Electrically forced microthreading of highly viscous dielectric liquids

The behaviour of three high viscosity (4875, 12 125 and 58 560 mPa s), dielectric liquids was investigated at flow rates of 10⁻¹⁰, 10⁻¹² and 10⁻¹⁴ m³ s⁻¹ and the applied voltage range 6–15 kV. In these experiments, due to the low electrical conductivity of the liquids (10⁻¹³ S m⁻¹) and therefore the ensuing high electrical relaxation time, classical electrohydrodynamic atomization conditions are not satisfied. Only dripping and unstable jetting were observed at 4875 mPa s. A transition from no jetting to stable microthreading was observed for the 12 125 and 58 560 mPa s samples. The relics accompanying the transition were found to change from discrete droplets to a continuous filament. Stable microthreading, which generates uniform filaments, was obtained for the 12 125 mPa s sample at flow rates 10⁻¹⁰ and 10⁻¹² m³ s⁻¹ and in the case of the 58 560 mPa s sample at all the flow rates investigated. The high viscosity assisted stable microthreading with the filament diameter decreasing with increasing applied voltage and more dramatically decreasing with reducing flow rate.     

The effect of viscosity on the free stream in transonic flow over a corner point

An asymptotic analysis of the system of Navier–Stokes equations for describing the flow which arises from the subsonic free stream in the neighbourhood of the vertex of a convex corner with curvilinear generatrices is presented for Reynolds numbers approaching infinity. It is assumed that, in limiting non-viscous flow, the subsonic free stream reaches the velocity of sound at the vertex of the corner and, in the first approximation, is described by the Vaglio–Laurin solution. It is shown that the flow can have a different form depending on the value of the pressure gradient, which is formed in the neighbourhood of the corner point. However, irrespective of the steady form of the flow, as a result of the interaction of the Vaglio–Laurin flow with the boundary layer, the latter induces perturbations in the outer flow, which “rounds off” the vertex of the corner when there is a transonic flow around it.     

Global and local optimization using radial basis function response surface models

The focus of this paper is the optimization of complex multi-parameter systems. We consider systems in which the objective function is not known explicitly, and can only be evaluated through computationally intensive numerical simulation or through costly physical experiments. The objective function may also contain many local extrema which may be of interest. Given objective function values at a scattered set of parameter values, we develop a response surface model that can dramatically reduce the required computation time for parameter optimization runs. The response surface model is developed using radial basis functions, producing a model whose objective function values match those of the original system at all sampled data points. Interpolation to any other point is easily accomplished and generates a model which represents the system over the entire parameter space. This paper presents the details of the use of radial basis functions to transform scattered data points, obtained from a complex continuum mechanics simulation of explosive materials, into a response surface model of a function over the given parameter space. Response surface methodology and radial basis functions are discussed in general and are applied to a global optimization problem for an explosive oil well penetrator.     

On control of linear spring–mass chains

We consider a finite chain of mass points consecutively linked by linear springs with one of the end points acted upon by an external control force pointing along the chain. Moreover the system is observable by the coordinate of the other end point of the chain. We show that such a system is completely controllable and is completely observable for all choices of the physical parameters.     

Vibrations of a solid sphere or shell of Functionally Graded Materials

We have solved the equation of equilibrium for torsional vibrations of a sphere in which the density and rigidity are functions of the radial distance and co-latitude. Making use of the particular forms of heterogeneity the exact frequency equations are derived. The work is motivated by the recent research activity on functionally graded materials (FGM), i.e. materials with spatially varying properties tailored to satisfy particular engineering applications.     

Optimal timing of a sequence of tasks with general completion costs

Scheduling a sequence of tasks––in the acceptation of finding the execution times––is not a trivial problem when the optimization criterion is irregular as for instance in earliness–tardiness problems. This paper presents an efficient dynamic programming algorithm to solve the problem with general cost functions depending on the end time of the tasks, idle time costs and variable durations also depending on the execution time of the tasks. The algorithm is also valid when the precedence graph is a tree and it can be adapted to determine the possible execution windows for each task not exceeding a maximum fixed cost.     

Dispensing picoliter droplets on substrates using dielectrophoresis

Liquid dielectrophoresis is exploited to initiate rapid, transient flow of aqueous liquids along co-planar electrodes patterned on insulating substrates. The flow induced by the non-uniform electric field leads to a new electrostatic equilibrium. A reduced-order model predicts the transient motion of the rivulet. When the field is removed, capillary instability breaks up the rivulet into regularly spaced droplets. Periodic circular bumps patterned on the structure, when spaced according to the most unstable wavelength based on Rayleigh's inviscid theory for the cylindrical liquid jet, lead to uniformly spaced and sized droplets. A correction factor, based on the dimensionless Ohnesorge number, accounts successfully for the effect of viscosity.     

Control of adiabatic two-phase dielectric fluid flow distribution with EHD conduction pumping

Electrohydrodynamic (EHD) conduction pumping is associated with the heterocharge layers of finite thickness in the vicinity of the electrodes, which are based on the process of dissociation of the neutral electrolytic species and recombination of the generated ions. This paper presents the successful control of dielectric liquid/vapor flow distribution between two parallel branch lines utilizing an EHD conduction pump at a select mass flux level under adiabatic condition.     

Simulation of micro- and nano-scale flows via the lattice Boltzmann method

We use the lattice Boltzmann method (LBM) for analysis of high and moderate Knudsen number phenomena. Simulation results are presented for microscale Couette and Poiseuille flows. The slip velocity, nonlinear pressure drop, and mass flow rate are compared with previous numerical results and/or experimental data. The Knudsen minimum is successfully predicted for the first time within the LBM framework. These results validate the usage of the LBM based commercial, arbitrary geometry code PowerFLOW for simulating nanoscale problems.