Todd Salamon

Isoflux Nusselt Number and Slip Length Formulae for Superhydrophobic Microchannels

We analytically and numerically consider the hydrodynamic and thermal transport behavior of fully developed laminar flow through a superhydrophobic (SH) parallel-plate channel. Hydrodynamic slip length, thermal slip length and heat flux are prescribed at each surface. We first develop a general expression for the Nusselt number valid for asymmetric velocity profiles. Next, we demonstrate that, in the limit of Stokes flow near the surface and an adiabatic and shear-free liquid–gas interface, both thermal and hydrodynamic slip lengths can be found by redefining existing solutions for conduction spreading resistances. Expressions for the thermal slip length for pillar and ridge surface topographies are determined. Comparison of fundamental half-space solutions for the Laplace and Stokes equations facilitate the development of expressions for hydrodynamic slip length over pillar-structured surfaces based on existing solutions for the conduction spreading resistance from an isothermal source. Numerical validation is performed and an analysis of the idealized thermal transport behavior suggests conditions under which superhydrophobic microchannels may enhance heat transfer.

Simulation of power evolution and control dynamics in optical transport systems

The design and analysis of control strategies for high-capacity, reconfigurable optical transmission systems require an understanding of optical system dynamics involving the time-dependent interaction of many components. This paper describes system simulation software that couples continuous physical-layer models of optical transmission components with discrete models for events such as channel add/drops. The simulator computes detailed time traces of signal and noise power propagation along a line system consisting of multiple controlled transmission elements and monitoring devices in response to a particular discrete event. Examples are given illustrating the rich variety of experimentation modes the software supports, including the evaluation of control algorithms, systematic exploration of design parameters, and investigation of cost reduction plans. Details of the development effort are presented, illustrating the contributions of the optical physicists, applied mathematicians, system engineers, and computer scientists who were involved in this collaborative project.

Determination of Electrical Contact Resistivity in Thermoelectric Modules (TEMs) From Module-Level Measurements

An experimental apparatus was developed to characterize the performance of a thermoelectric module (TEM) and heat sink assembly when the TEM was operated in refrigeration mode. A numerical model was developed to simulate the experiments. Bulk and interfacial Ohmic heating, the Peltier effect, Thomson effect and temperature-dependent bulk material properties, i.e., Seebeck coefficient and electrical conductivity were considered. A novel, self-consistent characterization methodology was developed to obtain the electrical contact resistivity at the interconnects in a TEM from the numerical simulations and the experiments. The electrical contact resistivity of the module tested was determined to be approximately 1.0 × 10-9 Ωm . The predictions are consistent with electrical contact resistivity obtained based on the performance specifications (ΔTmax) of the TEM.

Numerical Simulation of Fluid Flow in Microchannels With Superhydrophobic Walls

The three-dimensional flow of a Newtonian fluid in a microchannel with superhydrophobic walls is computed using a finite element analysis. Calculations of the fully-developed laminar flow of water under a pressure gradient of 1 psi/cm in an 80 μm high channel with superhydrophobic upper and lower surfaces containing a 2 μm pitch array of 0.2 μm square posts shows a 40 percent flow enhancement relative to the smooth, non-patterned surface case, and an apparent slip length of 5.4 μm. A sharp gradient is observed in the axial velocity field within 0.5 μm of the post surface and normal to the post center. The calculated axial velocity field away from the superhydrophobic surface agrees well with the analytical solution for two-dimensional channel flow with Navier’s slip condition applying at the channel wall. Mesh refinement studies indicate the important role that adequate resolution of the sharp gradient in the velocity field adjacent to the post surface plays in obtaining accurate flow enhancement predictions. Decreasing the relative contact area of the fluid with the solid portion of the channel surface, either by increasing the post-to-post spacing or decreasing the post size, results in a monotonic increase in the flow enhancement. Wetting of the fluid into the post structure is shown to dramatically decrease the calculated flow enhancement. Calculations of the flow enhancement for fixed surface properties and varying channel heights result in apparent slip lengths that agree to within 1 percent, suggesting that the macroscopic flow behavior is adequately characterized in terms of an apparent slip model, with the magnitude of the slip length a function of the post size, post spacing and wetting behavior that characterize the local flow field.© 2005 ASME

Friction Factors and Nusselt Numbers in Microchannels With Superhydrophobic Walls

