Volume 25, Issue 7, July 2013
Index of content:

Suspensions of active particles, such as motile microorganisms and artificial microswimmers, are known to undergo a transition to complex largescale dynamics at high enough concentrations. While a number of models have demonstrated that hydrodynamic interactions can in some cases explain these dynamics, collective motion in experiments is typically observed at such high volume fractions that steric interactions between nearby swimmers are significant and cannot be neglected. This raises the question of the respective roles of steric vs hydrodynamic interactions in these dense systems, which we address in this paper using a continuum theory and numerical simulations. The model we propose is based on our previous kinetic theory for dilute suspensions, in which a conservation equation for the distribution function of particle configurations is coupled to the Stokes equations for the fluid motion [D. Saintillan and M. J. Shelley, “Instabilities, pattern formation, and mixing in active suspensions,” Phys. Fluids20, 123304 (Year: 2008)]10.1063/1.3041776. At high volume fractions, steric interactions are captured by extending classic models for concentrated suspensions of rodlike polymers, in which contacts between nearby particles cause them to align locally. In the absence of hydrodynamic interactions, this local alignment results in a transition from an isotropic base state to a nematic base state when volume fraction is increased. Using a linear stability analysis, we first investigate the hydrodynamic stability of both states. Our analysis shows that suspensions of pushers, or rearactuated swimmers, typically become unstable in the isotropic state before the transition occurs; suspensions of pullers, or headactuated swimmers, can also become unstable, though the emergence of unsteady flows in this case occurs at a higher concentration, above the nematic transition. These results are also confirmed using fully nonlinear numerical simulations in a periodic cubic domain, where pusher and puller suspensions are indeed both found to exhibit instabilities at sufficiently high volume fractions; these instabilities lead to unsteady chaotic states characterized by largescale correlated motions and strong density fluctuations. While the dynamics in suspensions of pushers are similar to those previously reported in the dilute regime, the instability of pullers is novel and typically characterized by slower dynamics and weaker hydrodynamic velocities and active input power than in pusher suspensions at the same volume fraction.
 SPECIAL TOPIC: PAPERS FROM THE INTERNATIONAL UNION OF THEORETICAL AND APPLIED MATHEMATICS (IUTAM) SYMPOSIUM ON MOBILE PARTICULATE SYSTEMS: KINEMATICS, RHEOLOGY AND COMPLEX PHENOMENA (2327 JANUARY 2012, BANGALORE, INDIA)


Report on the IUTAM Symposium on Mobile Particulate Systems: Kinematics, Rheology, and Complex Phenomena, Bangalore, India, 2012
View Description Hide DescriptionThis report summarizes the presentations and discussions conducted during the symposium, which was held under the aegis of the International Union of Theoretical and Applied Mechanics during 23–27 January 2012 in Bangalore, India.

Pairparticle dynamics and microstructure in sheared colloidal suspensions: Simulation and Smoluchowski theory
View Description Hide DescriptionThe Smoluchowski equation (SE) approach reduced to pair level provides an accepted method for analysis of the pair microstructure, i.e., the pair distribution function g(r), in sheared colloidal suspensions. Under dilute conditions, the resulting problem is welldefined, but for concentrated suspensions the coefficients of the pair SE are unclear. This work outlines a recently developed theoretical approach for analytical and numerical study of the pair SE for concentrated colloidal suspensions of spheres in shear flow, and then focuses upon evaluation of coefficients and related properties of the problem from Stokesian Dynamics simulation, over a wide range of particle volume fraction, ϕ, and Péclet number (ratio of shear to Brownian motion). The pair distribution function determined from the SE theory is in generally good agreement with Stokesian Dynamics, as are the computed viscosity and normal stresses of the material. The primary focus of the work is to consider the pair relative velocity predicted by the theory in comparison to Stokesian Dynamics simulations, as well as to evaluate quantities related to the hydrodynamic dispersion needed in the theoretical approach. The pair dynamics for moderate particle volume fraction, 0.20 ⩽ ϕ ⩽ 0.35, are found to be remarkably different from the form for an isolated pair of spheres, and at ϕ ⩾ 0.40 a qualitative change is again seen. Agreement of the theory and simulation on the primary features of the particle motion and structure is good, and discrepancies are clearly delineated.

