The vibrations of bubbles and balloons

Bubbles and balloons are two examples of structures that feature a pressure difference across the skin, a thin, tensioned membrane, and a doubly curved interface surface. While mathematical models have been formulated for bubble vibrations, no such model exists for balloon vibrations. This paper reviews a model of bubble vibrations, and compares its predicted natural frequencies and modeshapes to those of a rubber balloon. It is shown that the bubble model consistently underpredicts the balloon's natural frequencies, and it is concluded that the nonlinear elasticity present in the balloon skin accounts for this result.

Mixing and internal dynamics of droplets impacting and coalescing on a solid surface.

The coalescence and mixing of a sessile and an impacting liquid droplet on a solid surface are studied experimentally and numerically in terms of lateral separation and droplet speed. Two droplet generators are used to produce differently colored droplets. Two high-speed imaging systems are used to investigate the impact and coalescence of the droplets in color from a side view with a simultaneous gray-scale view from below. Millimeter-sized droplets were used with dynamical conditions, based on the Reynolds and Weber numbers, relevant to microfluidics and commercial inkjet printing. Experimental measurements of advancing and receding static contact angles are used to calibrate a contact angle hysteresis model within a lattice Boltzmann framework, which is shown to capture the observed dynamics qualitatively and the final droplet configuration quantitatively. Our results show that no detectable mixing occurs during impact and coalescence of similar-sized droplets, but when the sessile droplet is sufficiently larger than the impacting droplet vortex ring generation can be observed. Finally we show how a gradient of wettability on the substrate can potentially enhance mixing.

Damage development in an armor ceramic under quasi-static indentation

The objective of the present study is to assess the capabilities of a recently developed mechanism-based model for inelastic deformation and damage in structural ceramics. In addition to conventional lattice plasticity, the model accounts for microcrack growth and coalescence as well as granular flow following comminution. The assessment is made through a coupled experimental/computational study of the indentation response of a commercial armor ceramic. The experiments include examinations of subsurface damage zones along with measurements of residual surface profiles and residual near-surface stresses. Extensive finite element computations are conducted in parallel. Comparisons between experiment and simulation indicate that the most discriminating metric in the assessment is the spatial extent of subsurface damage following indentation. Residual stresses provide additional validation. In contrast, surface profiles of indents are dictated largely by lattice plasticity and thus provide minimal additional insight into the inelastic deformation resulting from microcracking or granular flow. A satisfactory level of correlation is obtained using property values that are either measured directly or estimated from physically based arguments, without undue reliance on adjustable (nonphysical) parameters. © 2011 The American Ceramic Society.

Evidence of print gap airflow affecting web printing quality

The current study extends our earlier investigation on the real-time dynamics of print gap airflow around a single jetted drop over a moving substrate. In the present work, simulated web press printing was performed using a stationary grey-scale commercial inkjet print head to print full-width block of solid colour images onto a paper substrate with extended print gaps. The resultant printed images exhibit patterns or 'wood-graining' effects which become more prevalent as the relevant Reynolds number (Re) increases. The high-resolution scans of the printed images revealed that the patterns are created by oscillation and coalescence of neighboring printed tracks across the web. The phenomenon could be a result of drop stream perturbations caused by unsteady print gap airflow of the type similar to that observed in the previous study. ©2013; Society for Imaging Science and Technology.

Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid

The influence of surfactant on the breakup of a prestretched bubble in a quiescent viscous surrounding is studied by a combination of direct numerical simulation and the solution of a long-wave asymptotic model. The direct numerical simulations describe the evolution toward breakup of an inviscid bubble, while the effects of small but non-zero interior viscosity are readily included in the long-wave model for a fluid thread in the Stokes flow limit. The direct numerical simulations use a specific but realizable and representative initial bubble shape to compare the evolution toward breakup of a clean or surfactant-free bubble and a bubble that is coated with insoluble surfactant. A distinguishing feature of the evolution in the presence of surfactant is the interruption of bubble breakup by formation of a slender quasi-steady thread of the interior fluid. This forms because the decrease in surface area causes a decrease in the surface tension and capillary pressure, until at a small but non-zero radius, equilibrium occurs between the capillary pressure and interior fluid pressure. The long-wave asymptotic model, for a thread with periodic boundary conditions, explains the principal mechanism of the slender thread's formation and confirms, for example, the relatively minor role played by the Marangoni stress. The large-time evolution of the slender thread and the precise location of its breakup are, however, influenced by effects such as the Marangoni stress and surface diffusion of surfactant. © 2008 Cambridge University Press.

Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid

In a previous study [M. Hameed, J. Fluid Mech. 594, 307 (2008)] the authors investigated the influence of insoluble surfactant on the evolution of a stretched, inviscid bubble surrounded by a viscous fluid via direct numerical simulation of the Navier-Stokes equations, and showed that the presence of surfactant can cause the bubble to contract and form a quasisteady slender thread connecting parent bubbles, instead of proceeding directly toward pinch-off as occurs for a surfactant-free bubble. Insoluble surfactant significantly retards pinch-off and the thread is stabilized by a balance between internal pressure and reduced capillary pressure due to a high concentration of surfactant that develops during the initial stage of contraction. In the present study we investigate the influence of surfactant solubility on thread formation. The adsorption-desorption kinetics for solubility is in the diffusion controlled regime. A long-wave model for the evolution of a capillary jet is also studied in the Stokes flow limit, and shows dynamics that are similar to those of the evolving bubble. With soluble surfactant, depending on parameter values, a slender thread forms but can pinch-off later due to exchange of surfactant between the interface and exterior bulk flow. © 2009 American Institute of Physics.

Stabilising terminal cost and terminal controller for ℓasso- MPC: Enhanced optimality and region of attraction

In recent literature, ℓ1-regularised MPC, or ℓasso-MPC, has been recommended for control tasks involving complex requirements on the control signals, for instance, the simultaneous solution of regulation and sharp control allocation for redundantly-actuated systems. This is due to the implicit thresholding ability of LASSO regression. In this paper, a stabilising terminal cost featuring a mixed ℓ1/ℓ2 2 penalty is presented. Then, a candidate terminal controller is computed, with the aim of enlarging the region of attraction. © 2013 EUCA.

The effect of an insoluble surfactant on the skin friction of a bubble

In this paper, we develop a novel moving mesh method suitable for solving axisymmetric free-boundary problems, including the Marangoni effect induced by surfactant or temperature variation. This method employs a body-fitted grid system where the gas-liquid interface is one line of the grid system. We model the surfactant equation of state with a non-linear Langmuir law, and, for simplicity, we limit ourselves to the situation of an insoluble surfactant. We solve complicated dynamic boundary conditions accurately on the gas-liquid interface in the framework of finite-volume methods. Our method is used to study the effect of a surfactant on the skin friction of a bubble in a uniaxial flow. For the limiting case where the surface diffusivity is zero, the effect of a tangential stress generated by the surface tension gradient, allows us to explain a new phenomenon in high concentration regimes: larger surface tension, but also larger deformation. Furthermore, this condition leads to the formation of boundary layers and flow separation at high Reynolds numbers. The influence of these complex flow patterns is examined. © 2005 Elsevier SAS. All rights reserved.