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Pre-metered coating flow models with Goma 7: Workflow Tutorial

Tutorials for modeling of slot-die and slide-die coating flows with Goma 7, an open source finite element code, are presented. The tutorials cover the workflow to attaining steady state solutions for these flows, and continuation strategies for navigating the operating windows. Advanced topics of coating window prediction, automated multiparameter continuation, non-Newtonian rheology, dynamic contact line modeling, and some more solution strategies are also covered.

08 HYDROGEN↗

MANTLE: A finite element program for the thermal-mechanical analysis of mantle convection. A user's manual with examples

A finite element computer code for the analysis of mantle convection is described. The coupled equations for creeping viscous flow and heat transfer can be solved for either a transient analysis or steady-state analysis. For transient analyses, either a control volume or a control mass approach can be used. Non-Newtonian fluids with viscosities which have thermal and spacial dependencies can be easily incorporated. All material parameters may be written as function statements by the user or simply specified as constants. A wide range of boundary conditions, both for the thermal analysis and the viscous flow analysis can be specified. For steady-state analyses, elastic strain rates can be included. Although this manual was specifically written for users interested in mantle convection, the code is equally well suited for analysis in a number of other areas including metal forming, glacial flows, and creep of rock and soil.

Thompson, E.↗

Non-Newtonian Fluid Model Incorporated into Elastohydrodynamic Lubrication of Rectangular Contacts

A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed, load, materials, and sliding velocity and limiting-shear-strength proportionality constant on dimensionless minimum film thickness was investigated. Fourteen cases were used in obtaining the minimum-film-thickness equation for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.

Jacobson, B. O.↗

Non-Newtonian fluid model incorporated into elastohydrodynamic lubrication of rectangular contacts

A procedure is outlined for the numerical solution of the complete elastohydrodynamic lubrication of rectangular contacts incorporating a non-Newtonian fluid model. The approach uses a Newtonian model as long as the shear stress is less than a limiting shear stress. If the shear stress exceeds the limiting value, the shear stress is set equal to the limiting value. The numerical solution requires the coupled solution of the pressure, film shape, and fluid rheology equations from the inlet to the outlet. Isothermal and no-side-leakage assumptions were imposed in the analysis. The influence of dimensionless speed, load, materials, and sliding velocity and limiting-shear-strength proportionality constant on dimensionless minimum film thickness was investigated. Fourteen cases were used in obtaining the minimum-film-thickness equation for an elastohydrodynamically lubricated rectangular contact incorporating a non-Newtonian fluid model. Computer plots are also presented that indicate in detail pressure distribution, film shape, shear stress at the surfaces, and flow throughout the conjunction.

Jacobson, B. O.↗

Effects of depth-variations in creep laws on the formation of plates in mantle dynamics

The influences of depth-varying rheologies on the structure of mantle convection and the near surface flow fields are studied. Upwelling flows crossing the upper-lower mantle boundary become considerably thinner and faster. Streamlines are concentrated near the surface and other platelike characteristics are enhanced by this type of rheological stratification in which the averaged effective viscosity of the upper mantle is about two orders of magnitude lower than that of the lower mantle. The presence of a lithosphere with a higher nonlinear dependence in the flow law further promotes platelike behavior. Platelike character of the top boundary-layer is encouraged by a decreasing depth-dependent viscosity in the non-Newtonian upper-mantle and by greater convective vigor.

Van Den Berg, Arie P.↗

Finite amplitude instability of second-order fluids in plane Poiseuille flow.

The hydrodynamic stability of plane Poiseuille flow of second-order fluids to finite amplitude disturbances is examined using the method of Stuart and Watson as extended by Reynolds and Potter. For slightly non-Newtonian fluids subcritical instabilities are predicted. No supercritical equilibrium states are expected if the entire spectrum of disturbance wavelengths is present. Possible implications with respect to the Toms phenomenon are discussed.