Rheometry of granular materials in cylindrical Couette cells: Anomalous stress caused by gravity and shear
View Description Hide DescriptionThe cylindrical Couette device is commonly employed to study the rheology of fluids, but seldom used for dense granular materials. Plasticity theories used for granular flows predict a stress field that is independent of the shear rate, but otherwise similar to that in fluids. In this paper we report detailed measurements of the stress as a function of depth, and show that the stress profile differs fundamentally from that of fluids, from the predictions of plasticity theories, and from intuitive expectation. In the static state, a part of the weight of the material is transferred to the walls by a downward vertical shear stress, bringing about the wellknown Janssen saturation of the stress in vertical columns. When the material is sheared, the vertical shear stress changes sign, and the magnitudes of all components of the stress rise rapidly with depth. These qualitative features are preserved over a range of the Couette gap and shear rate, for smooth and rough walls and two model granular materials. To explain the anomalous rheological response, we consider some hypotheses that seem plausible a priori, but show that none survive after careful analysis of the experimental observations. We argue that the anomalous stress is due to an anisotropic fabric caused by the combined actions of gravity, shear, and frictional walls, for which we present indirect evidence from our experiments. A general theoretical framework for anisotropic plasticity is then presented. The detailed mechanics of how an anisotropic fabric is brought about by the abovementioned factors is not clear, and promises to be a challenging problem for future investigations.

A modified kinetic theory for frictional granular flows in dense and dilute regimes
View Description Hide DescriptionContinuum modeling of granular and gassolid flows generally involves the use of a kinetictheory (KT) model for the particulate phase, and the most widely used KT models have been derived for dilute flows of smooth, frictionless spheres. In reality, however, granular particles are frictional and can achieve dense packing, and these features must be taken into account to improve rheological predictions in these flow scenarios. Existing approaches in the literature for producing closedform KTbased models employ empirical modifications to adapt the original models for use in dense and frictional systems. In this article, we investigate the capacity for such modifications to improve the rheological predictions of the Garzó–Dufty (GD) KT model[V. Garzó and J. W. Dufty, “Dense fluid transport for inelastic hard spheres,” Phys. Rev. E59, 5895–5911 (Year: 1999)]10.1103/PhysRevE.59.5895. On the basis of molecular dynamics simulations of homogeneous, simple shear flows of soft, frictional spheres, we propose a new expression for the radial distribution function at contact as well as modifications to the GD expressions for shear stress and energy dissipation rate. These changes account for denseregime scalings observed in inertialnumber models as well as the effects of interparticle friction while preserving the dynamic nature of the KT model.

The effect of base roughness on the development of a dense granular flow down an inclined plane
View Description Hide DescriptionThe development of the flow of a granular material down an inclined plane starting from rest is studied as a function of the base roughness. In the simulations, the particles are rough frictional spheres interacting via the Hertz contact law. The rough base is made of a random configuration of fixed spheres with diameter different from the flowing particles, and the base roughness is decreased by decreasing the diameter of the base particles. The transition from an ordered to a disordered flowing state at a critical value of the base particle diameter, first reported by Kumaran and Maheshwari [Phys. Fluids24, 053302 (Year: 2012)]10.1063/1.4710543 for particles with the linear contact model, is observed for the Hertzian contact model as well. The flow development for the ordered and disordered flows is very different. During the development of the disordered flow for the rougher base, there is shearing throughout the height. During the development of the ordered flow for the smoother base, there is a shear layer at the bottom and a plug region with no internal shearing above. In the shear layer, the particles are layered and hexagonally ordered in the plane parallel to the base, and the velocity profile is well approximated by Bagnold law. The flow develops in two phases. In the first phase, the thickness of the shear layer and the maximum velocity increase linearly in time till the shear front reaches the top. In the second phase, after the shear layer encompasses the entire flow, there is a much slower increase in the maximum velocity until the steady state is reached.

