Contact in a viscous fluid. Part 1. A falling wedge

2010 ◽  
Vol 646 ◽  
pp. 327-338 ◽  
Author(s):  
C. J. CAWTHORN ◽  
N. J. BALMFORTH
Keyword(s):  
Viscous Fluid ◽  
Stokes Flow ◽  
Finite Time ◽  
Approximate Analytical Solution ◽  
Plane Surface ◽  
Two Dimensional ◽  
Infinite Time ◽  
Logarithmic Divergence ◽  
Sharp Corners ◽  
Made In

Computations are presented of the upward force on a two-dimensional wedge descending towards a plane surface due to the Stokes flow of an intervening viscous fluid. The predictions are compared with those of lubrication theory and an approximate analytical solution; all three predict a logarithmic divergence of the force with the minimum separation. An object falling vertically under gravity will therefore make contact with an underlying plane surface in finite time if roughened by asperities with sharp corners (with smooth surfaces, contact is made only after infinite time). Contact is still made in finite time if the roughened object also moves horizontally or rotates as it falls.

Contact in a viscous fluid. Part 2. A compressible fluid and an elastic solid

2010 ◽  
Vol 646 ◽  
pp. 339-361 ◽  
Author(s):  
N. J. BALMFORTH ◽  
C. J. CAWTHORN ◽  
R. V. CRASTER
Keyword(s):  
Viscous Fluid ◽  
Half Space ◽  
Compressible Fluid ◽  
Finite Time ◽  
Asymptotic Methods ◽  
Elastic Solid ◽  
Two Dimensional ◽  
Infinite Time ◽  
Elastic Wall ◽  
Final Approach

A lubrication theory is presented for the effect of fluid compressibility and solid elasticity on the descent of a two-dimensional smooth object falling under gravity towards a plane wall through a viscous fluid. The final approach to contact, which takes infinite time in the absence of both effects, is determined by numerical and asymptotic methods. Compressibility can lead to contact in finite time either during inertially generated oscillations or if the viscosity decreases sufficiently quickly with increasing pressure. The approach to contact is invariably slowed by allowing the solids to deform elastically; specific results are presented for an underlying elastic wall modelled as a foundation, half-space, membrane or beam.

scholarly journals Semi-analytical solutions for two-dimensional elastic capsules in Stokes flow

2012 ◽  
Vol 468 (2146) ◽  
pp. 2915-2938 ◽  
Author(s):  
Michael Higley ◽  
Michael Siegel ◽  
Michael R. Booty
Keyword(s):  
Analytical Solutions ◽  
Stokes Flow ◽  
Finite Time ◽  
Capillary Number ◽  
Time Dependent ◽  
Two Dimensional ◽  
Elastic Interfaces ◽  
Critical Capillary Number ◽  
Field Velocity ◽  
Elastic Capsules

Elastic capsules occur in nature in the form of cells and vesicles and are manufactured for biomedical applications. They are widely modelled, but there are few analytical results. In this paper, complex variable techniques are used to derive semi-analytical solutions for the steady-state response and time-dependent evolution of two-dimensional elastic capsules with an inviscid interior in Stokes flow. This provides a complete picture of the steady response of initially circular capsules in linear strain and shear flows as a function of the capillary number Ca . The analysis is complemented by spectrally accurate numerical computations of the time-dependent evolution. An imposed nonlinear strain that models the far-field velocity in Taylor's four-roller mill is found to lead to cusped steady shapes at a critical capillary number Ca c for Hookean capsules. Numerical simulation of the time-dependent evolution for Ca > Ca c shows the development of finite-time cusp singularities. The dynamics immediately prior to cusp formation are asymptotically self-similar, and the similarity exponents are predicted analytically and confirmed numerically. This is compelling evidence of finite-time singularity formation in fluid flow with elastic interfaces.

scholarly journals Stokes Flow between Two Cylinders

2012 ◽  
Vol 36 (1) ◽  
pp. 123-135
Author(s):  
A Murad ◽  
SK Sen
Keyword(s):  
Viscous Fluid ◽  
Stokes Flow ◽  
Hydrodynamic Force ◽  
Outer Cylinder ◽  
Fluid Motion ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Line Sink ◽  
Academy Of Sciences ◽  
Viscous Fluid Motion

The two-dimensional slow viscous fluid motion between two co-axial circular cylinders showed  the inner cylinder is shear-free and the outer one is rigid. The flow is due to the presence of a line source and a line sink of equal strength on the outer cylinder. The stream function for the flow in the annular region is established. The hydrodynamic force on the inner shear-free cylinder has been  evaluated. Some numerical values for the force have been presented in a table and compared with  corresponding known values where both inner and outer cylinders are rigid. DOI: http://dx.doi.org/10.3329/jbas.v36i1.10928 Journal of Bangladesh Academy of Sciences, Vol. 36, No. 1, 123-135, 2012