Mcintire, L. V.↗

Surface Structures of Hawaiian Lavas

Surface and internal lava structures can be valid indicators of lava viscosity and rheology, provided that care is taken to identify and eliminate structures which are strain-rate-dependent. Here, a spectrum of types among Hawaiian basaltic flows is found ranging from pahoehoe to a'a, that are interpreted as marking a progression in lava viscosity and a change in rheology. The most fluid type in this spectrum is normal pahoehoe that has a smooth but commonly wrinkled or folded (ropy) surface. The next type, distinctly more viscous and probably non-Newtonian in rheology, is spiny pahoehoe which is characterized by a spinose surface and an absence of ropy structures. Preliminary studies on the long lavas of Mauna Loa indicated, perhaps surprisingly, that there is no clear-cut correlation of lava length with type in this spectrum of lavas, indicating that viscosity/yield strength of the basaltic lavas per se are not the primary controls determining flow length. Flowage of the lava through lava tubes, while it may help to account for the long flow distance of some lavas, is not a generally applicable explanation for long flow length.

Rowland, S. K.↗

Models of recurrent strike-slip earthquake cycles and the state of crustal stress

Numerical models of the strike-slip earthquake cycle, assuming a viscoelastic asthenosphere coupling model, are examined. The time-dependent simulations incorporate a stress-driven fault, which leads to tectonic stress fields and earthquake recurrence histories that are mutually consistent. Single-fault simulations with constant far-field plate motion lead to a nearly periodic earthquake cycle and a distinctive spatial distribution of crustal shear stress. The predicted stress distribution includes a local minimum in stress at depths less than typical seismogenic depths. The width of this stress 'trough' depends on the magnitude of crustal stress relative to asthenospheric drag stresses. The models further predict a local near-fault stress maximum at greater depths, sustained by the cyclic transfer of strain from the elastic crust to the ductile asthenosphere. Models incorporating both low-stress and high-stress fault strength assumptions are examined, under Newtonian and non-Newtonian rheology assumptions. Model results suggest a preference for low-stress (a shear stress level of about 10 MPa) fault models, in agreement with previous estimates based on heat flow measurements and other stress indicators.

Lyzenga, Gregory A.↗

Error analysis for reducing noisy wide-gap concentric cylinder rheometric data for nonlinear fluids - Theory and applications

This work discusses the propagation of errors for the recovery of the shear rate from wide-gap concentric cylinder viscometric measurements of non-Newtonian fluids. A least-square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod (1953) and Pawlowski (1953) ('power-law' approximation) and for the first term of the series developed by Krieger (1968). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger-Elrod-Pawlowski series ('infinite radius' approximation) and the power-law approximation may recover the shear rate with equal accuracy as the full Krieger-Elrod-Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest than during shearing, and that, for the range of shear rates investigated, a four-parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma.

Borgia, Andrea↗

The non-Newtonian heat and mass transport of He 2 in porous media used for vapor-liquid phase separation

This investigation of vapor-liquid phase separation (VLPS) of He 2 is related to long-term storage of cryogenic liquid. The VLPS system utilizes porous plugs in order to generate thermomechanical (thermo-osmotic) force which in turn prevents liquid from flowing out of the cryo-vessel (e.g., Infrared Astronomical Satellite). An apparatus was built and VLPS data were collected for a 2 and a 10 micrometer sintered stainless steel plug and a 5 to 15 micrometer sintered bronze plug. The VLPS data obtained at high temperature were in the nonlinear turbulent regime. At low temperature, the Stokes regime was approached. A turbulent flow model was developed, which provides a phenomenological description of the VLPS data. According to the model, most of the phase separation data are in the turbulent regime. The model is based on concepts of the Gorter-Mellink transport involving the mutual friction known from the zero net mass flow (ZNMF) studies. The latter had to be modified to obtain agreement with the present experimental VLPS evidence. In contrast to the well-known ZNMF mode, the VLPS results require a geometry dependent constant (Gorter-Mellink constant). A theoretical interpretation of the phenomenological equation for the VLPS data obtained, is based on modelling of the dynamics of quantized vortices proposed by Vinen. In extending Vinen's model to the VLPS transport of He 2 in porous media, a correlation between the K*(GM) and K(p) was obtained which permits an interpretation of the present findings. As K(p) is crucial, various methods were introduced to measure the permeability of the porous media at low temperatures. Good agreement was found between the room temperature and the low temperature K(p)-value of the plugs.

