Strong Viscous Effects Research Articles

Scale model experiments of fire whirls over the non-fuel zone around an L-shaped fire source

The Hifukusho-ato fire whirl (HAFW) is a catastrophic fire accident in Tokyo in 1923 and a representative fire whirl phenomenon that occurs over the non-fuel zone around an L-shaped fire source. Previous studies have mainly focused on fire whirls above fire sources, while very limited work reported the HAFW-type fire whirls, which were found to be scale-dependent (more easily to occur in a large-scale wind tunnel test facility than small-scale ones due to the strong viscous effects in the latter) and thus not precisely discussed. In this study, a scale-independent method is proposed by fitting an additional fire source in the inside bend of an L-shaped fire source to mimic the flame-overhang region observed in the large-scale tests; the HAFW-type fire whirl is then successfully reconstructed in a small-scale test model (1/10,000th of the HAFW prototype). Meanwhile, the results show that the average fire whirl occurrence position in the flow direction in a large-scale test model (1/2,000th of the HAFW prototype) does not collapse with those in a small-scale test model (1/10,000th of the HAFW prototype without additional fire sources installed), but with those in the aforesaid scale-independent test model; such collapse can be summarized by a linear fitting correlation between a normalized fire whirl occurrence position and a modified Froude number under different fire source scales and lateral wind velocities. Based on the above experimental facts, updated scaling law to reproduce HAFW-type fire whirls and similar fire whirl occurrence positions is provided. This work advances a fundamental understanding of fire whirls generated by an L-shaped fire source; thus, helping guide fire-rescue operations, and benefiting future fire whirl model development.

Collisional drift wave instability in an ultracold neutral plasma

We study the linear stability of a collisional drift wave in an ultracold neutral plasma (UNP) with the aim of investigating the effect of strong coupling effects on its propagation characteristics. The dispersion relation obtained using the generalized hydrodynamic model for the ultracold ion dynamics is solved analytically in various limits for the real frequency and growth rate of the mode. It is found that strong coupling-induced viscous effects lead to a weakening of the growth rate and an enhancement in the real frequency of the mode. The impact is particularly pronounced in the “kinetic” regime, i.e., when the ion–ion correlation time is much larger than the wave period. In the regime where the density gradient is weak, we find that collisional effects can destabilize the transverse shear waves and longitudinal waves. We discuss the relevance and potential application of our results in future experimental and numerical simulation studies of UNPs.

Forced oscillation dynamics of surface nanobubbles.

Surface nanobubbles have potential applications in the manipulation of nanoscale and biological materials, waste-water treatment, and surface cleaning. These spherically capped bubbles of gas can exist in stable diffusive equilibrium on chemically patterned or rough hydrophobic surfaces, under supersaturated conditions. Previous studies have investigated their long-term response to pressure variations, which is governed by the surrounding liquid's local supersaturation; however, not much is known about their short-term response to rapid pressure changes, i.e., their cavitation dynamics. Here, we present molecular dynamics simulations of a surface nanobubble subjected to an external oscillating pressure field. The surface nanobubble is found to oscillate with a pinned contact line, while still retaining a mostly spherical cap shape. The amplitude-frequency response is typical of an underdamped system, with a peak amplitude near the estimated natural frequency, despite the strong viscous effects at the nanoscale. This peak is enhanced by the surface nanobubble's high internal gas pressure, a result of the Laplace pressure. We find that accurately capturing the gas pressure, bubble volume, and pinned growth mode is important for estimating the natural frequency, and we propose a simple model for the surface nanobubble frequency response, with comparisons made to other common models for a spherical bubble, a constant contact angle surface bubble, and a bubble entrapped within a cylindrical micropore. This work reveals the initial stages of growth of cavitation nanobubbles on surfaces, common in heterogeneous nucleation, where classical models based on spherical bubble growth break down.

