Nanoscale Transport during Liquid Film Thinning Inhibits Bubble Coalescing Behavior in Electrolyte Solutions.

The long-standing puzzle of why two colliding bubbles in an electrolyte solution do not coalesce immediately upon contact is resolved. The water film between the bubbles needs to be drained out first before its rupture, i.e., coalescence. Experiments reveal clearly that the film thinning exhibits a rather sudden slowdown (around 30-50 nm), which is orders of magnitude smaller than similar experiments involving surfactants. A critical step in explaining this phenomenon is to realize that the solute concentration is different in bulk and at the surface. During thinning, this will generate an electrolyte concentration difference in film solution along the interacting region, which in turn causes a Marangoni stress to resist film thinning. We develop a film drainage model that explains the experimentally observed phenomena well. The underlying physical mechanism, that confused the scientific community for decades, is now finally revealed.

Waves generated by a vibrating rigid sphere with an elastic shell submerged in a fluida).

An analytical solution for the sound and elastic waves generated by a rigid sphere with a shell made of elastic material submerged in an infinite fluid is introduced. The sphere oscillates up and down at a fixed frequency and generates elastic waves (both longitudinal and transverse) in the shell, which are then transmitted to the fluid. The effects of the acoustic boundary layer are included (thus, no implicit arbitrary "slip" on the surface as in the usual fluid acoustic model is present). An example of a 1 mm radius sphere with an elastic shell is analyzed in detail for several conditions to understand the physical phenomena involved in such a system.

Water Film Drainage between a Very Viscous Oil Drop and a Mica Surface.

We investigate thin film drainage between a viscous oil drop and a mica surface, clearly illustrating the competing effects of Laplace pressure and viscous normal stress (τ_{v}) in the drop. τ_{v} dominates the initial stage of drainage, leading to dimple formation (h_{d}) at a smaller critical thickness with an increase in the drop viscosity (the dimple is the inversion of curvature of the drop in the film region). Surface forces and interfacial tension control the last stage of film drainage. A scaling analysis shows that h_{d} is a function of the drop size R and the capillary numbers of the film (Ca_{f}) and drop (Ca_{d}), which we estimate by h_{d}=0.5Rsqrt[Ca_{f}/(1+2Ca_{d})]. This equation clearly indicates that the drop viscosity needs to be considered when Ca_{d}>0.1. These results have implications for industrial systems where very viscous liquids are involved, for example, in 3D printing and heavy oil extraction process.

Field-only surface integral equations: scattering from a perfect electric conductor.

A field-only boundary integral formulation of electromagnetics is derived without the use of surface currents that appear in the Stratton-Chu formulation. For scattering by a perfect electrical conductor (PEC), the components of the electric field are obtained directly from surface integral equation solutions of three scalar Helmholtz equations for the field components. The divergence-free condition is enforced via a boundary condition on the normal component of the field and its normal derivative. Field values and their normal derivatives at the surface of the PEC are obtained directly from surface integral equations that do not contain divergent kernels. Consequently, high-order elements with fewer degrees of freedom can be used to represent surface features to a higher precision than the traditional planar elements. This theoretical framework is illustrated with numerical examples that provide further physical insight into the role of the surface curvature in scattering problems.

Field-only surface integral equations: scattering from a dielectric body.

An efficient field-only nonsingular surface integral method to solve Maxwell's equations for the components of the electric field on the surface of a dielectric scatterer is introduced. In this method, both the vector wave equation and the divergence-free constraint are satisfied inside and outside the scatterer. The divergence-free condition is replaced by an equivalent boundary condition that relates the normal derivatives of the electric field across the surface of the scatterer. Also, the continuity and jump conditions on the electric and magnetic fields are expressed in terms of the electric field across the surface of the scatterer. Together with these boundary conditions, the scalar Helmholtz equation for the components of the electric field inside and outside the scatterer is solved by a fully desingularized surface integral method. Compared with the most popular surface integral methods based on the Stratton-Chu formulation or the Poggio-Miller-Chew-Harrington-Wu-Tsai (PMCHWT) formulation, our method is conceptually simpler and numerically straightforward because there is no need to introduce intermediate quantities such as surface currents, and the use of complicated vector basis functions can be avoided altogether. Also, our method is not affected by numerical issues such as the zero-frequency catastrophe and does not contain integrals with (strong) singularities. To illustrate the robustness and versatility of our method, we show examples in the Rayleigh, Mie, and geometrical optics scattering regimes. Given the symmetry between the electric field and the magnetic field, our theoretical framework can also be used to solve for the magnetic field.