Coarsegrained local and objective continuum description of threedimensional granular flows down an inclined surface
View Description Hide DescriptionDry, frictional, steadystate granular flows down an inclined, rough surface are studied with discrete particle simulations. From this exemplary flow situation, macroscopic fields, consistent with the conservation laws of continuum theory, are obtained from microscopic data by timeaveraging and spatial smoothing (coarsegraining). Two distinct coarsegraining length scale ranges are identified, where the fields are almost independent of the smoothing length w. The smaller, subparticle length scale, w ≪ d, resolves layers in the flow near the base boundary that cause oscillations in the macroscopic fields. The larger, particle length scale, w ≈ d, leads to smooth stress and density fields, but the kinetic stress becomes scaledependent; however, this scaledependence can be quantified and removed. The macroscopic fields involve density, velocity, granular temperature, as well as strainrate, stress, and fabric (structure) tensors. Due to the plane strain flow, each tensor can be expressed in an inherently anisotropic form with only four objective, coordinate frame invariant variables. For example, the stress is decomposed as: (i) the isotropic pressure, (ii) the “anisotropy” of the deviatoric stress, i.e., the ratio of deviatoric stress (norm) and pressure, (iii) the anisotropic stress distribution between the principal directions, and (iv) the orientation of its eigensystem. The strain rate tensor sets the reference system, and each objective stress (and fabric) variable can then be related, via discrete particle simulations, to the inertial number, I. This represents the plane strain special case of a general, local, and objective constitutive model. The resulting model is compared to existing theories and clearly displays small, but significant deviations from more simplified theories in all variables – on both the different length scales.

Quantitative test of the time dependent GintzburgLandau equation for sheared granular flow in two dimensions
View Description Hide DescriptionWe examine the validity of the timedependent GinzburgLandau equation of granular fluids for a plane shear flow under the LeesEdwards boundary condition derived from a weakly nonlinear analysis through the comparison with the result of discrete element method. We verify quantitative agreements in the time evolution of the area fraction and the velocity fields, and also find qualitative agreement in the granular temperature.

Instabilities and nonlinear dynamics of concentrated active suspensions
View Description Hide DescriptionSuspensions of active particles, such as motile microorganisms and artificial microswimmers, are known to undergo a transition to complex largescale dynamics at high enough concentrations. While a number of models have demonstrated that hydrodynamic interactions can in some cases explain these dynamics, collective motion in experiments is typically observed at such high volume fractions that steric interactions between nearby swimmers are significant and cannot be neglected. This raises the question of the respective roles of steric vs hydrodynamic interactions in these dense systems, which we address in this paper using a continuum theory and numerical simulations. The model we propose is based on our previous kinetic theory for dilute suspensions, in which a conservation equation for the distribution function of particle configurations is coupled to the Stokes equations for the fluid motion [D. Saintillan and M. J. Shelley, “Instabilities, pattern formation, and mixing in active suspensions,” Phys. Fluids20, 123304 (Year: 2008)]10.1063/1.3041776. At high volume fractions, steric interactions are captured by extending classic models for concentrated suspensions of rodlike polymers, in which contacts between nearby particles cause them to align locally. In the absence of hydrodynamic interactions, this local alignment results in a transition from an isotropic base state to a nematic base state when volume fraction is increased. Using a linear stability analysis, we first investigate the hydrodynamic stability of both states. Our analysis shows that suspensions of pushers, or rearactuated swimmers, typically become unstable in the isotropic state before the transition occurs; suspensions of pullers, or headactuated swimmers, can also become unstable, though the emergence of unsteady flows in this case occurs at a higher concentration, above the nematic transition. These results are also confirmed using fully nonlinear numerical simulations in a periodic cubic domain, where pusher and puller suspensions are indeed both found to exhibit instabilities at sufficiently high volume fractions; these instabilities lead to unsteady chaotic states characterized by largescale correlated motions and strong density fluctuations. While the dynamics in suspensions of pushers are similar to those previously reported in the dilute regime, the instability of pullers is novel and typically characterized by slower dynamics and weaker hydrodynamic velocities and active input power than in pusher suspensions at the same volume fraction.