Design and Optimization Method for Hypersonic Quasi-Waverider

The waverider has an extensive application prospect in the design of hypersonic vehicles due to its excellent aerodynamic efficiency. However, it is known that the original cone-derived waverider is longitudinally unstable. To solve the problem, a design method for hypersonic quasi-waverider configuration is first proposed and then a genetic algorithm optimization framework is constructed to obtain optimum quasi-waveriders with different constraints. During the optimization, the aerodynamic performance is evaluated by an efficient aerodynamic model that considers the impacts of strong viscous interaction effects. Results from numerical simulations show that, for the optimum quasi-waveriders without constraints, good shock wave attachment along the leading edge is achieved, and the maximum lift-to-drag ratio () is even higher than that of the original waverider. Optimized quasi-waveriders are also generated based on the constraints of volumetric efficiency and stability. The first increases and then decreases with the increase in volumetric efficiency. In addition, an interesting phenomenon is found that the is reduced almost linearly with the increase in the degree of stability at each design condition. Furthermore, a linear relationship is also constructed between the variation of with respect to degree of stability and the viscous interaction parameter .

Viscous diffusion effects on the self-induced distortions of rectangular vortex rings

Large eddy simulation, stereoscopic particle image velocimetry, and hot-wire anemometry are conducted to study the viscous diffusion effects on the self-induced deformations of the aspect ratio 2 rectangular vortex rings at Reynolds numbers Ri = UDh/ν = 355, 877.5, 1775, 8775, 17 750 (i = 1, …, 5). The differences between the axis-switching of isolated vortex rings and rectangular jets are explained. At increased viscous effects, the rotational content of the vortices diffuses and grows in size. The high curvature corners of the rectangular vortex rings induce additional velocities which distort the topology until it appears to be rotated for 90°, the so-called axis-switching phenomenon. Strong viscous effects (R1) diffuse the ring before the switching is completed, while reduced viscous effects allow for the first (R2, R3) and second (R4, R5) switching. For R2 and R3, the rotated rectangular rings bifurcate into a pair of semi-circular topologies. Space-time mapping of the instantaneous streamwise velocity at the vortex ring axis reveals strong correlation spots for the occurrence of each axis-switching. Vortex rings are found to decelerate more quickly with increased viscous effects and hence exhibit reduced penetration rates. The temporal variation of the advection velocity of the vortex ring demonstrates major peaks in accordance with the number of axis-switchings. Trajectories of the vortex cores in two orthogonal planes demonstrate contractions/expansions conforming to the sine/cosine waves associated with the varicose instability modes. A pair of orthogonal varicose modes interacts with the phase lagging/leading equal to the quarter of a full cycle which is interestingly equal to the axis-switching frequency.

Biomechanics of swimming in developing larval fish.

Most larvae of bony fish are able to swim almost immediately after hatching. Their locomotory system supports several vital functions: fish larvae make fast manoeuvres to escape from predators, aim accurately during suction feeding and may migrate towards suitable future habitats. Owing to their small size and low swimming speed, larval fish operate in the intermediate hydrodynamic regime, which connects the viscous and inertial flow regimes. They experience relatively strong viscous effects at low swimming speeds, and relatively strong inertial effects at their highest speeds. As the larvae grow and increase swimming speed, a shift occurs towards the inertial flow regime. To compensate for size-related limitations on swimming speed, fish larvae exploit high tail beat frequencies at their highest speeds, made possible by their low body inertia and fast neuromuscular system. The shifts in flow regime and body inertia lead to changing functional demands on the locomotory system during larval growth. To reach the reproductive adult stage, the developing larvae need to adjust to and perform the functions necessary for survival. Just after hatching, many fish larvae rely on yolk and need to develop their feeding systems before the yolk is exhausted. Furthermore, the larvae need to develop and continuously adjust their sensory, neural and muscular systems to catch prey and avoid predation. This Review discusses the hydrodynamics of swimming in the intermediate flow regime, the changing functional demands on the locomotory system of the growing and developing larval fish, and the solutions that have evolved to accommodate these demands.

Surface pressure determination: a comparison between PIV-based methods and PSP measurements