On the derivation of the Smoluchowski result of electrophoretic mobility.

One of the most enduring, broadly applicable and widely used theoretical results of electrokinetic theory is the Smoluchowski expression for the electrophoretic mobility. It is a limiting form that holds for any solid particle of arbitrary shape in an electrolyte of any composition provided the thickness of the electrical double layer is "infinitely" thin compared to the particle size and the particle has uniform surface potential. The familiar derivation of this result that is a simplified version of the original Smoluchowski analysis in 1903, considers the motion of the electrolyte adjacent to a planar surface. The theory is deceptively simple but as a result much of the interesting physics and characteristic hydrodynamic behavior around the particle have been obscured, leading to a significantly incorrect picture of the fluid velocity profile near the particle surface. This paper provides a derivation of this key theoretical result by starting from Smoluchowski's original 1903 analysis but brings out overlooked details of the hydrodynamic features near and far from the particle that have not been canvassed in detail. The objective is to draw together all the key physical features of the electrophoretic problem in the thin double layer regime to provide an accessible and complete exposition of this important result in colloid science.

Coalescence or Bounce? How Surfactant Adsorption in Milliseconds Affects Bubble Collision.

The coalescence between two colliding bubbles in ultraclean water can be 3 or 4 orders of magnitude faster than coalescence in contaminated solutions. This surprising result can be mostly explained by the mobile or immobile boundary conditions at the air-water interface. In this work, we employ a rising bubble technique to study bubble collisions in aqueous solutions with up to 2 mM surfactant. The experimental results clearly show that freshly generated bubbles can coalesce within milliseconds if they collide right after generation. However, once the bubbles reside in the bulk for tens of milliseconds, the coalescence is heavily hindered. Considering these results, we conclude that a clean air-water interface, rather than clean water, is required to achieve the mobile boundary condition that allows quick coalescence. These findings provide fundamental understanding for further improvements in bubble generation that will benefit industrial processes such as mineral flotation, oil extraction, and wastewater treatment.

The unusual fluid dynamics of particle electrophoresis.

The classical problem of the electrophoretic motion of a spherical particle has been treated theoretically by Overbeek in his 1941 PhD thesis and almost 40 years later by O'Brien & White. Although both approaches used identical assumptions, the details are quite different. Overbeek solved for the pressure, velocity fields as well as the electrostatic potential, whereas O'Brien & White obtained the electrophoretic mobility without the need to consider the pressure and velocity explicitly. In this paper, we establish the equivalence of these two approaches that allow us to show that the tangential component of the fluid velocity has a maximum near the surface of the particle and outside the double layer, the velocity decays as 1/r3, where r is the distance from the sphere, instead of 1/r in normal Stokes flow. Associated with this behavior is that of an irrotational outer flow field. This is consistent with the fact that a sphere moving with a constant electrophoretic velocity experiences zero net force. A study of the forces on the particle also provides a physical explanation of the independence of the electrophoretic mobility on the electrostatic boundary conditions or dielectric permittivity of the particle. These results are important in situations where inter-particle interaction is considered, for instance, in electrokinetic deposition.

Coalescence of Bubbles with Mobile Interfaces in Water.

The fluid flow inside a thin liquid film can be dramatically modified by the hydrodynamic boundary condition at the interfaces. Aqueous systems can be easily contaminated by trace amounts of impurities, rendering the air-liquid interface immobile, thereby significantly resisting the fluid flow. Using high speed interferometry, rapid thinning of the liquid film, on the order of the collision speed, was observed between two fast approaching air bubbles in water, indicating negligible resistance and a fully mobile boundary condition at the air-water interface. By adding trace amounts of surfactants that changed the interfacial tension by 10^{-4} N/m, a transition from mobile to immobile was observed. This provides a fundamental explanation why the bubble coalescence time can vary by over 3 orders of magnitude.

Field-only integral equation method for time domain scattering of electromagnetic pulses.

The scattering of electromagnetic pulses is described using a non-singular boundary integral method to solve directly for the field components in the frequency domain, and Fourier transform is then used to obtain the complete space-time behavior. This approach is stable for wavelengths both small and large relative to characteristic length scales. Amplitudes and phases of field values can be obtained accurately on or near material boundaries. Local field enhancement effects due to multiple scattering of interest to applications in microphotonics are demonstrated.

Self-determined shapes and velocities of giant near-zero drag gas cavities.

