scholarly journals Complete Solutions to Extended Stokes' Problems

2008 ◽  
Vol 2008 ◽  
pp. 1-18 ◽  
Author(s):  
Chi-Min Liu
Keyword(s):  
Viscous Flow ◽  
Fluid Motion ◽  
Flow Characteristics ◽  
Integral Transforms ◽  
Transient Solutions ◽  
Stokes Problems ◽  
Moving Plane ◽  
Mathematical Techniques ◽  
Oscillating Motion ◽  
Complete Solutions

The main object of the present study is to theoretically solve the viscous flow of either a finite or infinite depth, which is driven by moving plane(s). Such a viscous flow is usually named as Stokes' first or second problems, which indicates the fluid motion driven by the impulsive or oscillating motion of the boundary, respectively. Traditional Stokes' problems are firstly revisited, and three extended problems are subsequently examined. Using some mathematical techniques and integral transforms, complete solutions which can exactly capture the flow characteristics at any time are derived. The corresponding steady-state and transient solutions are readily determined on the basis of complete solutions. Current results have wide applications in academic researches and are of significance for future studies taking more boundary conditions and non-Newtonian fluids into account.

scholarly journals Extended Stokes' Problems for Relatively Moving Porous Half-Planes

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Chi-Min Liu
Keyword(s):  
Exact Solutions ◽  
Integral Transform ◽  
Initial Conditions ◽  
Integral Transforms ◽  
Momentum Equation ◽  
Transform Method ◽  
Stokes Problems ◽  
Flow Phenomena ◽  
Mass Influx ◽  
Mathematical Techniques

A shear flow motivated by relatively moving half-planes is theoretically studied in this paper. Either the mass influx or the mass efflux is allowed on the boundary. This flow is called the extended Stokes' problems. Traditionally, exact solutions to the Stokes' problems can be readily obtained by directly applying the integral transforms to the momentum equation and the associated boundary and initial conditions. However, it fails to solve the extended Stokes' problems by using the integral-transform method only. The reason for this difficulty is that the inverse transform cannot be reduced to a simpler form. To this end, several crucial mathematical techniques have to be involved together with the integral transforms to acquire the exact solutions. Moreover, new dimensionless parameters are defined to describe the flow phenomena more clearly. On the basis of the exact solutions derived in this paper, it is found that the mass influx on the boundary hastens the development of the flow, and the mass efflux retards the energy transferred from the plate to the far-field fluid.

Effects of Side Walls on the Motion Induced by an Infinite Plate that Applies Shear Stresses to an Oldroyd-B Fluid

2013 ◽  
Vol 68 (12) ◽  
pp. 725-734 ◽  
Author(s):  
Mehwish Rana ◽  
Nazish Shahid ◽  
Azhar Ali Zafar
Keyword(s):  
Steady State ◽  
Exact Solutions ◽  
Fluid Motion ◽  
Infinite Plate ◽  
Integral Transforms ◽  
Second Grade ◽  
Shear Stresses ◽  
Transient Solutions ◽  
Side Walls ◽  
Similar Solutions

Unsteady motions of Oldroyd-B fluids between two parallel walls perpendicular to a plate that applies two types of shears to the fluid are studied using integral transforms. Exact solutions are obtained both for velocity and non-trivial shear stresses. They are presented in simple forms as sums of steady-state and transient solutions and can easily be particularized to give the similar solutions for Maxwell, second-grade and Newtonian fluids. Known solutions for the motion over an infinite plate, applying the same shears to the fluid, are recovered as limiting cases of general solutions. Finally, the influence of side walls on the fluid motion, the distance between walls for which their presence can be neglected, and the required time to reach the steady-state are graphically determined.