The present work investigates the challenges in measuring the surface pressure distribution using particle image velocimetry (PIV) in comparison with pressure sensitive paint (PSP) measurements. The aim of the investigation is to assess if PIV may be regarded as a complementary method to PSP, or even as a possible replacement at least for 2D flow analysis or at low speed, where PSP fails. The investigation is based on two different test cases: (1) the attached flow around a NACA-0012 airfoil and (2) the separated flow around a backward-facing step (BFS). Both cases are investigated at transonic flow conditions. For the airfoil, both PIV and PSP measurements were conducted for a direct comparison. At such high Reynolds number, the boundary layer thickness is very small, and therefore, the pressure in the flow field outside the boundary layer can be easily determined from the velocity data with an isentropic flow assumption. The results of the PIV-based surface pressure reconstruction and the one of PSP are compared with the static pressure taps installed on the model surface. For the BFS test case, synthetic PIV images are produced from a Large Eddy Simulation (LES). In this case, flow separation as well as strong viscous effects appear which inhibit the use of the isentropic flow assumption. Therefore, the Reynold averaged momentum equation is directly used and the pressure is determined solving the Poisson equation which is obtained by applying the divergence operator to the momentum equation. The results are compared with the pressure distribution on the surface given by the LES simulation. This case aims to analyze the accuracy of PIV-based surface pressure determination in case of massive flow separation. It will be shown that the deviations to the expected results are caused by the spatially discretization as well as by spatially averaging, which occurs in a standard PIV measurement. In addition, the effect of the velocity uncertainty on the estimated surface pressure distribution biases the result significantly. This implies that PSP will be hardly replaced by PIV.

Effects of wing shape, aspect ratio and deviation angle on aerodynamic performance of flapping wings in hover

This numerical study is focused on assessing the effect on the aerodynamic hovering performance of wing shapes defined by the radius of the first moment of the wing area (r1¯) and aspect ratio (AR). In addition, the effect of introducing a deviation angle in the kinematics is examined. The performance of r1¯=0.43, 0.53, and 0.63 wings with AR of 1.5, 2.96, 4.5, and 6.0 is investigated at Reynolds numbers (Re) = 12, 400, and 13 500. The performance trends of the wing shapes have been observed to be independent of Re for both 2-angle and 3-angle kinematics. This is because high suction pressures associated with the leading-edge vortex are predominantly spread in the distal (away from the wing root) and leeward regions (towards the trailing-edge) of high flapping velocities for all the cases. While the deviation angle is detrimental to the production of lift and power economy (PE, defined as the ratio of the mean lift coefficient to the mean aerodynamic power coefficient) at Re = 12 due to strong viscous effects, it improves PE at Re = 400 and 13 500. A high instantaneous angle of attack at the stroke reversal results in high lift peak for 3-angle kinematics but its effect at Re = 400 and 13 500 is attenuated by strong vortical structures on the underside of the wing. Maximum PE is achieved at AR = 2.96, as a low AR wing does not produce enough lift and high AR wings consume more aerodynamic power. Although the lift is maximized using high r1¯ and AR wings, our results show that low r1¯ and high AR wings are best for maximizing PE for a given lift in insects.

Energy Exchanges between Density Fronts and Near-Inertial Waves Reflecting off the Ocean Surface

AbstractInertial waves propagating upward in a geostrophically balanced front experience critical reflections against the ocean surface. Such reflections naturally create oscillations with small vertical scales, and viscous friction becomes a dominant process. Here, friction modifies the polarization relations of internal waves and allows energy from the balanced front to be exchanged with the ageostrophic motions and eventually dissipated. In addition, while in the well-known inviscid case internal waves propagate on only two characteristics, this study demonstrates using an analytical model that strong viscous effects introduce additional oscillatory modes that can exchange energy with the front. Moreover, during a linear, near-critical reflection, the superposition of several of these oscillations induces an even stronger energy exchange with the front. When the Richardson number based on the frontal thermal wind shear is O(1), the rate of energy exchange peaks at wave frequencies that are near inertial and is comparable in magnitude to the energy flux of the incident, upward-propagating waves. Two-dimensional, linear numerical experiments confirm this finding. The analytical model also demonstrates that this process is qualitatively insensitive to the actual value of the viscosity or the form of the boundary condition at the surface. In fully nonlinear experiments, the authors recover these qualitative conclusions. However, nonlinear wave–wave interactions and turbulence in particular, strongly modify the amount of energy that is exchanged with the front. In practice, such nonlinear effects are only active when the incident waves have frequencies higher than the Coriolis frequency, since these configurations are conducive to near-resonant triad interactions between incident and reflected waves.

Study of Physical Aspects of Rarefied Gas Flow Through Micro/Nano Scale Channels Using DSMC

Rarefied gas flow through micro/nano electro mechanical systems does not perform exactly as that in macro-scale devices. The main goal of this study was to investigate mixed subsonic–supersonic flows in micro/nano channels and to provide physical descriptions on their behaviours. We use DSMC method as a reliable numerical tool to extend our simulation because it provides accurate solution for the Boltzmann equations over the entire range of rarefied flow regime or Knudsen numbers. As is known, the appearance of oblique/normal shocks at the inlet of a channel adds to the complexity of internal flow field analyses. We found some very unique physical aspects of micro/nano flows including mixed supersonic–subsonic flow regimes in constant area ducts and the attenuation of emitted shocks, which are attributed to the strong viscous forces and dominant rarefaction effects at micro/nano scales.

