Particles accelerate the detachment of viscous liquids

During detachment of a viscous fluid extruded from a nozzle, a filament linking the droplet to the latter is formed. Under the effect of surface tension, the filament thins until pinch-off and final detachment of the droplet. In this paper, we study the effect of the presence of individual particles trapped in the filament on the detachment dynamics using granular suspensions of small volume fractions (??<?6 %). We show that even a single particle strongly modifies the detachment dynamics. The particle perturbs the thinning of the thread, and a large droplet of fluid around the particle is formed. This perturbation leads to an acceleration of the detachment of the droplet compared to the detachment observed for a pure fluid. We quantify this acceleration for single particles of different sizes and link it to similar observations for suspensions of small volume fractions. Our study also gives more insight into particulate effects on detachment of denser suspensions and allows to explain the accelerated detachment close to final pinch-off observed previously (Bonnoit et al. Phys Fluids 24(4):043304, 2012).     

Fundamental sloshing frequencies of stratified two-fluid systems in closed prismatic tanks

The solution to the irrotational eigenvalue problem for internal waves in closed tanks is simple but not easily accessible. Solutions are given for two geometries frequently encountered in industry. It is recommended that acoustic rather than structural elements be used in finite-element calculations of complex geometries     

Natural convection flow of a viscous incompressible fluid in a rectangular porous cavity heated from below with cold sidewalls

We consider the flow, which is induced by differential heating on the boundaries of a porous cavity heated from below. In particular we allow the sidewalls to have the same cold temperature as the upper surface, and thus the problem is a variant of the Darcy-Bénard convection problem, but one where there is flow at all non-zero Grashof numbers. Attention is focused on how the flow and heat transfer is affected by variations in the cavity aspect ratio, the Grashof number and the Darcy number. The flow becomes weaker as the Darcy number decreases from the pure fluid limit towards the Darcy-flow limit. In addition the number of cells which form in the cavity varies primarily with the aspect ratio and is always even due to the symmetry imposed by the cold sidewalls.     

Coupled frequencies of a hydroelastic viscous liquid system

The coupled frequencies of a hydroelastic system consisting of an elastic shell and a viscous liquid layer with a free surface have been treated. The system exhibits no z-dependency and may be either an annular liquid layer around an elastic center shell or a liquid layer inside an elastic container. The first case has been evaluated numerically, where the influence of the liquid surface tension parameter, the elasticity parameter of the shell and the thickness of the layer have been determined. In contrast to the hydroelastic system with an ideal liquid, the system with viscous liquid exhibits instability of the liquid surface as well as the shell.     

Film thickness in blade coating of viscous and viscoelastic liquids

Coating of viscous and viscoelastic liquids is examined both theoretically and experimentally. A rigid blade, accurately positioned over a rotating roll, provides an experimental system in which coating thickness is measured as a function of geometric parameters. A perturbation solution to the Navier—Stokes equations yields a lubrication theory which shows agreement with the data to an extent depending on the specific geometry.The effect of a non-Newtonian viscosity is explored by adopting a purely viscous power-law model. The lubrication equations are solved by the method of Horowitz and Steidler [1], and predict an increase in coating thickness relative to the Newtonian case. Data for viscoelastic fluids show both an increase and a decrease in coating thickness compared with Newtonian liquids depending on the relative magnitude of shear thinning and elastic effects.     

Modeling of aerated stirred tanks with shear-thinning power law liquids

Detailed simulations of aerated stirred tanks with shear-thinning power law liquids are presented. The lattice-Boltzmann scheme was used to discretize the filtered conservation equations of the liquid phase. The motion of bubbles was tracked based on the Euler–Lagrange approach with a bubble cluster concept. The collision, breakup and coalescence of bubbles were modeled as stochastic events. The predicted flow field of a single-phase stirred tank with shear-thinning power law liquid shows reasonable agreement with experimental data. For aerated systems, qualitatively similar gas holdup distribution was achieved when comparing the predicted result with experiments. Using the proposed modeling approach, it was found that a change in rheology alters the number mean diameter, Sauter diameter and the shape of bubble size distribution.     

