In 1980, high-performance computing was becoming limited by the heat dissipated in semiconductor chips. IBM was introducing a new chip packaging technology that featured a specific thermal conductance of about 5000 W/m(2).degrees C and occupied approximately 1 liter of space in order to cool 300 W. IBM was also developing a superconducting computer technology to circumvent the thermal problem posed by continued scaling of semiconductor chips. The following year, two of us (DBT and RFWP) showed theoretically and experimentally that by scaling down the dimensions of a conventional plate-fin liquid-cooled heat sink to a channel width of similar to 50 mu m, operating in the laminar flow regime, and integrated within the silicon chip, we could achieve in a laboratory demonstration at least a 20-fold improvement in specific thermal conductance, and more than 1000-fold greater volumetric heat removal. The reception of this advance was mixed, but what really stalled its adoption was the emergence of high-speed low-power CMOS semiconductor circuitry. Two decades later even scaled CMOS circuitry was getting too hot, and various commercialization attempts were then undertaken; some were successful, others not.New commercialization opportunities are now appearing including ones that enable society's more efficient use of energy. A specific example of one such opportunity will be described, i.e., the use of microchannels. in a novel, highly efficient regenerative heat-exchanger configuration, intended for heat-treating low-viscosity liquids for purposes such as pasteurization. Water was successfully heat-treated in continuous-flow tests of an experimental scaled-down prototype ultrahigh-temperature (UHT) pasteurizer incorporating a linear counterflow microchannel (50 mu m parallel-plate channel separation) heat exchanger having an integrated electric heater at the hot end. The use of an integral electric heater permitted a unique manifold-less arrangement for reversing the flow directions at the hot end, wherein perfect local mass balance was enforced locally (i.e., between every pair of adjacent counter-flowing microchannels), eliminating a major potential source of flow maldistribution that would have otherwise reduced heat-exchanger effectiveness. Water entered the device at room temperature, steadily heated to 135 degrees C in about 2.5 s, was maintained at 135 degrees C for similar to 2.5 s, and then cooled in similar to 2.5 s, exiting at no more than 2 degrees C above its original temperature, indicative of high heat-exchanger effectiveness. Heat leaks to ambient air required an excess of heater power, but those could be mostly eliminated in a scaled-up design and with proper attention to exterior insulation. Subsequent tests with milk flowing in heated microchannels revealed that fouling can be a severe problem (perhaps exacerbated by the long-tailed residence-time distribution characteristic of laminar flow), limiting continuous use to less than 2 hours for UHT pasteurization conditions. Conventional high-temperature short-time (HTST) milk pasteurization employs much lower peak temperatures and it is more likely that a practical microchannel system could be constructed for that application.

Dynamics of formation of drops of non-Newtonian liquids from capillary tubes is studied computationally. The rheology of the drop liquids is described by a constitutive relation that accounts for both deformation-rate-thinning and -thickening. The analysis is expedited by reducing the original system of three-dimensional but axisymmetric equations to a system of one-dimensional slender-jet equations. The slender-jet equations are solved by a method of lines using a finite element method for spatial discretization and an adaptive finite difference method for time integration. The simulations follow the formation in time of thousands of drops in sequence, including any satellites that may be produced upon the breakup of a thin thread connecting an about-to-form primary drop to the rest of the liquid attached to the tube. Rate-thickening is shown to produce bead-on-string patterns, which are typically attributed to viscoelastic effects, along the thin threads as they near pinch-off. Rate-thinning, on the other hand, is demonstrated to reduce the length of such thin threads. Simulations are used to identify conditions that may lead to minimization and/or elimination of unwanted satellites. Analysis of dripping or leaky faucets of non-Newtonian liquids reveals rich nonlinear dynamical behavior. As with Newtonian liquids, simple periodic or P-1, where P stands for period, dripping at low flow rates gives way to more complex responses as flow rate is increased. In addition to P-1, P-2, and P-4 responses seen in recent computational analyses of dripping faucets of Newtonian liquids, the new non-Newtonian simulations have also uncovered difficult-to-find P-3 responses as well as chaotic states. Rate-thinning and low viscosities are shown to enhance the complexity of observed responses. Rate-thickening, on the other hand, lowers the critical value of the flow rate for the onset of complexity but narrows the range of flow rates over which the dynamics is complex. The possibility of hysteresis is demonstrated and the effect of fluid rheology on the value of the flow rate for transition from dripping to jetting is determined.

