Journal of Engineering Mathematics
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Extensional flow at low Reynolds number with surface tension
Journal of Engineering Mathematics - Tập 70 - Trang 321-331 - 2010
The extensional flow and break-up of fluids has long interested many authors. A slender viscous fluid drop falling under gravity from beneath a horizontal surface is examined. After reviewing previous work which has neglected surface tension, a one-dimensional model which describes the evolution of such a drop, beginning with a prescribed initial drop shape and including the effects of gravity and......
Waves of high frequency in suspensions near the critical point of the particulate pressure-density dependence
Journal of Engineering Mathematics - - 2000
The paper considers theoretically the propagation of weakly nonlinear high-frequency waves in homogeneous gas-solid suspensions. The governing equations include the equation of particle conservation and the equation of mean motion of the particles. These equations are supplemented by a barotropic dependence of the particulate pressure on the particle volume fraction which has a point of maximum (c......
Surface-tension-driven flow on a moving curved surface
Journal of Engineering Mathematics - Tập 45 - Trang 283-308 - 2003
The leading-order equations governing the flow of a thin viscous film over a moving curved substrate are derived using lubrication theory. Three possible distinguished limits are identified. In the first, the substrate is nearly flat and its curvature enters the lubrication equation for the film thickness as a body force. In the second, the substrate curvature is constant but an order of magnitude......
A note on the solution of a differential equation arising in boundary-layer theory
Journal of Engineering Mathematics - Tập 18 - Trang 31-36 - 1984
The differential equation f′‴ + ff″ + λf′2 = 0 (where dashes denote differentiation with respect to the independent variable η) subject to the boundary conditions f(0)=0, f′(∞)=0 and either f′(0)=1 or f″(0)=−1 is considered. It is shown that by using p≡f′ as dependent variable and ϕ=C−f (where C=f(∞)) as independent variable and then expanding in powers of ϕ, a very good approximation to the solut......
The discrete temporal eigenvalue spectrum of the generalised Hiemenz flow as solution of the Orr-Sommerfeld equation
Journal of Engineering Mathematics - Tập 28 - Trang 241-259 - 1994
A spectral collocation method is used to obtain the solution to the Orr-Sommerfeld stability equation. The accuracy of the method is established by comparing against well documented flows, such as the plane Poiseuille and the Blasius Boundary layers. The focus is then placed on the generalised Hiemenz flow, an exact solution to the Navier-Stokes equations constituting the base flow at the leading ......
Convergence and computational cost analysis of a boundary integral method applied to a rigid body moving in a viscous fluid in close proximity to a fixed boundary
Journal of Engineering Mathematics - - 2021
The Boundary Integral Method (BIM) applied to the unsteady Stokes and continuity equations is a standard method used to simulate problems of bodies oscillating in fluids. Despite the technique providing accurate numerical results, current implementations are computationally expensive. In this work, we focus on the flow around an infinitely thin beam oscillating near a solid surface and we show tha......
Preventing buoyancy-driven flows of two Bingham fluids in a closed pipe – Fluid rheology design for oilfield plug cementing
Journal of Engineering Mathematics - Tập 36 - Trang 327-348 - 1999
The mechanically unstable situation of a heavy Bingham fluid resting on top of a light Bingham fluid in an inclined closed-ended pipe can be stabilised if the fluids have sufficiently large yield stresses. This paper focuses on determining the yield stresses that are sufficient to keep the fluids statically stable for a given fluid density difference, pipe diameter and pipe inclination. The result......
Generalization of an asymptotic model for constant-rate aerosol reactors
Journal of Engineering Mathematics - Tập 47 - Trang 45-60 - 2003
An asymptotic model was previously developed to predictbehaviors of constant-rate aerosol reactors operating with particles in the free-molecular or continuum limits. This model considered the limiting cases of having either condensation or nucleation dominate during a nucleation burst that occurs from steady addition of condensable monomer. In the present article, this model is generalized to all......
Rayleigh–Taylor instability of classical diffusive density profiles for miscible fluids in porous media: a linear stability analysis
Journal of Engineering Mathematics - Tập 132 - Trang 1-18 - 2021
A Rayleigh–Taylor instability typically develops when a denser layer overlies a less dense one in the gravity field. In that case, the initial base state density profile is a step function for which linear stability analysis results are well known. We investigate here analytically the linear stability analysis of other classical diffusive density profiles for porous media flows. We find that, for ......
An oscillatory flow phenomenon in microtube flows of thermally responsive fluids
Journal of Engineering Mathematics - Tập 71 - Trang 31-53 - 2010
A simple asymptotic model for the flow of a thermally responsive fluid in a microtube is derived. At low temperatures these fluids behave as a Newtonian fluid; however, above a critical temperature they (reversibly) form gel-like structures. Also, because of the small length scales involved in microfluidic flows, viscous heating can become significant. This can lead to gelation simply from the tem......
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