 LETTERS


On the Kolmogorov inertial subrange developing from RichtmyerMeshkov instability
View Description Hide DescriptionWe present results of wellresolved direct numerical simulations (DNS) of the turbulent flow evolving from RichtmyerMeshkov instability (RMI) in a shocktube with square cross section. The RMI occurs at the interface between a mixture of O2 and N2 (light gas) and SF6 and acetone (heavy gas). The interface between the light and heavy gas is accelerated by a Ma = 1.5 planar shock wave. RMI is triggered by a welldefined multimodal initial disturbance at the interface. The DNS exhibit gridresolution independent statistical quantities and support the existence of a Kolmogorovlike inertial range with a k −5/3 scaling unlike previous simulations found in the literature. The results are in excellent agreement with the experimental data of Weber et al. [“Turbulent mixing measurements in the RichtmyerMeshkov instability,” Phys. Fluids24, 074105 (Year: 2012)]10.1063/1.4733447.

 ARTICLES


Biofluid Mechanics

Computational modeling of unsteady surfactantladen liquid plug propagation in neonatal airways
View Description Hide DescriptionSurfactantfree and surfactantladen liquid plug propagation in neonatal airways in various generations representing the upper and lower airways are investigated computationally using a finitedifference/fronttracking method. Emphasis is placed on the unsteady surfactantladen plug propagation as a model for Surfactant Replacement Therapy (SRT) and airway reopening. The numerical method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations coupled with the incompressible NavierStokes equations. Available experimental data for surfactant Survanta are used to relate surface tension coefficient to surfactant concentration at the interface. It is found that, for the surfactantfree case, the trailing film thickness is in good agreement with Taylor's law for plugs with plug length greater than the airway width. Mechanical stresses that could be injurious to epithelial cells such as pressure and shear stress and their gradients are maximized on the front and rear menisci with increasing magnitudes in the lower generations. These mechanical stresses, especially pressure and pressure gradient, are diminished with the introduction of surfactants. Surfactant is absorbed onto the trailing film and thickens it, eventually leading to either plug rupture or, if totally consumed prior to rupture, to steadily propagating plug. In the upper airways, initially small plugs rupture rapidly and plugs with comparable initial plug length with the airway width persist and propagate steadily. For a more effective SRT treatment, we recommend utilization of plugs with initial plug length greater than the airway width. Increasing surfactant strength or increasing the initially instilled surfactant concentration is found to be ineffective.

Penetrative phototactic bioconvection in an isotropic scattering suspension
View Description Hide DescriptionPhototaxis is a directed swimming response dependent upon the light intensity sensed by microorganisms. Positive (negative) phototaxis denotes the motion directed towards (away from) the source of light. Using the phototaxis model of Ghorai, Panda, and Hill [“Bioconvection in a suspension of isotropically scattering phototactic algae,” Phys. Fluids22, 071901 (Year: 2010)]10.1063/1.3457163, we investigate twodimensional phototactic bioconvection in an absorbing and isotropic scattering suspension in the nonlinear regime. The suspension is confined by a rigid bottom boundary, and stressfree top and lateral boundaries. The governing equations for phototactic bioconvection consist of Navier–Stokes equations for an incompressible fluid coupled with a conservation equation for microorganisms and the radiative transfer equation for light transport. The governing system is solved efficiently using a semiimplicit secondorder accurate conservative finitedifference method. The radiative transfer equation is solved by the finite volume method using a suitable step scheme. The resulting bioconvective patterns differ qualitatively from those found by Ghorai and Hill [“Penetrative phototactic bioconvection,” Phys. Fluids17, 074101 (Year: 2005)]10.1063/1.1947807 at a higher critical wavelength due to the effects of scattering. The solutions show transition from steady state to periodic oscillations as the governing parameters are varied. Also, we notice the accumulation of microorganisms in two horizontal layers at two different depths via their mean swimming orientation profile for some governing parameters at a higher scattering albedo.

