventional laminar flow theory. A significant difference between the experimental data and the theoretical predictions was found. Experimental results indicate that pressure gradient and flow friction in microchannels are higher than those given by the conventional laminar flow theory. The measured higher pressure gradient and flow friction maybe be due to the effect of surface roughness of the microchannels. A roughness–viscosity model is proposed to interpret the experimental data.

Microchannels for applications in liquid dosing and flow-rate measurement

To investigate the performance of microengineered fluid channels in liquid dosing applications, flow-rate measurements have been performed with various channel geometries in a range from 0.01 to 1000 μl min -1. An optical flow-measurement technique has been developed to enhance the measurement range into the desired low flow range (10 -3 to 1 μl min -1), and is compared to a standard gravimetric method, which is preferably used for flow rates above 1 μl min -1. In addition, influences of the temperture-dependent viscosity and effects arising from fluidmechanical characteristics are studied. These influences are also calculated from laminar flow theory and semi-emprical models to obtain a theoretical model. It is found that the theoretical model is able to describe the measurement results well in the whole flow range. The model is implemented on a PC-based system, which measures the pressure drop across the microchannel and the fluid temperature and calculates the flow. In a temperature range from 20 to 50°C excellent agreement is found.

Instability of Laminar Natural Convection Boundary Layer Flow on a Vertical Porous Flat Plate

The effects of uniform suction and injection on the linear stability theory of laminar natural convection boundary layer flow along a vertical porous flat plate which is maintained at a constant temperature are studied. The nonsimilar boundary layer equations for the basic steady flow have been solved numerically employing a very efficient finite difference scheme in combination with an iterative method for solving the resulting ordinary differential equations. The temporal neutral stability theory for wavelike disturbances of Tollmien-Schlichting type are then presented for the velocity and temperature functions. The corresponding eigenvalue problem for the disturbance amplitude functions is also solved numerically using a very accurate method. Results are presented graphically for both the basic and disturbance velocity and temperature profiles for some values of the modified local Grashof number G and suction or injection parameter X. The Prandtl number Pr is taken to be 0.73 (air) throughout this paper. The results show clearly the important role that suction or injection parameter X may have on the basic and disturbance flow characteristics in this problem.

Effective medium treatment of laminar flow in magnetic filtration

A theory for laminar flow through randomly distributed magnetic spheres which uses an effective medium treatment (EMT) is presented. In the EMT, the system of fluid and spheres is replaced by a composite sphere—a representative sphere of radius a enclosed by a fluid shell of radius b—embedded in an effective medium of different viscosity. The velocity fields in the fluid shell and in the effective medium as a function of sphere volume packing fraction (γ3=a3/b3) or density of spheres in liquid are determined by using Green’s theorem and proper boundary conditions. The results are applied to study the capture of paramagnetic and diamagnetic particles by an assemblage of spheres. The capture radius as a function of γ and applied magnetic field (H0) is obtained and compared with results from previous study based on Happel’s theory. The dependence of capture radius on H0 is also given for various fixed values of γ. Finally, filter efficiency is predicted for varying γ and H0.

Flow characteristics of a micromachined diaphragm valve designed for liquid flows above 1 ml min-1

Micromachined silicon diaphragm valves are fabricated and flow characteristics are related with laminar and turbulent flow theory. Simultaneous measurements of flow, pressure and lift height are presented. Flow rates of 200 ml min-1 at 0.7 bar are demonstrated, making these valves suitable as pilot valves in various applications such as refrigeration and hydraulics.