Fluid flow analysis of cilia beating in a curved channel in the presence of magnetic field and heat transfer

2020 ◽  
Vol 98 (2) ◽  
pp. 191-197 ◽  
Author(s):  
Hina Sadaf ◽  
S. Nadeem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Velocity Profile ◽  
Flow Analysis ◽  
Fluid Motion ◽  
Flow Characteristics ◽  
Physical Parameters ◽  
Curved Channel ◽  
Radial Magnetic Field ◽  
Fluid Flow Analysis

This paper investigates fluid motion generated by cilia and a pressure gradient in a curved channel. The flow analysis is carried out in the presence of heat transfer and radial magnetic field. The leading equations are simplified under the familiar suppositions of large wavelength and small Reynolds number approximations. An exact solution has been developed for the velocity profile. The flow characteristics of the viscous fluid are computed in the presence of cilia and metachronal wave velocity. The effects of several stimulating parameters on the flow and heat transfer are studied in detail through graphs. It is found that symmetry of the velocity profile is broken owing to bending of the channel. The radially varying magnetic field decreases the velocity field, but near the left ciliated wall it induces the opposite behavior. It is also found that velocity profile increases due to increase in buoyancy forces throughout the domain. Numerical consequences for velocity profile are also accessible in the table for diverse values of the physical parameters.

scholarly journals Closed-Form Non-Stationary Solutionsfor Thermo and Chemovibrational Viscous Flows

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 175 ◽  
Author(s):  
Dmitry Bratsun ◽  
Vladimir Vyatkin
Keyword(s):  
Viscous Flow ◽  
Closed Form ◽  
General Procedure ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Chemical Transformations ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations

A class of closed-form exact solutions for the Navier–Stokes equation written in the Boussinesq approximation is discussed. Solutions describe the motion of a non-homogeneous reacting fluid subjected to harmonic vibrations of low or finite frequency. Inhomogeneity of the medium arises due to the transversal density gradient which appears as a result of the exothermicity and chemical transformations due to a reaction. Ultimately, the physical mechanism of fluid motion is the unequal effect of a variable inertial field on laminar sublayers of different densities. We derive the solutions for several problems for thermo- and chemovibrational convections including the viscous flow of heat-generating fluid either in a plain layer or in a closed pipe and the viscous flow of fluid reacting according to a first-order chemical scheme under harmonic vibrations. Closed-form analytical expressions for fluid velocity, pressure, temperature, and reagent concentration are derived for each case. A general procedure to derive the exact solution is discussed.

scholarly journals Nonlinear Interactions between Gravity Waves in Water of Constant Depth

2015 ◽  
Vol 62 (1-2) ◽  
pp. 3-25
Author(s):  
Kazimierz Szmidt ◽  
Benedykt Hedzielski
Keyword(s):  
Water Waves ◽  
Fluid Motion ◽  
Power Series Expansion ◽  
Nonlinear Boundary Conditions ◽  
Constant Depth ◽  
Infinite Domain ◽  
Starting Point ◽  
Transient Solutions ◽  
Nonlinear Character ◽  
Approximate Formulation

AbstractThe paper deals with interactions between water waves propagating in fluid of constant depth. In formulation of this problem, a nonlinear character of these interactions is taken into account. In particular, in order to simplify a solution to nonlinear boundary conditions at the free surface, a system of material coordinates is employed as independent variables in the description of the phenomenon. The main attention is focused on the transient solutions corresponding to fluid motion starting from rest. With respect to the initial value problem considered, we confine our attention to a finite fluid domain. For a finite elapse of time, measured from the starting point, the solution in a finite fluid area mimics a solution within an infinite domain, inherent for wave propagation problems. Because of the complicated structure of equations describing nonlinear waves, an approximate formulation is considered, which is based on a power series expansion of dependent variables with respect to a small parameter. Such a solution is assumed to be accurate in describing the main features of the phenomenon. Numerical experiments are conducted to illustrate the approximate formulation developed in this paper.