The thermal management of electronics is becoming an increasing concern as industry continues to simultaneously push performance while shrinking the size of electronic devices. Microchannel cooling is a promising technology to accommodate the heat dissipation rates and associated fluxes projected for future generations of electronics while also satisfying the need for a reduced footprint to accommodate ever-shrinking device sizes. One shortfall of microchannel cooling, however, is the large pressure drop associated with pumping liquids through microchannels, i.e., channels in which the smallest dimension is between about 1 micron and 1 mm. Superhydrophobic surfaces combine roughness features with low surface energy coatings to create materials with substantially decreased wettability and drag resistance in laminar flows and represent a promising technology for reducing the flow resistance of microchannels. The presence of an (insulating) air layer that is trapped within the superhydrophobic surface, and which separates the microchannel wall from the working fluid, gives rise to a low shear-stress region responsible for the observed reduction in flow resistance. There have been a limited number of studies on the fluid mechanics in superhydrophobic microchannels and, to our knowledge, heat transfer has not been examined. Quantifying the trade-off between the enhanced heat transfer due to pressure drop reduction versus the insulating characteristics of the air layer is of paramount importance for determining the viability of superhydrophobic surfaces as a technology for enhancing microchannel heat transfer. In this work we compute friction factors and Nusselt numbers for the fully-developed (with respect to energy and momentum) flow of a fluid in a parallel-plane microchannel with different heat flux and momentum boundary conditions at the upper and lower channel walls. Two approximations are taken for modeling the superhydrophobic microchannel. In the first case we study the single-phase flow of a fluid in a microchannel where one or both microchannel walls is assumed to be superhydrophobic and where the superhydrophobicity is modeled via application of Navier’s slip model at the microchannel wall. Solutions for the velocity profiles are then employed to calculate theoretical friction factors and Nusselt numbers for the constant heat flux condition. This analysis is then extended to examine the implications on the thermal resistance of a superhydrophobic surface due to the presence of a purely conductive air layer. In the second case we model the fluid flow in the presence of a recirculating air layer that separates the fluid from the microchannel wall. In this instance the low-viscosity air layer gives rise to apparent fluid slip for the working fluid which is dependant on the thickness of the air layer and the viscosity ratio of the two working fluids. This case represents an upper apparent-slip limit as the characteristic spacing of the surface roughness becomes large relative to the channel height and air-layer thickness.Copyright

Three-dimensional superhydrophobic structures printed using solid freeform fabrication tools

Superhydrophobic surfaces are of fundamental and commercial interest as water does not wet the surface, leading to unique properties such as low slip angle, high contact angle, and icephobicity. These behaviours are achieved through a combination of low surface energy materials and high surface roughness. Two printing techniques were used to fabricate hydrophobic polymers into superhydrophobic surfaces. In one approach, a commercially available multi-jet modelling rapid prototyping machine was used to fabricate 3D superhydrophobic objects including helical conduits and porous membranes, using the standard printer resins. A robotic dispensing tool was also developed that enables greater freedom of material selection and feature shape. Both approaches were used to fabricate arrays of high aspect ratio surface features on which water assumes a nearly spherical shape and easily rolls off the surface at low tilt angles. The fabrication and wetting properties of surfaces made using these two techniques will be discussed.

Analysis and Simulation of Heat Transfer in a Superhydrophobic Microchannel

The transport behavior of a superhydrophobic Hele-Shaw channel subject to arbitrary velocity slip, temperature slip, and constant heat flux boundary conditions is analyzed, resulting in a general expression for the Nusselt number. The results of a scaling analysis and numerical simulation are then presented characterizing the thermal behavior of an idealized pillar-structured superhydrophobic surface in the low pillar concentration limit that treats the trapped gas phase as adiabatic. When thermal behavior is uncoupled from the flow, the temperature slip length is shown to follow the same φs −1/2 dependency on pillar solid fraction as the velocity slip length. Further analysis and simulation including the effects of Marangoni stress, so that the thermal and flow fields are no longer decoupled, yields a further geometric scaling parameter. It is demonstrated that the apparent slip length may be increased against an adverse channel temperature gradient due to the local non-equilibrium of temperature in the vicinity of each pillar.Copyright

Monitoring and Diagnostics of Power Anomalies in Transparent Optical Networks

Challenges in monitoring optically-transparent networks are highlighted for dynamically-controlled Raman amplification systems. We use models of amplifier physics together with statistical estimation to automatically discriminate between measurement errors, anomalous losses, and pump failures.

Analysis of heat flow in optical fiber devices that use microfabricated thin film heaters

This paper describes finite element analysis of heat flow in a new class of tunable optical fiber devices that uses thin film resistive heaters microfabricated on the surface of the fiber. The high rate of heat loss from these cylindrical microstructures and the relatively low thermal diffusivity of the glass yield thermal properties (e.g. short axial thermal diffusion lengths, small radial temperature gradients and good power efficiency) that can be exploited for tuning the optical properties of in-fiber gratings. The modeling captures important thermal characteristics of these devices and anticipates their suitability for dynamic dispersion compensation and other applications in high bit rate lightwave communication systems.

Effects of Interfacial Position on Drag Reduction in a Superhydrophobic Microchannel

The use of superhydrophobic surfaces in confined flows is of particular interest as these surfaces have been shown to exhibit a drag reduction effect that is orders of magnitude larger than those due to molecular slip. In this paper we present experimental results of the pressure-driven flow of water in a parallel-plate microchannel having a no-slip upper wall and a superhydrophobic lower wall. Pressure-drop versus flow-rate measurements characterize the apparent slip behavior of the superhydrophobic surfaces with varying pillar-to-pillar pitch spacing and pillar diameter. The superhydrophobic surface consists of a square array of cylindrical pillars that are fabricated by deep reactive ion etching on silicon and coated with a hydrophobic fluoropolymer. A major challenge, in correlating our experimental results with existing theoretical predictions, is uncertainty in the location of the gas/liquid interface and the associated gas/liquid/solid contact line within the pillar features comprising the superhydrophobic surface. We present experimental results, from laser-scanning confocal microscopy, that measure the location of the gas-liquid interface and associated contact line for fluid flowing through a parallel-plate microchannel. Knowledge of the contact line location is then used to correlate experimental pressure-drop versus flow-rate data with a theoretical model based on porous-flow theory that takes into account partial penetration of liquid into a superhydrophobic surface.Copyright