An Experimental Study of Subcooled Film Boiling on a Vertical Surface—Hydrodynamic Aspects

Interface and liquid velocities near the leading edge of a vertical wall 6.3 cm wide and 10.3 cm high were measured during subcooled film boiling of water at 1 atm pressure. The interface and liquid velocities in the boundary layer adjacent to the interface were measured using the hydrogen bubble flow visualization method. Photographs taken from the front and side showed the existence of a finite vapor layer at the leading edge and the existence of ripples and large-amplitude waves (bulges) on the interface. The bulges and ripples did not slide on the interface but moved in unison with the interface. The wave amplitude and wavelength were also measured. For a given subcooling and wall superheat, the amplitude, the interfacial velocity, and the wavelength were found to attain an equilibrium value several millimeters downstream of the leading edge. The waves were highly nonlinear and the interface velocities, which are found to be governed by the wave amplitude, were much larger than those predicted from the smooth interface, laminar flow theory. Streamlines in the liquid were found to expand into the wave valleys. At the wave peaks the streamlines appeared to be clustered together and the measured interface velocity gradients were high. The overall picture is one of expansion in the wave valleys and contraction (of flow) at the wave peaks. The flow field in turn is found to affect the liquid side heat transfer in subcooled film boiling significantly.

A Boundary Value Problem with Multiple Solutions from the Theory of Laminar Flow

The equation considered is \[ f^{iv} + R\left( {ff''' - f'f''} \right) = 0,\] with boundary conditions \[ f(0) = f''(0) = 0,\quad f(1) = 1,\quad f'(1) = 0.\] It is shown that for all R there is at least one solution, and for sufficiently large R there are at least three solutions. The asymptotic behavior as $R \to - \infty $ is also studied. This equation arises in studying laminar flow in a porous channel.

油圧管路の断面縮小部における流れのＬＤＶ計測

Velocity distributions of converging oil flows in a pipe with a cross-sectional change in which the Reynolds numbers are much less than those of air or water due to high viscosity of oil have been measured with LDV. The measurements have also been compared with the numerical predictions by the laminar flow theory, giving fairly good agreement between the two. As a result, the findings are as follows : (1) Regardless of the convergence ratio and Reynolds number, the convergent flow region reaches the axial direction as far as the pipe radius upstream from the changing cross-section. (2) Within the Reynolds numbers employed in the present experiments, which have been as high as about 5000, distinct turbulence has not appeared in the convergent flow. Actually, the flow convergence rather helps reduce turbulence produced at and transmitted from upstream. (3) After convergence the flow is restored to a Poiseuille one in a downstream pipe when the Reynolds number is smaller than 2000. The restoration distance depends on Re, of which relation is substantially predicted by FUJIMOTO's empiric equation.

A numerical analysis of the backflow between the leaflets of a St Jude Medical cardiac valve prosthesis

Clinically significant, unexplained hemolysis has been reported to occur in St Jude Medical (SJM) cardiac valve prostheses. The leakage phase of backflow is identified as having the most hemolytic potential, when compared with the other phases of the cardiac cycle. A two-dimensional, laminar, constant fluid property finite element analysis (FEA) is used to calculate the peak shear stress obtained in the flow through the narrow slit formed by the closed leaflets of an idealized size 29 mm (tissue annulus diameter) SJM cardiac valve prosthesis, during the leakage phase of backflow. The flow geometry was such that the simple laminar flow theory (SLFT) could be used to model the flow through the region of peak shear stresses with reasonable accuracy. The SLFT predicts that the maximum shear stress depends upon the thickness of the clearance space and the average velocity through that space. These results suggest that the magnitude of the peak shear stress is of the order of 700–1000 Pa for a duration of the order of 0.5–0.4 ms for pressure drops across the valve of 150–300 torr. This suggests that hemolysis is possible for certain unfortunate combinations of clearances and pressure conditions. However, further research is needed before this flow phenomenon can be associated with the reported clinical hemolysis.