Oscillating Rectilinear Fluid Flow Generator

1968 ◽  
Vol 35 (4) ◽  
pp. 663-668 ◽  
Author(s):  
W. H. Hoppmann ◽  
Edward Kiss
Keyword(s):  
Fluid Flow ◽  
Constitutive Equations ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Flow Characteristics ◽  
Viscosity Coefficient ◽  
Longitudinal Axis ◽  
Navier Stokes ◽  
Flow Generator ◽  
External Tube

A Rectilinear Fluid Flow Generator of an oscillating type has been developed for the purpose of studying the rheological properties and flow characteristics of both Newtonian and non-Newtonian liquids [1]. It consists essentially of two long horizontal concentric cylinders, in which the annulus is filled with a liquid. The external tube is mounted on elastic supports, while the internal tube can be harmonically oscillated axially at a predetermined frequency and amplitude. The motion of the external tube and the resultant force (liquid drag) acting on it are readily measurable at any time. The principle of the apparatus depends on the fact that the outside tube motion is dynamically coupled to the inside tube motion by the liquid in the annulus which itself is caused to move by the controlled oscillations of the inside tube. It is assumed, at least in principle, that if the motion of the outside tube is known for a given motion of the inside tube, the constitutive equations for the liquid can be determined. Or conversely, if the constitutive equations are known, the motion of the outside tube can be calculated for a given motion of the inside driving cylinder. It has been shown that the solution of the Navier-Stokes equations can be obtained for the flow of a viscous liquid within the annulus between two infinitely long concentric tubes, for the case where the fluid motion is generated by a rectilinear harmonic motion of the inner tube while the outer tube is assumed to be supported by elastic springs and moving parallel to its longitudinal axis. The velocity and shear stress in the fluid have been obtained, and asymptotic solution for drag force, and tube motions, as well as a method for determining the liquid viscosity coefficient are discussed. It is shown that the theoretical solution is important for the study of the motions of the Rectilinear Fluid Flow Generator.

scholarly journals Starfish-inspired Ultrasound Ciliary Bands for Microrobotic Systems

2021 ◽  
Author(s):  
Cornel Dillinger ◽  
Nitesh Nama ◽  
Daniel Ahmed
Keyword(s):  
Small Amplitude ◽  
Fluid Motion ◽  
Flow Characteristics ◽  
Nonlinear Acoustics ◽  
Physical Principle ◽  
Particle Manipulation ◽  
Short Hair ◽  
Bulk Fluid ◽  
Feeding Mechanism ◽  
Natural Systems

Abstract Cilia are short, hair-like appendages ubiquitous in various biological systems, which have evolved to manipulate and gather food in liquids at regimes where viscosity dominates inertia. Inspired by these natural systems, synthetic cilia have been developed and cleverly utilized in microfluidics and microrobotics to achieve functionalities such as propulsion, liquid pumping and mixing, and particle manipulation. In this article, we present the first demonstration of ultrasound-activated synthetic ciliary bands that mimic the natural arrangements of ciliary bands on the surface of starfish larva. Our system leverages nonlinear acoustics at microscales to drive bulk fluid motion via acoustically actuated small-amplitude oscillations of synthetic cilia. By arranging the planar ciliary bands angled towards (+) or away (–) from each other, we achieve bulk fluid motion akin to a flow source or sink. We further combine these flow characteristics with a novel physical principle to circumvent the scallop theorem and realize acoustic-based propulsion at microscales. Finally, inspired by the feeding mechanism of a starfish larva, we demonstrate an analogous microparticle trap by arranging + and – ciliary bands adjacent to each other.

scholarly journals Computation of Viscous Flow Inside a Double-Channel Centrifugal Pump

2014 ◽  
Vol 8 (1) ◽  
pp. 613-618
Author(s):  
Su-Lu Zheng ◽  
Xiang-Ping Wang ◽  
Rui-Hang Zheng ◽  
Ai-Ping Xia ◽  
Yi-Nian Wang ◽  
...  
Keyword(s):  
Viscous Flow ◽  
Centrifugal Pump ◽  
Design Method ◽  
Pure Water ◽  
Flow Characteristics ◽  
Internal Flow ◽  
Solid Particles ◽  
Water Medium ◽  
Centrifugal Pumps ◽  
Double Channel

