One approach recently proposed for reducing the frictional resistance to liquid flow in microchannels is the patterning of microribs and cavities on the channel walls. When treated with a hydrophobic coating, the liquid flowing in the microchannel wets only the surfaces of the ribs, and does not penetrate the cavities, provided the pressure is not too high. The net result is a reduction in the surface contact area between channel walls and the flowing liquid. For microribs and cavities that are aligned normal to the channel axis (principal flow direction), these micropatterns form a repeating, periodic structure. This paper presents results of a study exploring the momentum transport in a parallel-plate microchannel with such microengineered walls. The investigation explored the entire laminar flow Reynolds number range and characterized the influence of the vapor cavity depth on the overall flow field. The liquid-vapor interface (meniscus) in the cavity regions is treated as flat in the numerical analysis and two conditions are explored with regard to the cavity region: (1) The liquid flow at the liquid-vapor interface is treated as shear-free (vanishing viscosity in the vapor region), and (2) the liquid flow in the microchannel core and the vapor flow within the cavity are coupled by matching the velocity and shear stress at the interface. Regions of slip and no-slip behavior exist and the velocity field shows distinct variations from classical laminar flow in a parallel-plate channel. The local streamwise velocity profiles, interfacial velocity distributions, and maximum interfacial velocities are presented for a number of scenarios and provide a sound understanding of the local flow physics. The predictions and accompanying measurements reveal that significant reductions in the frictional pressure drop (enhancement in effective fluid slip at the channel walls) can be achieved relative to the classical smooth-channel Stokes flow. Reductions in the friction factor and enhancements in the fluid slip are greater as the cavity-to-rib length ratio is increased (increasing shear-free fraction) and as the channel hydraulic diameter is decreased. The results also show that the slip length and average friction factor–Reynolds number product exhibit a flow Reynolds dependence. Furthermore, the predictions reveal the global impact of the vapor cavity depth on the overall frictional resistance.

This paper reports results of an analytical and experimental investigation of the laminar flow in a parallel-plate microchannel with ultrahydrophobic top and bottom walls. The walls are fabricated with microribs and cavities that are oriented parallel to the flow direction. The channel walls are modeled in an idealized fashion, with the shape of the liquid-vapor meniscus approximated as flat. An analytical model of the vapor cavity flow is employed and coupled with a numerical model of the liquid flow by matching the local liquid and vapor phase velocity and shear stress at the interface. The numerical predictions show that the effective slip length and the reduction in the classical friction factor-Reynolds number product increase with increasing relative cavity width, increasing relative cavity depth, and decreasing relative microrib/cavity module length. Comparisons were also made between the zero shear interface model and the liquid-vapor cavity coupled model. The results illustrate that the zero shear interface model underpredicts the overall flow resistance. Further, the deviation between the two models was found to be significantly larger for increasing values of both the relative rib/cavity module width and the cavity fraction. The trends in the frictional pressure drop predictions are in good agreement with experimental measurements made at similar conditions, with greater deviation observed at increasing size of the cavity fraction. Based on the numerical predictions, an expression is proposed in which the friction factor-Reynolds number product may be estimated in terms of the important variables.

This paper reports particle image velocimetry (PIV) measurements characterizing turbulent flow in a channel with superhydrophobic surfaces, structured and wetting surfaces, and smooth bottom surfaces. The superhydrophobic and structured surfaces are fabricated with alternating ribs and cavities. Both longitudinal and transverse rib/cavity orientations were considered and the surfaces were made superhydrophobic by application of a Teflon coating. The widths of the ribs and cavities were 8 and 32μm, respectively, and the depth of the cavities was 15μm. PIV measurements were acquired for all surfaces considered over the Reynolds numbers range from 4800 to 10 000. Results from the smooth bottom wall measurements were used as a basis for comparison. The hydraulic diameter of the channel was nominally 8.2mm with an aspect ratio of 8.9. The PIV data captured aggregate velocities over multiple rib/cavity modules, such that a spanwise-averaged (over the width of the laser beam) velocity profile was obtained at the channel centerline. The time-averaged velocity profiles reveal no discernible time-mean slip velocity at the superhydrophobic wall. However, the different surfaces are shown to exhibit a systematic influence on the turbulence intensities, total and turbulent shear stress distributions, turbulence production in the channel, and local friction factors. Superhydrophobic surfaces with the ribs and cavities aligned with the flow are shown to yield an 11% decrease in the friction factor while the same surfaces aligned in the transverse direction are shown to cause a modest increase in the friction factor.

Recent developments in superhydrophobic surfaces have enabled significant reduction in the frictional drag for liquid flow through microchannels. There is an apparent risk when using such surfaces, however, that under some conditions the liquid meniscus may destabilize and, consequently, the liquid will wet the entire patterned surface. This paper presents analytical and experimental results that compare the laminar flow dynamics through microchannels with superhydrophobic walls featuring ribs and cavities oriented both parallel and transverse to the direction of flow under both wetting and non-wetting conditions. The results show the reduction in the total frictional resistance is much greater in channels when the liquid phase does not enter the cavity regions. Further, it is demonstrated that the wetting and non-wetting cavity results represent limiting cases between which the experimental data lie. Generalized expressions enabling prediction of the classical friction factor-Reynolds number product as a function of the relevant governing dimensionless parameters are also presented for both the superhydrophobic and wetting states. Experimental results are presented for a range of parameters in the laminar flow regime.

This paper presents the solution to a nonlinear model of a circular foil heat flux gauge that is exposed to a blackbody source in a vacuum environment. This is the scenario typically used to calibrate a circular foil heat flux gauge. The nonlinear model is solved using a Green's function approach. This approach results in an integral equation for the steady-state temperature profile in the gauge, which is solved using the method of successive approximations. A relationship between the incident radiative heat flux and the temperature profile is developed using this model. This relationship is compared to relationships that were derived using linear models. The first and simplest linear model neglects emission from the foil. The second linear model is obtained by linearizing the emissive power of the gauge. It is shown that these linear models only produce accurate results when the gauge design and operating conditions result in a nearly uniform foil temperature. A procedure based on the nonlinear model is proposed for optimizing the design of a circular foil heat flux gauge. A calibration procedure based on the nonlinear model is also proposed. NomenclatureH=T 4 R c = calibration function constants d = calibration function constants f = calibration functions depending on A G = Green's function H = irradiation, W=m 2 h r = radiation heat transfer coefficient, W=m 2 K I o = modified Bessel function k = thermal conductivity of the constantan foil, W=m K N c = conduction-to-radiation parameter, kt=R 2 T 3 R n = calibration function constant R = radius of the constantan foil, m r = radial coordinate, m T = temperature, K t = thickness of the constantan foil, m = relaxation factor = dimensionless temperature difference = Dirac delta function " = emittance = dimensionless temperature, T=T R = dimensionless radial coordinate, r=R = Stefan-Boltzmann constant, 5:67e-8, W=m 2 K 4 Subscripts a = approximate L = linear o = temperature at center of heat flux gauge, K R = temperature of the copper heat sink, K 1-7 = index for calibration functions and constants Superscript i = iteration number