A transient solution for vesicle electrodeformation and relaxation
View Description Hide DescriptionA transient analysis for vesicle deformation under directcurrent electric fields is developed. The theory extends from a droplet model, with the additional consideration of a lipid membrane separating two fluids of arbitrary properties. For the latter, both a membranecharging and a membranemechanical model are supplied. The vesicle is assumed to remain spheroidal in shape for all times. The main result is an ordinary differential equation governing the evolution of the vesicle aspect ratio. The effects of initial membrane tension and pulse length are examined. The model prediction is extensively compared with experimental data, and is shown to accurately capture the system behavior in the regime of no or weak electroporation. More importantly, the comparison reveals that vesicle relaxation obeys a similarity law regardless of the means of deformation. The process is governed by a single time scale that is a function of the vesicle initial radius, the fluid viscosity, and the initial membrane tension. This similarity scaling law can be used to calculate membrane properties from experimental data.

The wobblingtoswimming transition of rotated helices
View Description Hide DescriptionA growing body of work aims at designing and testing micronscale synthetic swimmers. One method, inspired by the locomotion of flagellated bacteria, consists of applying a rotating magnetic field to a rigid, helically shaped, propeller attached to a magnetic head. When the resulting device, termed an artificial bacteria flagellum, is aligned perpendicularly to the applied field, the helix rotates and the swimmer moves forward. Experimental investigation of artificial bacteria flagella shows that at low frequency of the applied field, the axis of the helix does not align perpendicularly to the field but wobbles around the helix, with an angle decreasing as the inverse of the field frequency. Using numerical computations and asymptotic analysis, we provide a theoretical explanation for this wobbling behavior. We numerically demonstrate the wobblingtoswimming transition as a function of the helix geometry and the dimensionless Mason number which quantifies the ratio of viscous to magnetic torques. We then employ an asymptotic expansion for nearstraight helices to derive an analytical estimate for the wobbling angle allowing to rationalize our computations and past experimental results. These results can help guide future design of artificial helical swimmers.

Aerodynamic effects of wing corrugation at gliding flight at low Reynolds numbers
View Description Hide DescriptionCorrugation gives an insectwing the advantages of low mass, high stiffness, and low membrane stress. Researchers are interested to know if it is also advantageous aerodynamically. Previous works reported that corrugation enhanced the aerodynamic performance of wings at gliding flight. However, Reynolds numbers considered in these studies were higher than that of gliding insects. The present study showed that in the Reynolds number range of gliding insects, corrugation had negative aerodynamic effects. We studied aerodynamic effects of corrugation at gliding motion using the method of computational fluid dynamics, in the Reynolds number range of Re = 200–2400. Different corrugation patterns were considered. The effect of corrugation on aerodynamic performance was identified by comparing the aerodynamic forces between the corrugated and flatplate wings, and the underlying flow mechanisms of the corrugation effects were revealed by analyzing the flow fields and surface pressure distributions. The findings are as follows: (1) the effect of corrugation is to decrease the lift, and change the drag only slightly (at 15°–25° angles of attack, lift is decreased by about 16%; at smaller angles of attack, the percentage of lift reduction is even larger because the lift is small). (2) Two mechanisms are responsible for the lift reduction. One is that the pleats at the lower surface of the corrugated wing produce relatively strong vortices, resulting in local lowpressure regions on the lower surface of the wing. The other is that corrugation near the leading edge pushes the leadingedgeseparation layer slightly upwards and increases the size of the separation bubble above the upper surface, reducing the “suction pressure,” or increasing the pressure, on the upper surface.

On the acoustic radiation of a pitching airfoil
View Description Hide DescriptionWe examine the acoustic far field of a thin elastic airfoil, immersed in lowMach nonuniform stream flow, and actuated by smallamplitude sinusoidal pitching motion. The nearfield fluidstructure interaction problem is analyzed using potential thinairfoil theory, combined with a discrete vortex model to describe the evolution of airfoil trailing edge wake. The leading order dipolesound signature of the system is investigated using PowellHowe acoustic analogy. Compared with a pitching rigid airfoil, the results demonstrate a twofold effect of structure elasticity on airfoil acoustic field: at actuation frequencies close to the system least stable eigenfrequency, elasticity amplifies airfoil motion amplitude and associated sound levels; however, at frequencies distant from this eigenfrequency, structure elasticity acts to absorb system kinetic energy and reduce acoustic radiation. In the latter case, and with increasing pitching frequency ω p , a rigidairfoil setup becomes significantly noisier than an elastic airfoil, owing to an increase of its direct motion noise component. Unlike rigid airfoil signature, it is shown that wake sound contribution to elastic airfoil radiation is significant for all ω p . Remarkably, this contribution contains, in addition to the fundamental pitching frequency, its odd multiple harmonics, which result from nonlinear interactions between the airfoil and the wake. The results suggest that structure elasticity may serve as a viable means for design of flapping flight noise control methodologies.