Measurements of turbulence in a microscale multi-inlet vortex nanoprecipitation reactor

The microscale multi-inlet vortex reactor (MIVR) is designed for use in Flash NanoPrecipitation (FNP), a promising technique for producing nanoparticles within small particle size distribution. Fluid mixing is crucial in the FNP process, and due to mixing’s strong dependence upon fluid kinematics, investigating velocity and turbulence within the reactor is crucial to optimizing reactor design. To this end, microscopic particle image velocimetry has been used to investigate flow within the MIVR. Three Reynolds numbers are studied, namely, Rej = 53, 93 and 240. At Rej = 53, the flow is laminar and steady. Due to the strong viscous effects at this Reynolds number, distinct flow patterns are observed at different distances from the reactor top and bottom walls. The viscous effects also retard the tangential motions within the reactor, resulting in a weaker vortex than appears at the higher Reynolds numbers. As the Reynolds number is increased to 93, the flow becomes more homogeneous over the depth of the reactor due to weaker viscous effects, yet the flow is still steady. The diminishing effects of viscosity also result in a stronger vortex. At the highest Reynolds number investigated, the flow is turbulent. Turbulent statistics including tangential and radial velocity fluctuations and Reynolds shear stresses are analyzed for this case in addition to the mean velocity field. The tangential motions of the flow are strongest at Rej = 240. Both the tangential and radial velocity fluctuations increase as the flow spirals toward the center of the reactor. The magnitudes of the tangential and radial velocity fluctuations are similar, suggesting that the turbulence is locally isotropic.

On the gravitational collapse of a gas cloud in the presence of bulk viscosity

We analyse the effects induced by the bulk (or second) viscosity on the dynamics associated with the extreme gravitational collapse. The aim of the work is to investigate whether the presence of viscous corrections to the evolution of a collapsing gas cloud influences the top-down fragmentation process. To this end, we generalize the approach presented by Hunter (1962 Astrophys. J. 136 594) to include in the dynamics of the (uniform and spherically symmetric) cloud the negative pressure contribution associated with the bulk viscosity phenomenology. Within the framework of a Newtonian approach (whose range of validity is outlined), we extend to the viscous case either the Lagrangian or the Eulerian motion of the system addressed in Hunter (1962 Astrophys. J. 136 594) and we treat the asymptotic evolution in correspondence with a viscosity coefficient of the form ζ = ζ0 ρ5/6(ρ being the cloud density and ζ0= const). We show how the adiabatic-like behaviour of the gas (i.e. when the polytropic index γ takes values 4/3 < γ ⩽ 5/3) is deeply influenced by viscous correction when its collapse reaches the extreme regime toward the singularity. In fact, for sufficiently large viscous contributions, density contrasts associated with a given scale of the fragmentation process acquire, asymptotically, a vanishing behaviour which prevents the formation of sub-structures. Since in the non-dissipative case density contrasts diverge (except for the purely adiabatic behaviour γ = 5/3 in which they remain constant), we can conclude that in the adiabatic-like collapse the top-down mechanism of structure formation is suppressed as soon as enough strong viscous effects are taken into account. Such a feature is not present in the isothermal-like (i.e. 1 ⩽ γ < 4/3) collapse because the sub-structure formation is yet present and outlines the same behaviour as in the non-viscous case. We emphasize that in the adiabatic-like collapse the bulk viscosity is also responsible for the appearance of a threshold scale (dependent on the polytropic index) beyond which perturbations begin to increase; this issue, absent in the non-viscous case, is equivalent to dealing with a Jeans length. A discussion of the physical character that the choice ν = 5/6 takes place in the present case is provided.