Minimizing the retarding force on a solid moving in liquid is the canonical problem in the quest for energy saving by friction and drag reduction. For an ideal object that cannot sustain any shear stress on its surface, theory predicts that drag force will fall to zero as its speed becomes large. However, experimental verification of this prediction has been challenging. We report the construction of a class of self-determined streamlined structures with this free-slip surface, made up of a teardrop-shaped giant gas cavity that completely encloses a metal sphere. This stable gas cavity is formed around the sphere as it plunges at a sufficiently high speed into the liquid in a deep tank, provided that the sphere is either heated initially to above the Leidenfrost temperature of the liquid or rendered superhydrophobic in water at room temperature. These sphere-in-cavity structures have residual drag coefficients that are typically less than [Formula: see text] those of solid objects of the same dimensions, which indicates that they experienced very small drag forces. The self-determined shapes of the gas cavities are shown to be consistent with the Bernoulli equation of potential flow applied on the cavity surface. The cavity fall velocity is not arbitrary but is uniquely predicted by the sphere density and cavity volume, so larger cavities have higher characteristic velocities.

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

A robust and accurate formulation of molecular and colloidal electrostatics.

This paper presents a re-formulation of the boundary integral method for the Debye-Hückel model of molecular and colloidal electrostatics that removes the mathematical singularities that have to date been accepted as an intrinsic part of the conventional boundary integral equation method. The essence of the present boundary regularized integral equation formulation consists of subtracting a known solution from the conventional boundary integral method in such a way as to cancel out the singularities associated with the Green's function. This approach better reflects the non-singular physical behavior of the systems on boundaries with the benefits of the following: (i) the surface integrals can be evaluated accurately using quadrature without any need to devise special numerical integration procedures, (ii) being able to use quadratic or spline function surface elements to represent the surface more accurately and the variation of the functions within each element is represented to a consistent level of precision by appropriate interpolation functions, (iii) being able to calculate electric fields, even at boundaries, accurately and directly from the potential without having to solve hypersingular integral equations and this imparts high precision in calculating the Maxwell stress tensor and consequently, intermolecular or colloidal forces, (iv) a reliable way to handle geometric configurations in which different parts of the boundary can be very close together without being affected by numerical instabilities, therefore potentials, fields, and forces between surfaces can be found accurately at surface separations down to near contact, and (v) having the simplicity of a formulation that does not require complex algorithms to handle singularities will result in significant savings in coding effort and in the reduction of opportunities for coding errors. These advantages are illustrated using examples drawn from molecular and colloidal electrostatics.

The hydrodynamics of bubble rise and impact with solid surfaces.

A bubble smaller than 1mm in radius rises along a straight path in water and attains a constant speed due to the balance between buoyancy and drag force. Depending on the purity of the system, within the two extreme limits of tangentially immobile or mobile boundary conditions at the air-water interface considerably different terminal speeds are possible. When such a bubble impacts on a horizontal solid surface and bounces, interesting physics can be observed. We study this physical phenomenon in terms of forces, which can be of colloidal, inertial, elastic, surface tension and viscous origins. Recent advances in high-speed photography allow for the observation of phenomena on the millisecond scale. Simultaneous use of such cameras to visualize both rise/deformation and the dynamics of the thin film drainage through interferometry are now possible. These experiments confirm that the drainage process obeys lubrication theory for the spectrum of micrometre to millimetre-sized bubbles that are covered in this review. We aim to bridge the colloidal perspective at low Reynolds numbers where surface forces are important to high Reynolds number fluid dynamics where the effect of the surrounding flow becomes important. A model that combines a force balance with lubrication theory allows for the quantitative comparison with experimental data under different conditions without any fitting parameter.

The impact and bounce of air bubbles at a flat fluid interface.

The rise and impact of bubbles at an initially flat but deformable liquid-air interface in ultraclean liquid systems are modelled by taking into account the buoyancy force, hydrodynamic drag, inertial added mass effect and drainage of the thin film between the bubble and the interface. The bubble-surface interaction is analyzed using lubrication theory that allows for both bubble and surface deformation under a balance of normal stresses and surface tension as well as the long-range nature of deformation along the interface. The quantitative result for collision and bounce is sensitive to the impact velocity of the rising bubble. This velocity is controlled by the combined effects of interfacial tension via the Young-Laplace equation and hydrodynamic stress on the surface, which determine the deformation of the bubble. The drag force that arises from the hydrodynamic stress in turn depends on the hydrodynamic boundary conditions on the bubble surface and its shape. These interrelated factors are accounted for in a consistent manner. The model can predict the rise velocity and shape of millimeter-size bubbles in ultra-clean water, in two silicone oils of different densities and viscosities and in ethanol without any adjustable parameters. The collision and bounce of such bubbles with a flat water/air, silicone oil/air and ethanol/air interface can then be predicted with excellent agreement when compared to experimental observations.