Separating forces in blade coating of viscous and viscoelastic liquids

Coating of viscous and viscoelastic liquids is examined both theoretically and experimentally. A single simple geometry, a blade over a rotating roll, is considered. A perturbation solution to the Navier-Stokes equations yields a lubrication theory with first order corrections for curvature and inertia. A numerical solutions by the Finite Element Method (FEM) is compared to the analytical solutions. For Newtonian fluids, agreement between these mathematical models, and data on blade loading, is quite good.The effect of a non-Newtonian viscosity is explored by adopting a purely viscous power law model. The zeroth-order (lubrication) equations are solved by the method of Steidler and Horowitz, and predictions for coating thickness and blade loading agree quite well with those obtained from a FEM solution of the full equations of motion for a power law fluid. Data on blade loading, obtained using a strongly elastic polymer solution, are compared to these mathematical models, and discrepancies are noted.     

Thermodynamic activation functions of viscous flow of non-polar liquids

The thermodynamic activation function of viscous flow may be determined from the expression for the pre-exponential factor in the Eyring relationship (the viscosity coefficient), which is a function of density and relative permittivity, together with the thermal dependence of the viscosity coefficient. This method of determination is demonstrated for a series of n-alkanes C₆–C₂₀.List of symbols A, B, C parameters in empirical viscosity-temperature dependence - E molecular bond energies of liquid calculated from heat of evaporation in vacuum - E _v viscous flow activation energy - G activation Gibbs function of viscous flow - H _v heat of evaporation - H _vb heat of evaporation at boiling point - H viscous flow activation enthalpy - k Boltzmann constant - m weight of molecule - M relative molecular weight - N _A Avogadro constant - q total number of bonds in one mole of liquid - R gas constant - S _id entropy of one mole of compound in ideal gas state - S _sat entropy of one mole of compound in saturated vapour state - S activation entropy of viscous flow - T absolute temperature - T _c critical temperature - T _r reduced temperature - T _c critical volume - T _f free volume of liquid per molecule - V ₀ molar volume of molecules - V _m molar volume of liquid - relative permittivity - viscosity - density - _r reduced density     

Van Rossum's investigation into the viscous lifting of liquids

A simple way of raising a viscous liquid from a tank is to pass a moving belt through it and to scrape off the liquid at a higher level. A reappraisal is made of van Rossum's analysis of his experiments on this method, and the results are presented in a form free from the objection that can be raised against the original working.     

Natural frequencies of thin,rectangular plates with holes or orthotropic “patches” carrying an elastically mounted mass

The approximate solution for the title problem is obtained in the case of simply supported and clamped rectangular plates made of isotropic or orthotropic materials. A variational approach (the well known Rayleigh–Ritz method) is used, where the displacement amplitude is expressed in terms of beam functions. This means that each coordinate function satisfies identically all the boundary conditions at the outer edge of the plate. Free vibration analysis has been performed on various different cases; solid isotropic and orthotropic plates, orthotropic plates with a hole and isotropic plates with an orthotropic inclusion or “patch”, carrying an elastically mounted concentrated mass. It is important to point out that the case of an orthotropic patch is interesting from a technological viewpoint since it constitutes a model of a repair implemented on the virgin structural element when it has suffered damage. This approach has been implemented by the aeronautical industry in some instances. The obtained results are in very good agreement with those of particular cases of simply supported plates available in the literature.     

Motion of two viscous immiscible incompressible liquids in a rotating cylinder

The shape of the interface is determined using the boundary layer method and the position of the center of mass of the liquid and the value of the braking torque exerted by the liquid on the walls of the rotating cylinder are calculated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 92–99. January–February, 1990.     

Natural frequencies of a hemispherical shell

An experimental study of the natural frequencies of a hemispherical thin shell with a clamped edge is described. For the particular shell model studied, the four lowest symmetric modes were identified conclusively by establishing the node-line patterns. The associated natural frequencies were found to be in excellent agreement with theoretical predictions. A great number of higher modes were also excited but could not be conclusively identified due to difficulties in establishing the node-line patterns. The symmetric frequency spectrum up to and including the 23rd mode was, however, established by means of a qualitative argument and showed good correlation with the theoretical spectrum. A number of natural frequencies were found to be present in a particular frequency band for the test shell resulting in a severe crowding in this region. This was found to be in agreement with the more general results for hemispherical shells which indicate that the crowding takes place around a frequency parameterp=1.0.     

Binnie's investigation into the viscous lifting of liquids by withdrawal

A simple way for coating thin liquid films on solid supports is by means of the upward motion of the solid through a bath of wetting liquid. The Van Rossum experimental relationship for this withdrawal problem has recently been recast in another form by Binnie. Alternative representations of with-drawal are given here for comparison with the work of Binnie.