Two-dimensional Brinkman flows and their relation to analogous Stokes flows

2019 ◽  
Vol 84 (5) ◽  
pp. 912-929 ◽  
Author(s):  
P A Martin
Keyword(s):  
Circular Cylinder ◽  
Stokes Flow ◽  
Fluid Velocity ◽  
Additional Term ◽  
Far Field ◽  
Two Dimensional ◽  
Logarithmic Divergence ◽  
Stokes Flows ◽  
Flow Past ◽  
Logarithmic Growth

Abstract 2D Stokes flows often exhibit the Stokes paradox: logarithmic growth of the fluid velocity in the far field. Analogous Brinkman flows are governed by the same equations apart from an additional term involving a parameter $\alpha$. Although these equations reduce to those for Stokes flow when $\alpha =0$, we show that the Brinkman solutions do not approach the corresponding Stokes solutions as $\alpha \to 0$; instead, logarithmic divergence with $\alpha$ is found. We also show that Brinkman flows do not exhibit a Stokes-like paradox. These results are given in detail for two specific problems, namely flow past a rigid circular cylinder and flow past a thin rigid strip.

Spectrophotometric measurements of objective-prism spectra

1966 ◽  
Vol 24 ◽  
pp. 118-119
Author(s):  
Th. Schmidt-Kaler
Keyword(s):  
Progress Report ◽  
Two Dimensional ◽  
Objective Prism ◽  
Made In

I should like to give you a very condensed progress report on some spectrophotometric measurements of objective-prism spectra made in collaboration with H. Leicher at Bonn. The procedure used is almost completely automatic. The measurements are made with the help of a semi-automatic fully digitized registering microphotometer constructed by Hög-Hamburg. The reductions are carried out with the aid of a number of interconnected programmes written for the computer IBM 7090, beginning with the output of the photometer in the form of punched cards and ending with the printing-out of the final two-dimensional classifications.

Chaotic Advection by Two-Dimensional Stokes Flow in a Semicircle

2004 ◽  
Vol 31 (4) ◽  
pp. 344-357
Author(s):  
T. A. Dunaeva ◽  
A. A. Gourjii ◽  
V. V. Meleshko
Keyword(s):  
Stokes Flow ◽  
Chaotic Advection ◽  
Two Dimensional

Wrist strength limitations to manual exertion capability

1998 ◽  
Vol 1 (2) ◽  
pp. 107-121
Author(s):  
Khaled W. Al-Eisawi ◽  
Carter J. Kerk ◽  
Jerome J. Congleton
Keyword(s):  
Biomechanical Modeling ◽  
Two Dimensional ◽  
Wrist Flexion ◽  
College Age ◽  
Biomechanical Models ◽  
Radial Deviation ◽  
Flexion Strength ◽  
Made In

This study evaluated wrist strength limitations to manual exertion capability in two-dimensional static biomechanical modeling. The researchers hypothesized that wrist strength does not limit manual exertion capability - an assumption commonly made in many strength biomechanical models. An experiment was conducted on 15 right-handed males of college age. Isometric wrist flexion strength was measured at two elbow angles: 90 degree and 135 degree and in two wrist positions: neutral and 45 degree extended. Isometric wrist radial deviation strength was measured at the same two elbow angles and in two wrist positions: neutral and 30 degree ulnarly deviated. Minimum wrist strength limits for which wrist strength does not limit maximal moments about the elbow in manual hand exertions were calculated and compared to their corresponding measured wrist strength moments using paired t-tests. In general, wrist strength was non-limiting. However, wrist flexion strength in the 45 degree extended wrist posture was limiting. Weak-wrist subjects showed more wrist strength limitations than strong-wrist subjects.

Design of finite-time guidance law based on observer and head-pursuit theory

2021 ◽  
pp. 095441002098456
Author(s):  
Chenqi Zhu
Keyword(s):  
Finite Time ◽  
Three Dimensional ◽  
Hypersonic Vehicle ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Reaching Law ◽  
Guidance Law ◽  
Fast Power ◽  
Simulation Results ◽  
Guidance Laws

In order to improve the guiding accuracy in intercepting the hypersonic vehicle, this article presents a finite-time guidance law based on the observer and head-pursuit theory. First, based on a two-dimensional model between the interceptor and target, this study applies the fast power reaching law to head-pursuit guidance law so that it can alleviate the chattering phenomenon and ensure the convergence speed. Second, target maneuvers are considered as system disturbances, and the head-pursuit guidance law based on an observer is proposed. Furthermore, this method is extended to a three-dimensional case. Finally, comparative simulation results further verify the superiority of the guidance laws designed in this article.

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