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The heat and mass transfer of deformable droplets in turbulent flows is crucial to a wide range of applications, such as cloud dynamics and internal combustion engines. This study investigates a single droplet undergoing phase change in isotropic turbulence using numerical simulations with a hybrid lattice Boltzmann scheme. Phase separation is controlled by a non-ideal equation of state and density contrast is taken into consideration. Droplet deformation is caused by pressure and shear stress at the droplet interface. The statistics of thermodynamic variables are quantified and averaged over both the liquid and vapour phases. The occurrence of evaporation and condensation is correlated to temperature fluctuations, surface tension variation and turbulence intensity. The temporal spectra of droplet deformations are analysed and related to the droplet surface area. Different modes of oscillation are clearly identified from the deformation power spectrum for low Taylor Reynolds number
, whereas nonlinearities are produced with the increase of
, as intermediate frequencies are seen to overlap. As an outcome, a continuous spectrum is observed, which shows a decrease in the power spectrum that scales as
. Correlations between the droplet Weber number, deformation parameter, fluctuations of the droplet volume and thermodynamic variables are also developed.
In this article, we present a modelling approach for rapid dynamic wetting based on the phase field theory. We show that in order to model this accurately, it is important to allow for a non-equilibrium wetting boundary condition. Using a condition of this type, we obtain a direct match with experimental results reported in the literature for rapid spreading of liquid droplets on dry surfaces. By extracting the dissipation of energy and the rate of change of kinetic energy in the flow simulation, we identify a new wetting regime during the rapid phase of spreading. This is characterized by the main dissipation to be due to a re-organization of molecules at the contact line, in a diffusive or active process. This regime serves as an addition to the other wetting regimes that have previously been reported in the literature.
Active feedback control was applied to suppress oscillations in thermocapillary convection in a half-zone liquid bridge. The experiment is on a unit-aspect-ratio liquid bridge where the most unstable azimuthal mode has wavenumber 2 when control is absent. Active control was realized by locally modifying the surface temperature using the local temperature measured at different locations fed back through a simple control law. The performance of the control process was quantified by analysing local temperature signals, and the flow structure was simultaneously identified by flow visualization. With optimal placement of sensors and heaters, proportional control can raise the critical Marangoni number by more than 40%. The amplitude of the oscillation can be suppressed to less than 30% of the initial value for a wide range of Marangoni number, up to 90% of the critical value. The proportional control was tested for a period-doubling state and it stabilized the oscillation to a periodic state. Weakly nonlinear control was applied by adding a cubic term to the control law to improve the performance of the control and alter the bifurcation characteristics.
The oxygen barrier properties of sol-gel derived inorganic-organic polymer coatings were investigated. By systematic variation of the ratios of the starting compounds and of the curing conditions, materials with different inorganic and organic network densities were obtained. The network densities were characterized using 29Si solid-state NMR and FT-Raman spectroscopy. It was found that the oxygen transmission rates decrease with increasing inorganic as well as organic network density.
We consider the continuous separation process of a monodispersed suspension flowing axially through a rotating circular cylinder. This stationary problem can be regarded as a basic flow case of rotating mixtures in conjunction with previous studies of time-dependent flows like spin-up and batch settling in a cylinder. The ‘mixture model’ for two-phase flow is used to formulate the problem, which is solved in the range of small Ekman and Rossby numbers by asymptotic analytical methods and by a numerical code. The gradual separation of the axially injected suspension is manifested as a stationary stratification of the mixture which induces a swirl component of the velocity, in analogy with the thermal wind in the Earth's atmosphere. The presence of the azimuthal motion and induced secondary flow due to Ekman-layer pumping clearly influences the character of the stratification. Analytical and numerical results are in excellent agreement.
We consider the problem of nonlinear thermal-solutal convection in the mushy zone accompanying unstable directional solidification of binary systems. Attention is focused on possible nonlinear mechanisms of chimney formation leading to the occurrence of freckles in solid castings, and in particular the coupling between the convection and the resulting porosity of the mush. We make analytical progress by considering the case of small growth Péclet number, δ, small departures from the eutectic point, and infinite Lewis number. Our linear stability results indicate a small O(δ) shift in the critical Darcy-Rayleigh number, in accord with previous analyses. We find that nonlinear two-dimensional rolls may be either sub- or supercritical, depending upon a single parameter combining the magnitude of the dependence of mush permeability on solids fraction and the variations in solids fraction owing to melting or freezing. A critical value of this combined parameter is given for the transition from supercritical to subcritical rolls. Three-dimensional hexagons are found to be transcritical, with branches corresponding to upflow and lower porosity in either the centres or boundaries of the cells. These general results are discussed in relation to experimental observations and are found to be in general qualitative agreement with them.
Rotational flow through narrow axial channels is considered in connection with a proposed technique to sort and separate particles according to sedimentation velocities. Nonlinear and linear axisymmetric flow through two channels connected by a slot in the vertical wall is studied numerically. A linearized formulation for the three-dimensional flow through a circumferentially blocked channel, with arbitrary positioning of the inlets and outlets, is examined analytically. Both approaches indicate that to have a sharp criteria for fractionation, the vertical shear layers on the channel walls must overlap. Otherwise, Coriolis effects, accompanying a strong azimuthal motion, make the sorting less precise. Results of an exploratory experiment with a simple two-stage machine demonstrate the feasibility of the basic process for simultaneous and continuous separation and fractionation.
We consider the flow of a suspension in a rotating, cylindrical container with inclined endwalls and a dividing harrier that hlocks any azimuthal motion around the axis. A boundary layer of clarified fluid appears when the influence of the Coriolis force is counteracted and although a bulk swirling motion is prevented by the meridional section, there is still an appreciable azimuthal flow in this thin purified-fluid layer. This flux produces an even more intense current on the leading side of the barrier (relative to the rotation direction) where the section meets the inclined wall.
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