Yuan, S. W. K.↗

Insights into mixing of non-isothermal multi-polymer melts for complex plastics recycling

Catalytic recycling or upcycling of plastics is often limited not by catalyst performance, but by transport, arising from highly viscous, non-Newtonian polymer melts. In this work, we develop a reactor-scale framework that integrates rheological measurements, constitutive modeling, computational fluid dynamics (CFD), and experiments to quantify mixing, heat transfer, and dispersion in surrogate hydrocarbon melts representing mixed plastics systems. Temperature- and shear rate-dependent viscosity of low-density polyethylene (LDPE) and high-density polyethylene (HDPE) is measured to create two surrogate polymers (PLD and PHD) that capture the dominant shear-thinning flow behavior while neglecting strong elastic effects, enabling tractable simulation of non-isothermal, polymer-melt mixing using a Carreau-Arrhenius generalized Newtonian framework. Three-dimensional CFD simulations are employed to evaluate impeller performance in PLD using mixing time, cavern volume, thermal uniformity, and interfacial area for regimes in which viscoelastic effects are not dominant. We show that magnetic stir bars commonly used in lab-scale studies produce large thermal gradients (~60 °C) and poor mixing, even under idealized power delivery and polymer flow conditions. In contrast, close-clearance anchor impellers achieve near-isothermal operation, reduce mixing times by up to 5×, and provide >90% active circulation volume. We further demonstrate that, at low pseudo-Deborah number (De*), motor power requirements can be predicted directly from shear rate-dependent rheology using the Carreau-Arrhenius framework, enabling rational selection of operating conditions. Extension to surrogate immiscible multi-polymer systems based on PLD and PHD shows that interfacial area is highly sensitive to operating conditions and impeller design, with coaxial anchor-turbine configurations enhancing dispersion by up to 4 × .

Close-clearance impellers↗

The role of a pressure-dependent rheology in the dynamics of mantle circulation

A thermomechanical model for upper mantle convection was constructed such that the thickness and the structure of the lithosphere are determined self consistently by the heat transported by convection. In this study of the interaction between the lithosphere and upper mantle, strongly temperature and pressure dependent rheologies for both Newtonian and non-Newtonian creep mechanisms are employed. For a strictly temperature dependent rheology an insignificant amount of heat, less than 12.5 mW/sq m, can be transported convectively for an interior viscosity, 0(10 sup 21 Pas), compatible with post glacial rebound. On the other hand, for similar values of the interior viscosity, steady heat fluxes between 20 and 40 mW/sq m are produced by introducing pressure dependence into the rheology. For the temperature and pressure dependent flow law the horizontally averaged interior temperature displays very little variation with the amount of heat evacuated, once all of the rheological parameters are fixed. This finding may have important ramifications for parameterized convection.

Yuen, D. A.↗

Asperity lubrication and cavitation in face seals

The basic aspect of parallel-surface lubrication that distinguishes it from other areas of lubrication technology is that classical lubrication theory does not predict the existence of a stable hydrodynamic film for steady-state, isothermal, incompressible flow between smooth, parallel surfaces. Hydrodynamic films between apparently parallel surfaces have been observed in practice and are often essential for the reliable performance of thrust bearings and seals. In order to account for this fortunate discrepancy between classical theory and experiment, load-support mechanisms relating to accidential features characteristic of seal performance, which relax one or more of the assumptions in the classical theory and permit the theoretical prediction of load support are proposed. Some of the features that have been analyzed are vibratory effects such as wobble and bounce, surface waviness, nonsymmetric rotation resulting from various types of misalignment, lubricant density change, non-Newtonian lubricant effects, and surface roughness.

Walowitt, J. A.↗

Mantle plumes - A boundary layer approach for Newtonian and non-Newtonian temperature-dependent rheologies

Stress is placed on the temperature dependence of both a linear Newtonian rheology and a nonlinear olivine rheology in accounting for narrow mantle flow structures. The boundary-layer theory developed incorporates an arbitrary temperature-dependent power-law rheology for the medium, in order to facilitate the study of mantle plume dynamics under real conditions. Thermal, kinematic, and dynamic structures of mantle plumes are modelled by a two-dimensional natural-convection boundary layer rising in a fluid with a temperature-dependent power-law relationship between shear stress and strain rate. An analytic similarity solution is arrived at for upwelling adjacent to a vertical isothermal stress-free plane. Newtonian creep as a deformation mechanism, thermal anomalies resulting from chemical heterogeneity, the behavior of plumes in non-Newtonian (olivine) mantles, and differences in the dynamics of wet and dry olivine are discussed.