The double-channel centrifugal pumps are widely used to transport the two-phase flow including big solid particles in industry and agriculture. However, the related design theory and the design method are immature by far. In practice, the revised design method based on the pure water medium is still the main method for the solid-liquid twophase double-channel pump. Therefore, it is very necessary to deeply study the flow characteristics on the condition of the pure water medium. In this paper, in order to study the flow characteristics inside a prototype double-channel centrifugal pump in the case that the delivered medium is the pure water, the SIMPLE algorithm, RNG κ-ε turbulence model, and frozen rotor method are employed to calculate the incompressible, viscous, three-dimensional internal flow. The calculation results display the variation characteristics of the internal flow field and the external performance. The results show that the predicted pump head drops with the increasing flow rate, which manifest that the pump model is of good operation stability at the whole range of working. At the design point, a strong and large vortex remain appears at the middle section of the double-channel impeller. The computational fluids dynamic technology is competent to assess the internal viscous flow inside a double-channel centrifugal pump.

scholarly journals Ultrasound-activated ciliary bands for microrobotic systems inspired by starfish

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Cornel Dillinger ◽  
Nitesh Nama ◽  
Daniel Ahmed
Keyword(s):  
Small Amplitude ◽  
Fluid Motion ◽  
Flow Characteristics ◽  
Nonlinear Acoustics ◽  
Physical Principle ◽  
Particle Manipulation ◽  
Short Hair ◽  
Bulk Fluid ◽  
Feeding Mechanism ◽  
Natural Systems

AbstractCilia are short, hair-like appendages ubiquitous in various biological systems, which have evolved to manipulate and gather food in liquids at regimes where viscosity dominates inertia. Inspired by these natural systems, synthetic cilia have been developed and utilized in microfluidics and microrobotics to achieve functionalities such as propulsion, liquid pumping and mixing, and particle manipulation. Here, we demonstrate ultrasound-activated synthetic ciliary bands that mimic the natural arrangements of ciliary bands on the surface of starfish larva. Our system leverages nonlinear acoustics at microscales to drive bulk fluid motion via acoustically actuated small-amplitude oscillations of synthetic cilia. By arranging the planar ciliary bands angled towards (+) or away (−) from each other, we achieve bulk fluid motion akin to a flow source or sink. We further combine these flow characteristics with a physical principle to circumvent the scallop theorem and realize acoustic-based propulsion at microscales. Finally, inspired by the feeding mechanism of a starfish larva, we demonstrate an analogous microparticle trap by arranging + and − ciliary bands adjacent to each other.

Some Unsteady Flows of a Jeffrey Fluid between Two Side Walls over a Plane Wall

2011 ◽  
Vol 66 (12) ◽  
pp. 745-752 ◽  
Author(s):  
Masood Khan ◽  
Faiza Iftikhar ◽  
Asia Anjum
Keyword(s):  
Infinite Plate ◽  
Unsteady Flows ◽  
Integral Transforms ◽  
Plane Wall ◽  
Second Grade ◽  
Jeffrey Fluid ◽  
Transient Solutions ◽  
Side Walls ◽  
Similar Solutions ◽  
Oscillating Plate

In this paper, some time-dependent flows of a non-Newtonian fluid between two side walls over a plane wall are investigated. The following three problems have been studied: (i) flow due to an oscillating plate, (ii) flow due to an accelerating plate, and (iii) flow due to applied constant stress. The explicit expressions for the velocity field are determined by using the integral transforms. The solutions that have been obtained, depending on the initial and boundary conditions, are written as sum of the steady state and transient solutions. The similar solutions for second-grade and Newtonian fluids can be deduced as limiting cases of our solutions. Furthermore, in absence of the side walls they reduce to the similar solutions over an infinite plate. The effects of some important parameters due to side walls on the flow field are investigated.

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