The drop weight method is an accurate yet simple technique for determining surface tension sigma. It relies on dripping a liquid of density rho at a low flow rate (Q) over tilde from a capillary of radius R into air and measuring the combined volumes of the primary and satellite drops that are formed. The method's origin can be traced to Tate, who postulated that the volume (V) over tilde (ideal) of the drop that falls from the capillary should be given by rho g (V) over tilde (ideal)=2 pi R sigma, where g is the gravitational acceleration. Since Tate's law is only an approximation and the actual drop volume (V) over tilde (f)<(V) over tilde (ideal), in practice the surface tension of the liquid-air interface is determined from the experimental master curve due to Harkins and Brown (HB). The master curve is a plot of the fraction of the ideal drop volume, Psi equivalent to(V) over tilde (f)/(V) over tilde (ideal), as a function of the dimensionless tube radius, Phi equivalent to R/(V) over tilde (1/3)(f). Thus, once the actual drop volume (V) over tilde (f), and hence Phi, is known, sigma is readily calculated upon determining the value of Psi from the master curve and that Psi=rho g (V) over tilde (f)/2 pi R sigma. Although HB proposed their master curve more than 80 years ago, a sound theoretical foundation for the drop weight method has heretofore been lacking. This weakness is remedied here by determining the dynamics of formation of many drops and their satellites in sequence by solving numerically the recently popularized one-dimensional (1-d) slender-jet equations. Computed solutions of the 1-d equations are shown to be in excellent agreement with HB's master curve when (Q) over tilde is low. Moreover, a new theory of the drop weight method is developed using the computations and dimensional analysis. The latter reveals that there must exist a functional relationship between the parameter Phi, where Phi(-3) is the dimensionless drop volume, and the gravitational Bond number G equivalent to rho gR(2)/sigma, the Ohnesorge number Oh equivalent to mu/(rho R sigma)(1/2), where mu is the viscosity, and the Weber number We equivalent to rho Q(2)/pi R-2(3)sigma. When We -> 0, the computed results show that Phi depends solely on G. In this limit, a new correlation is deduced which has a simple functional form, G=3.60 Phi(2.81), and is more convenient to use than that of HB. The computed results are also used to show how the original drop weight method can be extended to situations where We is finite and resulting drop volumes are not independent of Oh. (c) 2005 American Institute of Physics.

Pinch-off dynamics of slender liquid bridges of generalized Newtonian fluids without and with inertia are studied using asymptotic analysis and numerical computation. The deformation-rate-dependent rheology is described by power law and Carreau models. Because the bridges are slender, their dynamics are governed by a pair of spatially one-dimensional (1D), non-linear evolution equations for the bridge shape and axial velocity. A bridge of a power law fluid under creeping flow conditions exhibits self-similar dynamics in the vicinity of the axial location where the bridge radius is a minimum. The scaling exponents that determine the variation with time remaining to breakup of the bridge radius or radial length scale, axial length scale, and axial velocity are evaluated by a combined analytical and numerical approach. Similarity solutions are obtained by collapsing numerically computed profiles of both the bridge shape and the axial velocity in the vicinity of the axial location where the bridge radius is minimum by rescaling of the transient profiles with radial and axial scalings deduced from theory. This scaling behavior is transitory and inertial effects become significant as pinch-off is approached. Thereafter, a new balance is established between viscous, capillary, and inertial forces that leads to a new self-similar regime which persists until pinch-off. The scaling exponents appropriate to this regime are also determined. Moreover, it is shown theoretically that interface shapes in the vicinity of the singularity are non-slender for values of the power law exponent below 2/3. Similarity solutions are once again obtained in the same manner as that used in the creeping flow limit. Low-viscosity bridges of Carreau fluids are known to exhibit a transition from potential flow (PF) scaling to Newtonian scaling. Here it is demonstrated that high-viscosity bridges of Carreau fluids exhibit a transition from power law scaling to Newtonian scaling. The point of transition between the latter two regimes is predicted in terms of parameters of the Carreau model.

Deformation and breakup of bridges of Newtonian and non-Newtonian fluids held captive between two disks that are separated from one another at a constant speed are studied computationally. When the liquid bridge is at the incipience of breakup, a thin liquid thread connects two large volumes of fluid that are pendant from and sessile on the top and bottom disks. High viscosity and elasticity are known from experiments to lead to formation of long threads: these are precursors of satellite droplets which are usually unwanted in applications such as ink-jet printing. To investigate the role of shear-thinning in suppressing long threads and to separate the effect of elasticity from shear-thinning, the rheology of non-Newtonian fluids is described here by a Carreau model which simply accounts for shear-thinning behavior. When the dynamics is axially symmetric with respect to the common axis of the bridge and the disks, the physics is described by a spatially two-dimensional (2-D) theory. In addition to this fully 2-D theory, a one-dimensional (1-D) theory based on the slender-jet approximation is also developed here. Both the 2-D and 1-D problems are solved by a method of lines employing the finite element method for spatial discretization and an adaptive finite difference technique for time integration. The computational results show that the limiting bridge length Ld at breakup increases with increasing stretching speed U for both Newtonian and shear-thinning fluids. However, in the case of high-viscosity bridges, as compared to a Newtonian fluid with viscosity equal to the zero shear-rate viscosity of a shear-thinning fluid, the rate at which Ld of a shear-thinning fluid varies with U becomes less pronounced as U increases. Furthermore, in the case of low-viscosity bridges, the axial location along the thread at which the bridge breaks switches from the vicinity of the bottom of the bridge to its top and then back to its bottom again as U is increased. This switch in the breakup location has important implications in determining the fate of satellite droplets if any are formed. It is also shown that both the shape of the bridge and that of the liquid thread are profoundly affected by shear-thinning behavior. 1-D models have of course been previously used but often without direct comparison to experimental measurements or predictions made with exact 2-D models. It is shown here for the first time that 1-D models are remarkably accurate at low stretching speeds but fail at high stretching speeds. Furthermore, it is demonstrated that as the bridges thin, the dynamics in the vicinity of the location where the bridge radius is smallest follow scaling laws recently developed by others who have analyzed the local behavior of the governing equations close to pinch-off.