Yuen, D. A.↗

What can we learn about impact mechanics from large craters on Venus?

More than 50 unequivocal peak-ring craters and multiringed impact basins have been identified on Venus from Earth-based Arecibo, Venera 15/16, and Magellan radar images. These ringed craters are relatively pristine, and so serve as an important new dataset that will further understanding of the structural and rheological properties of the venusian surface and of impact mechanics in general. They are also the most direct analogues for craters formed on the Earth in Phanerozoic time. Finite-element simulations of basin collapse and ring formation were undertaken in collaboration with V. J. Hillgren (University of Arizona). These calculations used an axisymmetric version of the viscoelastic finite element code TECTON, modeled structures on the scale of Klenova or Meitner, and demonstrated two major points. First, viscous flow and ring formation are possible on the timescale of crater collapse for the sizes of multiringed basins seen on Venus and heat flows appropriate to the plant. Second, an elastic lithosphere overlying a Newtonian viscous asthenosphere results mainly in uplift beneath the crater. Inward asthenospheric flow mainly occurs at deeper levels. Lithospheric response is dominantly vertical and flexural. Tensional stress maxima occur and ring formation by normal faulting is predicted in some cases, but these predicted rings occur too far out to explain observed ring spacings on Venus (or on the Moon). Overall, these estimates and models suggest that multiringed basin formation is indeed possible at the scales observed on Venus. Furthermore, due to the strong inverse dependence of solid-state viscosity on stress, the absence of Cordilleran-style ring faulting in craters smaller than Meitner or Klenova makes sense. The apparent increase in viscosity of shock-fluidized rock with crater diameter, greater interior temperatures accessed by larger, deeper craters, and decreased non-Newtonian viscosity associated with larger craters may conspire to make the transition with diameter from peak-ring crater to Orientale-type multiringed basin rather abrupt.

Mckinnon, William B.↗

Flow-Driven Stretch Fluctuations Govern the Nonlinear Viscoelasticity of Elongating Associative Polymer Networks

We use nonequilibrium molecular dynamics simulations to verify recent tube-model predictions that associative polymer networks exhibit broad stretch fluctuations during elongational flow. Simulations further show that these fluctuating dynamics give rise to the rate-dependent extensional viscosity 𝜂 𝐸 measured in filament stretching experiments on H-bonding networks. Simulations model bivalent associative networks with a reactive bead-spring model for varying association strength and extensional strain rate. We observe that stretch fluctuations are driven by a new form of chain tumbling, where chains continually collapse and elongate as their associations break and reform within the advecting network. This produces a broad, nearly uniform distribution of chain stretch over a wide range of strain rates, manifesting as a rate-independent plateau in the extensional stress. Our results show that the nonlinear viscoelasticity of associative networks is dominated by large fluctuations in molecular response, which cannot be captured by current mean-field models.

biomimetic & bio-inspired materials↗

Filament extension atomizers: A study of integration potential into spray dryers for high-viscosity and non-Newtonian fluids

Filament extension atomizers (FEAs) are an emerging class of spray nozzles designed to atomize high-viscosity and non-Newtonian fluids that are challenging for conventional pressure or two-fluid nozzles. In this study, we investigate the influence of roller geometry, surface velocity, roller material, and fluid rheology on the atomization performance of FEA systems using concentrated whey protein suspensions (50–70 wt. %). Extensional and shear rheology experiments, along with high-speed imaging and particle image velocimetry, reveal that filament breakup dynamics are governed by competition between inertial, capillary, and viscoelastic stresses. High roller rotational velocity leads to narrower spray cones, contradicting rheology experiments and suggests a significant inertial contribution to filament breakup. Smaller rollers operating at the same rotational velocity led to broader spray cones consistent with expectations. An FEA nozzle was integrated into a conventional dryer producing particles in the 100 μm range. Results suggest that FEA technology enables atomization of highly viscous fluids at industrially relevant spray cone angles similar to those generated by pressure nozzles, offering a pathway to improve energy efficiency in spray drying by enabling higher solids loading feedstocks. Furthermore, these insights provide critical guidance for optimizing FEA nozzle designs and process parameters across a range of applications.

Energy efficiency↗