Simple Viscous Model Research Articles

Protoplanetary disc ‘isochrones’ and the evolution of discs in the M˙-Md plane

In this paper, we compare simple viscous diffusion models for the disc evolution with the results of recent surveys of the properties of young protoplanetary discs. We introduce the useful concept of `disc isochrones' in the accretion rate - disc mass plane and explore a set of Montecarlo realization of disc initial conditions. We find that such simple viscous models can provide a remarkable agreement with the available data in the Lupus star forming region, with the key requirement that the average viscous evolutionary timescale of the discs is comparable to the cluster age. Our models produce naturally a correlation between mass accretion rate and disc mass that is shallower than linear, contrary to previous results and in agreement with observations. We also predict that a linear correlation, with a tighter scatter, should be found for more evolved disc populations. Finally, we find that such viscous models can reproduce the observations in the Lupus region only in the assumption that the efficiency of angular momentum transport is a growing function of radius, thus putting interesting constraints on the nature of the microscopic processes that lead to disc accretion.

Dry patches in a flowing film: Predicting rewetting and the effects of inertia

We study the effects of inertia on the shape and stability of dry patches using liquids of decreasing viscosities. These dry patches are formed when a liquid film flows down along a substrate under partial wetting conditions. They become stationary and exhibit an “arch” shape well described by a simple viscous model developed long ago by Podgorski. Surprisingly, this “arch” shape appears to be robust when one decreases the fluid viscosity which increases inertial effects, but the evolution of the apex curvature upon flow rate is strongly affected. We here proposed an improved description of the dry patch evolution taking into account several physical effects as the hydrostatic pressure in the liquid film, the curvature of the contact line, and these inertial effects. These ones affect both the mechanical equilibrium of the rim surrounding the dry patch and the flow inside the rim. This model allows us to show that the dry patch shape remains extremely close to the viscous -Podgorski- prediction but with a rescaling of the apex curvature. It also allows us to get a better prediction of the apex curvature dependence upon flow rate and a prediction of the rewetting threshold above which dry patches are swept away by the film flow. This critical flow rate Γc is in good agreement with our experiments performed in the range of viscosity from 5 to 20 cP with silicon oils.

A Theoretical and Numerical Study of an Additional Viscosity Term in a Modified Elasto-Plastic Friction Model for Wet Friction Clutch Simulations

This paper deals with a theoretical and numerical study of various viscosity terms in the modified elasto-plastic friction model and their influence on the resulting friction force-torque, transmitted through the contact of the friction clutch. Various simple viscous definitions for fluids considering shear rate dependent viscosity were investigated. The Carreau fluid model was chosen as a basis for the research, since it can describe Newtonian, dilatant, and pseudo plastic fluids. In addition to theoretical investigations, numerical simulations under realistic friction clutch operation conditions were carried out. The results were compared to the results of a validation case for a dry friction clutch simulation using the modified elasto-plastic friction model. This research showed significant differences between various viscosity definitions and revealed the drawbacks of such approach, were simple viscous models were used. In addition to viscosity, calculating the heat generated due to friction and its influence on the contact temperatures are discussed briefly. The basic theory and equations are given along with the directions for future work. The requirements for an accurate temperature calculation in the friction contact are outlined.

Power dissipation in turbomolecular pumps at high pressure

The operating range of turbopumps is being extended to higher pressures as a consequence of many demanding applications. Varian VPT has specialized in the design of Gaede stages for extending the operating pressure of the pump. The present work is an extension of the activity made in the last five years in the direction of a good understanding of the behavior of the Gaede stage in viscous flow conditions. Starting from the analysis of the pressure distribution into a single stage, already presented in a previous paper, a transitional power consumption model is derived. The model allows to predict the power consumption of a single Gaede stage as a function of the pumping channel dimensions and clearances, the rotational speed, the nature of the gas pumped, and the operating pressure. The model is based on three main assumptions: (1) the pressure distribution along the channel satisfies a diffusion viscous model at zero net gas flow, (2) the gas flow boundary layer across channel is derived from a simple viscous model, and (3) the gas viscosity obeys a transition expression valid for the pumping channel geometry. Results are compared with the experimental data provided by different single Gaede stages, with different dimensions, at different speed and operating pressure. The behavior of the model with different pump stage clearances is analyzed and results are compared with the experimental evidence. A useful utilization of the model is in the optimization of the design of multistage Gaede pumps.

Nonlinear Dynamics of Coupled Shear Walls Using Transfer Matrices

An application of the transfer‐matrix technique to the nonlinear dynamic analysis of coupled shear walls is presented. Through the proposed method, the problem is reduced to a tractable size without the imposition of severe uniformity conditions on the structure. The dynamic response is determined by a step‐by‐step numerical approach in which the properties of the structural elements are updated according to the current state of deformation and yield. The transfer‐matrix formulation adopts established models of material behavior in dealing with inelastic beam deformation and load reversals. The dynamic solution assumes constant properties within short time increments, and relies on the kinematic relationships of the Wilson‐θ method. Damping has also been taken into account through a simple viscous model. The effectiveness and accuracy of the method, as well as its potential for further development, are assessed by comparing its predictions with measured displacements of model structures subjected to vario...

Gravity‐driven deformation of the crust on Venus

Intense horizontal deformation features are observed on the surface of Venus despite the apparent absence of terrestrial‐style plate tectonics. High surface temperature, low erosion rate, and regions of elevated terrain suggest that gravity spreading may be responsible for some of these features. Gravity spreading on the Earth is known to cause extensive deformation in certain thin‐skinned tectonic regions, where the uppermost layers become detached along a decollement. While the high pore pressures and soft sedimentary rocks frequently observed along decollements on the Earth are not plausible for Venus, temperature induced regions of ductile deformation may exist. Simple viscous models of gravity spreading above a ductile region of the crust are developed to examine the effects of rheology, thermal gradient, surface slope and crustal thickness on deformation. For a reasonable range of parameters, the models show that surface‐slope‐driven ductile deformation at relatively shallow depths in the crust is possible and may be capable of detaching the uppermost rigid portion of the crust, resulting in horizontal translation.

The Hump Deformation Preceding a Moving Load on a Layer of Soft Material

When a load, for instance a heavy roller, moves slowly along the surface of a solid mass of soft material, a “hump” deformation is often observed to precede it. The process of formation from an initially level surface, and the final form of hump established, are investigated analytically for a purely viscous material, in two-dimensional motion. It becomes evident that a material showing nonlinear creep, or a viscoelastic material, would show qualitatively similar behavior, the simple viscous model being adequate to exhibit the essential qualitative features.