Effects of Soluble Surfactants on the Deformation and Breakup of Stretching Liquid Bridges

Surfactants are routinely used to control the breakup of drops and jets in many applications such as inkjet printing, crop spraying, and DNA or protein microarraying. The breakup of surfactant-free drops and jets has been extensively studied. By contrast, little is known about the closely related problem of interface rupture when surfactants are present. Solutions of a nonionic surfactant, pentaethylene glycol monododecyl ether, or C12E5, in water and in 90 wt % glycerol/water are used to show the effects of surfactant and viscosity on the deformation and breakup dynamics of stretching liquid bridges. Equilibrium surface tensions for both solutions can be fitted with the Langmuir-Szyskowski equation. All experiments have been done at 24 degrees C. The critical micelle concentrations for C12E5 are 0.04 and 0.4 mM in water and the glycerol/water solution, respectively. With high-speed imaging, the dynamic shapes of bridges held captive between two rods of 3.15 mm diameter are captured and analyzed with a time resolution of 0.1-1 ms. The bridge lengths are 3.15 mm initially and about 5-7 mm at pinch-off. Breakup occurs after stretching for about 0.2-0.3 s, depending on the solution viscosity and the surfactant concentration. When the liquid bridges break up, the volume of the sessile drop left on the bottom rod is about 3 times larger than that of the pendant drop left on the top rod. This asymmetry is due to gravity and is influenced by the equilibrium surface tensions. Surfactant-containing low-viscosity water bridges are shown to break up faster than surfactant-free ones because of the effect of gravity. With or without surfactant, water bridges form satellite drops. Surfactant-containing high-viscosity glycerol/water bridges break up more slowly than surfactant-free ones because of strong viscous effects. Moreover, the shapes of the sessile drops close to breakup exhibit a "pear-like" tip; whether a satellite forms depends on the surface age of the bridge before stretching commences. These unexpected effects arising from the addition of surfactants are due to the capillary pressure reduction and Marangoni flows linked to dynamic surface tension.

A detailed experimental analysis of the flow in a highly loaded fixed compressor cascade: the iso-cascade co-operative programme on code validation

The ISO-Cascade programme, involving IHI, Snecma and ONERA, has been undertaken to perform a thorough experimental investigation of a highly loaded compressor cascade in order to validate Navier–Stokes solvers used in turbomachinery bladings design. The aim of this study was to reproduce in a two-dimensional fixed geometry the main physical features of the flow in a real compressor, including strong viscous effects. The flow produced in the ISO-Cascade has been qualified by surface flow visualisations, schlieren pictures, surface pressure and skin friction measurements, surveys by multi-hole pressure probes and extensive explorations with a three-component LDV system. The large amount of results thus obtained has allowed a consistent description of the flow topology and the constitution of an unrivalled data bank to validate computer codes.

Micro-Shock Waves Generated Inside a Fluid Jet Impinging on Plane Wall

An Nd:glass laser pulse (18 ns, 1.38 J) is focused in a tiny area of about 100-mum diam under ambient conditions to produce micro-shock waves. The laser is focused above a planar surface with a typical standoff distance of about 4 mm, The laser energy is focused inside a supersonic circular jet of carbon dioxide gas produced by a nozzle with internal diameter of 2.9 mm and external diameter of 8 mm, Nominal value of the Mach number of the jet is around 2 with the corresponding pressure ratio of 7.5 (stagnation pressure/static pressure at the exit of the nozzle), The interaction process of the micro-shock wave generated inside the supersonic jet with the plane wall is investigated using double-pulse holographic interferometry. A strong surface vortex field with subsequent generation of a side jet propagating outward along the plane wail is observed. The interaction of the micro-shock wave with the cellular structure of the supersonic jet does not seem to influence the near surface features of the flowfield. The development of the coherent structures near the nozzle exit due to the upstream propagation of pressure waves seems to be affected by the outward propagating micro-shock wave. Mach reflection is observed when the micro-shock wave interacts with the plane wall at a standoff distance of 4 mm, The Mach stem is slightly deflected, indicating strong boundary-layer and viscous effects near the wall. The interaction process is also simulated numerically using an axisymmetric transient laminar Navier-Stokes solver. Qualitative agreement between experimental and numerical results is good.