Bubbles with shock waves and ultrasound: a review.

The study of the interaction of bubbles with shock waves and ultrasound is sometimes termed 'acoustic cavitation'. It is of importance in many biomedical applications where sound waves are applied. The use of shock waves and ultrasound in medical treatments is appealing because of their non-invasiveness. In this review, we present a variety of acoustics-bubble interactions, with a focus on shock wave-bubble interaction and bubble cloud phenomena. The dynamics of a single spherically oscillating bubble is rather well understood. However, when there is a nearby surface, the bubble often collapses non-spherically with a high-speed jet. The direction of the jet depends on the 'resistance' of the boundary: the bubble jets towards a rigid boundary, splits up near an elastic boundary, and jets away from a free surface. The presence of a shock wave complicates the bubble dynamics further. We shall discuss both experimental studies using high-speed photography and numerical simulations involving shock wave-bubble interaction. In biomedical applications, instead of a single bubble, often clouds of bubbles appear (consisting of many individual bubbles). The dynamics of such a bubble cloud is even more complex. We shall show some of the phenomena observed in a high-intensity focused ultrasound (HIFU) field. The nonlinear nature of the sound field and the complex inter-bubble interaction in a cloud present challenges to a comprehensive understanding of the physics of the bubble cloud in HIFU. We conclude the article with some comments on the challenges ahead.

Force Balance Model for Bubble Rise, Impact, and Bounce from Solid Surfaces.

A force balance model for the rise and impact of air bubbles in a liquid against rigid horizontal surfaces that takes into account effects of buoyancy and hydrodynamic drag forces, bubble deformation, inertia of the fluid via an added mass force, and a film force between the bubble and the rigid surface is proposed. Numerical solution of the governing equations for the position and velocity of the center of mass of the bubbles is compared against experimental data taken with ultraclean water. The boundary condition at the air-water interface is taken to be stress free, which is consistent for bubbles in clean water systems. Features that are compared include bubble terminal velocity, bubbles accelerating from rest to terminal speed, and bubbles impacting and bouncing off different solid surfaces for bubbles that have already or are yet to attain terminal speed. Excellent agreement between theory and experiments indicates that the forces included in the model constitute the main physical ingredients to describe the bouncing phenomenon.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

Universal behavior of the initial stage of drop impact.

During the early stages of the impact of a drop on a solid surface, pressure builds up in the intervening thin lubricating air layer and deforms the drop. The extent of the characteristic deformation is determined by the competition between capillary, gravitational, and inertial forces that has been encapsulated in a simple analytic scaling law. For millimetric drops, variations of the observed deformation with impact velocity V exhibit a maximum defined by the Weber and Eötvös numbers: We=1+Eo. The deformation scales as V(1/2) at the low-velocity capillary regime and as V(-1/2) at the high-velocity inertia regime, in excellent agreement with a variety of experimental systems.

Microbubble-mediated sonoporation for highly efficient transfection of recalcitrant human B- cell lines.

Sonoporation has not been widely explored as a strategy for the transfection of heterologous genes into notoriously difficult-to-transfect mammalian cell lines such as B cells. This technology utilizes ultrasound to create transient pores in the cell membrane, thus allowing the uptake of extraneous DNA into eukaryotic and prokaryotic cells, which is further enhanced by cationic microbubbles. This study investigates the use of sonoporation to deliver a plasmid encoding green fluorescent protein (GFP) into three human B-cell lines (Ramos, Raji, Daudi). A higher transfection efficiency (TE) of >42% was achieved using sonoporation compared with <3% TE using the conventional lipofectamine method for Ramos cells. Upon further antibiotic selection of the transfected population for two weeks, we successfully enriched a stable population of GFP-positive Ramos cells (>70%). Using the same strategy, Raji and Daudi B cells were also successfully transfected and enriched to 67 and 99% GFP-positive cells, respectively. Here, we present sonoporation as a feasible non-viral strategy for stable and highly efficient heterologous transfection of recalcitrant B-cell lines. This is the first demonstration of a non-viral method yielding transfection efficiencies significantly higher (42%) than the best reported values of electroporation (30%) for Ramos B-cell lines.