Possibilities and limitations of coiling induced secondary flow in capillary supercritical fluid chromatography

AbstractThe possibility of enhancing radial mass transfer in capillary SFC by tightly coiling the column is discussed. The influence of coiling‐induced secondary flow on the plate height and the speed of analysis in capillary SFC is investigated. It is shown that the experimental plate height in tightly coiled metal or fused silica columns departs from the Golay theory for laminar flow. The effect of the pressure drop associated with the use of higher mobile phase linear velocities is studied. The capacity factors of retained components are used as sensitive probes for pressure drop over the column. Experimental plate heights in coiled columns are compared with values calculated from Tijssen's theory for coiling induced secondary flow. At low velocities a good quantitative agreement was observed between the theory and the experimental results. At intermediate velocities only a qualitative agreement is found. The speed of analysis in coiled columns was found to be up to 5 times higher than in straight capillaries. The largest gain in analysis speed was obtained for solutes with low capacity factors. It is shown that coiling the column can have a positive influence on the detectability. For tightly coiled 210 μm i.d. columns the advantages of coiling‐induced secondary flow could be fully exploited without adverse effects of the column pressure drop. For 50 μm columns the possibility to increase the speed of analysis by coiling was limited due to the high pressure drop.

Velocity Measurements on the Forward Portion of a Cylinder

Velocity measurements in the laminar boundary layer around the forward portion of a circular cylinder are presented. These results are compared to Blasius’ theory for laminar flow around a cylinder using a free-stream velocity distribution obtained from static pressure measurements on the cylinder. Even though the flow is periodically unsteady as a result of vortex shedding from the cylinder, it is found that the agreement is excellent.

Forced Convection Condensation on a Horizontal Tube—Experiments With Vertical Downflow of Steam

The paper reports an experimental investigation into the condensation of steam flowing vertically downward over a single horizontal tube. A limited number of experiments with steam-nitrogen mixtures are also reported. For the case of “pure” steam, data have been obtained at near atmospheric pressure for vapor approach velocities in the range 5 to 81 m/s and with superheats in the range 2 to 40 K. The results are compared with theory and earlier experimental data for steam and other fluids. The vapor-side heat transfer coefficients were found to increase with velocity. For vapor velocities in excess of 30 m/s, the rate of increase of the vapor-side coefficient was greater than predicted by laminar condensate flow theory. This behavior has also been observed by earlier workers for refrigerant-113 and ethylene glycol and may indicate onset of turbulence in the condensate film. Superheat had insignificant effect on the heat transfer coefficient for the condensate film. The results for steam-nitrogen mixtures were generally in good agreement with existing equations for the “gas-layer” resistance.

An asymptotic theory for laminar pipe flow of a non-Newtonian fluid

For a generalized Newtonian fluid the viscosity η* varies with the shear rate\(\dot \gamma *\). Instead of assuming a certain dependence like rheological models do, the viscosity is expanded in a Taylor serie with respect to\(\dot \gamma *\). Based on this expansion a perturbation approach to laminar pipe flow withqw = const. and viscous heating included is formulated. The basic flow (zero order solution) is that of a Newtonian fluid. Higher order terms successively account for the influence of a non-Newtonian fluid. — The asymptotic results compare reasonably well with those of specific rheological models like power law or Ellis model. — The influence of temperature dependent properties (including the viscosity) can be accounted for by the same kind of asymptotic approach. The influence of shear rate as well as temperature dependence thus can be combined in general results valid for all generalized Newtonian fluids.