Flow Phenomena on Rotary Wing Systems and their Modeling

Flow fields around rotary wings, especially around helicopter rotors, are extremely complex due to strong three-dimensional and viscous effects. Moreover, in yawed flow conditions of propellers and wind turbines as well as in helicopter forward flight, they are highly unsteady. Fluid-structure interactions require the treatment of the rotor blades as aeroelastic systems. Furthermore, helicopter and propeller flows may become transonic in some regions. Flow interaction effects and problems regarding noise generation must also be taken into account. Accordingly, the solution of the basic equations governing these problems is very difficult and usually only feasible with the help of numerical methods, since systems of nonlinear partial differential equations must be analyzed, A numerical investigation requires appropriate turbulence modeling for most technical applications. The paper presents several theoretical and numerical models for the simulation of the aforementioned flow phenomena.

A shock tube research facility for high-resolution measurements of compressible turbulence

A new shock tube facility with a 30.5 cm (1 ft) inside diameter is currently in operation that allows for high-spatial-resolution measurements of compressible turbulence. Small scales of turbulence behave very differently from large scales when they interact with shock or expansion waves. Highly resolved measurements can provide new information on the interaction at small scales. Another notable characteristic of the present facility is the ability to control the flow velocity behind the reflected shock through the porosity of the reflecting wall. Tests showed good flow quality with sufficiently long observation times. Measurements of piecewise average skin friction over short segments of the tube indicated strong viscous effects very close to the diaphragm where the shock is developing. The skin friction and the shock propagation speed virtually remained constant inside the working section of the shock tube in all investigated flow cases, even in low Mach number cases where viscous effects are stronger. The experimental results are compared with numerical simulations, including the effects of the reflecting porous wall and viscous effects.

Model for rotor tip vortex-airframe interaction. II - Comparison with experiment

The interaction between a vortex and a solid boundary involves the development of a variety of length and time scales, some of which are due to very strong viscous effects. Prediction of these phenomena from first principles would remove a major obstacle in the computation of flows around rotorcraft. Quantitative comparisons are made with experimental results for a rotor tip vortex approaching a cylindrical airframe with a hemispherical leading edge.

Numerical Study of Flow and Thrust Produced by Heaving and Combined Oscillations of 2D Hydrofoil

Unsteady viscous flow field around an oscillating 2D hydrofoil is studied numerically. The main objectives are to study the flow phenomena and the abilities of an oscillating foil to produce thrust. In the general case, the foil is performing a combination of symmetric pitching, heaving and surging oscillations. Numerical simulations are performed over a modified NAC0012 foil. Investigations consider the basic flow features and the effect of main governing parameters. Flow is simulated by solving the full 2D unsteady Navier-Stokes equations, in a vorticity-stream function formulation. An implicit numerical algorithm and a compact finite difference scheme are employed. The validity of the flow simulation is studied through the comparison with the available experimental results. Flow analysis designates that the strong unsteady viscous effects with massive flow separation and intensive vortical structures are valid for the most of the studied motions. Such flow patterns are result of the leading and trailing edge separation and the further flow evolution including a complicated wake interaction. From a propulsive point of view, the combined pitching and heaving motion with a shifted phase of pitching is the most effective one. Surging oscillations introduce additional dynamic effects. Governing parameters have an interrelated influence on the flow penomena and induced forces.

Heat and mass transfer in a single screw extruder for non-Newtonian materials

Numerical simulation of the transport processes arising in a single screw extruder for non-Newtonian fluids such as plastics and food is considered. The study is directed mainly at simulating the heat and mass transfer inside the screw channel, for a power-law fluid. Moisture is taken as the species for mass transfer, since it is of particular interest in food processing. Finite difference computations are carried out to solve the governing set of partial differential equations for the velocity, temperature and moisture fields, over a wide range of governing parameters. The variation of viscosity with temperature and moisture is taken into account. The basic physical approach for modeling the complicated heat and mass transfer processes for inelastic non-Newtonian materials is outlined. As an application of this analysis to starchbased food systems, the reactive nature of the food constituents is incorporated by including the rate of reaction (gelatinization) between moisture and food. Results are presented in terms of the velocity, temperature and moisture concentration contours. Strong viscous dissipation effects are found to arise for typical operating conditions. The moisture contours indicate that starch gelatinization typically occurs first at the screw root. The effect of the various governing parameters on pressure build-up within the extruder channel is determined and discussed in terms of the underlying physical processes. Experimental validation of some of the numerical results has been carried out, and the comparisons are quite good. Results are also presented for the residence time distribution (RTD), an important design parameter in extrusion. Though this study considers moisture transport, the basic approach presented may easily be extended to reactions and mass transfer of other species in polymers and in other non-Newtonian materials.