Entrance length

Abstract: Liquid flow in microchannels is investigated both experimentally and numerically. The experiments are carried out in microchannels with hydraulic diameters from 244 to 974 µ ma tReynolds numbers ranging from 230 to 6500. The pressure drop in these microchannels is measured in situ and is also determined by correcting global measurements for inlet and exit losses. Onset of turbulence is verified by flow visualization. The experimental measurements of pressure drop are compared to numerical predictions. Results show that conventional theory may be used to predict successfully the flow behavior in microchannels in the range of dimensions considered here. Nomenclature Dh =h ydraulic diameter, µm f = Darcy friction factor H = microchannel height, µm L = microchannel length, mm l = characteristic size of eddies in turbulent flow, m P = pressure, Pa Q =v olume flow rate, m 3 /s Re =R eynolds number U =a verage velocity in microchannel, m/s u = characteristic velocity scale of eddies in turbulent flow, m/s W = microchannel width, µm x + = entrance length, mm α = aspect ratio, H/W � P = pressure difference, Pa δ = uncertainty e = dissipation rate, m 2 /s 3 η =K olmogorov length scale, m µ = fluid viscosity, N · s/m 2 ν = kinematic viscosity, m 2 /s ρ = fluid density, kg/m 3 app = apparent fd = fully developed conditions

Abstract: Rarefied gas flow and heat transfer in the entrance region of rectangular microchannels are investigated numerically in the slip-flow regime. A control-volume based numerical method is used to solve the Navier–Stokes and energy equations with velocity-slip and temperature-jump conditions at the walls. The effects of Reynolds number ( 0.1 ⩽ Re ⩽ 10 ), channel aspect ratio ( 0 ⩽ α ∗ ⩽ 1 ), and Knudsen number ( Kn ⩽ 0.1 ) on the simultaneously developing velocity and temperature fields, and on the key flow parameters like the entrance length, the friction coefficient, and Nusselt number are examined in detail. In the entrance region, very large reductions are observed in the friction factor and Nusselt number due to rarefaction effects, which also extend to the fully developed region (though at much lower levels). Current results show that the friction and heat transfer coefficients are less sensitive to rarefaction effects in corner-dominated flows as in square channels when compared to flows between parallel plates. Practical engineering correlations are proposed for the friction and heat transfer coefficients in rectangular and trapezoidal channels.

Abstract: Equations are given that relate the entrance length to Reynolds number for pipe and channel geometries with a flat velocity profile as the initial condition. These equations are linear combinations of the creeping flow and boundary layer solutions. The former is obtained by minimization of the viscous dissipation using the finite element method. The equation for the pipe entrance is shown to be in good agreement with experimental data.

Abstract: The problem of determining the hydrodynamic entrance length in a rectangular channel is solved by the method of linearizing the Navier-Stokes equation. The resulting equation is regarded as an equation to generate a mathematical expression for the axial velocity in the entire region, making smooth transition from a uniform profile to the fully developed one. From this expression, the entrance length, defined as where 99 per cent of the fully developed center-line velocity is attained, is calculated for channels of six aspect ratios. The pressure drops are also calculated and presented herein. A comparison is made with the limited amount of experimental and theoretical data.

Abstract: A boundary integral method is used to model the flow of capsules into pores. An axisymmetric configuration is considered where the capsule and the pore axis coincide. The channel is a cylinder with hyperbolic entrance and exit regions. The capsule has a discoidal unstressed shape, is filled with a Newtonian liquid and is enclosed by a very thin membrane with various elastic properties (neo-Hookean or area-incompressible). The motion of the internal capsule liquid and of the suspending fluid is governed by the Stokes equations whose solution is expressed as boundary integrals. Those are computed by a collocation technique, where points are distributed on the capsule interface, on the channel walls and on the entrance and exit sections of the flow domain. The capsule interface mechanics follow the theory of large deformations of elastic membranes. The numerical model uses a forward time-stepping method, where the position and the deformation of the capsule are computed at each time step.The model allows the study of the effect of a number of parameters (capsule size and geometry, membrane elastic properties) on the flow. The entrance length in the pore, the steady additional pressure drop at equilibrium and the capsule deformed profiles are determined. It is found that the entrance of a capsule into a pore is not sensitive to downstream conditions; but the length of tube necessary to reach steady conditions depends strongly on capsule size and membrane behaviour. Bursting of capsules with a neo-Hookean membrane is predicted to occur through a phenomenon of continuous elongation. The flow of a capsule with a membrane that resists area dilatation depends strongly on particle size and shape.