Gas separation mechanisms in microporous modified γ-al 2o 3 membranes

The transport of pure gases and of binary gas mixtures through a microporous composite membrane is discussed. The membrane consists of an alumina support with a mean pore diameter of 160 nm and an alumina top (separation) layer with pores of 2-4 nm. The theory of Knudsen diffusion, laminar flow and surface diffusion is used to describe the transport mechanisms. It appears for the composite membrane that Knudsen diffusion occurs in the toplayer and combined Knudsen diffusion/laminar flow in the support at pressure levels lower than 200 kPa. For the inert gas mixture H 2/N 2 separation factors near 3 could be achieved which is 80% of the theoretical Knudsen separation factor. This value is shown to be the product of the separation factor of the support (1.9) and of the top layer (1.5). The value for the top layer is rather low due to the relatively small pressure drop across this layer. This situation can be improved by using composite membranes consisting of three or more layers resulting in a larger pressure drop across the separation layer. CO 2 surface diffusion occurs on the internal surface of the investigated alumina membranes. At 250-300 K and a pressure of 100 kPa the contribution of surface diffusion flow measured by counterdiffusion is of the same order of magnitude as that resulting from gas diffusion. The adsorption energy amounts —25 kJ/mol and the surface coverage is 20% of a monolayer at 293 K and 100 kPa. The calculated surface diffusion coefficient is estimated to be 2-5 x 10 -9 m 2/sec. Modification of the internal pore surface with MgO increases the amount of adsorbed CO 2 by 50-100%. Modifications with finely dispersed silver are performed to achieve O 2 surface diffusion.

On the Existence of Solutions of an Equation Arising in the Theory of Laminar Flow in a Uniformly Porous Channel with Injection

The existence of concave solutions of Berman's equation which describes the laminar flow in channels with injection through porous walls is established. It was found that the (unique) concave solutions exist for all injection Reynolds numbers R less than 0.

The heat balance of apple buds and blossoms. Part I. Heat transfer in the outdoor environment

The effect of temperature during the period of bud growth on final yield of apples and possible methods of modifying bud temperature are discussed. These methods utilise either the latent heat of fusion of ice to raise bud temperature above a critical sub-zero temperature or the latent heat of vaporisation of water to lower bud temperature during the day. If the rates of heat transfer between the bud and its environment can be estimated, the rates of water application for the latent heat effects can be determined. The relative values in the heat balance equation are examined. During the day, the net radiation of the bud is complex, but at night the heat balance equation can be solved (in the absence of moisture) and the heat transfer coefficient, h c, estimated at different stages of apple bud development. The bud is treated as a sphere and the heat transfer coefficient, h′ c, is estimated from bud dimensions and heat transfer theory for laminar flow. It is shown that the heat balance method of determining h c is satisfactory for the stages of development from ‘dormancy’ to ‘green cluster’. The ratio of h c h′ c varied from 1.2 for dormant buds to 2.1 at ‘green cluster’.

De-Entrainment of Liquid on Vertical Rods in Air/Water Cross Flow

Liquid holdup on a 101.6-mm-diam, 0.5588-m-long vertical rod has been measured in air/water cross flow at various air and water flow rates. The measurement technique involved the use of band-type capacitance probes, which are capable of measuring the average liquid film thickness around the rod circumference. The probe is able to provide useful information in the presence of nonuniform films around the rod as well as in rivulet flows. The data are shown to be consistent with previously obtained data on liquid drainage flow rates for a variety of air and water incident flow rates. A simple model, based on laminar flow theory, reasonably explains the trends in film thickness variation.

Second-order boundary-layer theory of laminar jet flows

Laminar jet flows are investigated by asymptotic expansions in terms of large Reynolds numbers and large distances from an orifice in a wall. For two-dimensional flow, previously known results are modified and extended. For axisymmetric flow, the expansion breaks down as the distance from the orifice tends to infinity. An error analysis indicates that the range of applicability of classical boundary layer theory is severely limited.

An Experimental Study of Laminar Heat Transfer Downstream of Backsteps

Results of a study of heat transfer in the vicinity of a backward-facing step of a uniform temperature are presented. Temperature distribution are measured using a Mach-Zehnder interferometer. The heat transfer upstream of the step is shown to be strongly enhanced by streamline curvature. Downstream of the step the heat transfer increases monotonically in the streamwise direction but is always less than the flat-plate value. For the largest step investigated, the average heat transfer in the reverse flow region is reduced to 56 percent of the flat-plate results, in agreement with an existing theory for laminar separated flow originally developed for a cavity. The heat transfer is systematically smaller for smaller steps. For all steps, the average heat transfer is described by the equation, St = 0.787(Res)−0.55 (s/xs)0.72.