Micro and Nanofluid Mechanics

Timedependent experimental analysis of a thermal transpiration rarefied gas flow
View Description Hide DescriptionThermal transpiration is the macroscopic movement induced in a rarefied gas by a temperature gradient. The gas moves from the lower to the higher temperature zone. An original method is proposed here to measure the stationary mass flow rate of gas created by thermal transpiration in a microtube heated at its outlet. In addition, by means of a timedependent study, parameters such as the pressure variation, the pressure variation speed, and the characteristic time of the system are analyzed. The experimental system is composed of a glass tube of circular cross section and two reservoirs positioned one at the inlet and one at the outlet of the capillary. The reservoirs are connected to two fast response time capacitance diaphragm gauges. By monitoring the pressure variation with time inside both reservoirs, it is possible to measure the macroscopic movement of the gas along the tube. Three gases, nitrogen, argon, and helium, are studied and three temperature differences ΔT = 37, 53.5, and 71 K are applied to the tube. The analyzed gas rarefaction conditions vary from near free molecular to slip regime. Finally, Poiseuille counter flows consistent with the experimental zero flow conditions of the thermal transpiration process are proved to be possible.

Interfacial Flows

Fluid transport in thin liquid films using traveling thermal waves
View Description Hide DescriptionUsing long wave theory and direct numerical solutions of the Navier–Stokes equations, we investigate thermocapillary flows arising in a thin liquid film covering a heated solid substrate with nonuniform temperature in the form of traveling thermal waves. Our results indicate that unidirectionally propagating interfacial waves are formed in the liquid film. The interfacial waves transport liquid, thereby creating a net pumping effect. We show that the frequency of thermal waves leading to the most efficient pumping is defined by their wave length and weakly depends on other system parameters. The results are useful for designing new methods for transporting liquids in open microfluidic devices.

Simulations of the breakup of liquid filaments on a partially wetting solid substrate
View Description Hide DescriptionWe report direct numerical simulations of liquid filaments breaking up into droplets on partially wetting substrates. It is motivated by recent experiments, linear stability analyses, and lubricationbased calculations. The fluid flow is governed by the Stokes equations and the contact line motion is handled by a phasefield model, which also serves to capture the interfacial motion. The coupled Stokes and CahnHilliard equations are solved using a finiteelement algorithm in three dimensions. This avoids additional approximations of the fluid flow or contact line motion, and allows us to compute arbitrary contact angles on the substrate. We simulate both the breakup of infinite liquid filaments via growing capillary waves and that of finite liquid filaments with drops pinching off from the ends, with a focus on the effect of the wetting angle. In both cases, substrate hydrophobicity promotes breakup of the thread, and decreases the spacing of the daughter drops. The results show the differences in the two processes and in the final drop size and spacing. The development of capillary waves agrees well with prior linear analysis and the endpinching results offer new insights into this poorly understood phenomenon.

Three dimensional flow structures in a moving droplet on substrate: A dissipative particle dynamics study
View Description Hide DescriptionIt is of both fundamental and practical interest to study the flow physics in the manipulation of droplets. In this paper, we investigate complex flow in liquid droplets actuated by a linear gradient of wettability using dissipative particle dynamics simulation. The wetting property of the substrate ranging from hydrophilic to hydrophobic is achieved by adjusting the conservative solidliquid interactions which results in a variation of solidliquid surface tension. The internal threedimensional velocity field with transverse flow in droplet is revealed and analyzed in detail. When the substrate is hydrophobic, it is found that there is slight deformation but strong flow circulation inside the droplet, and the droplet rolling is the dominant mechanism for the movement. However, large deformation of the droplet is generated after the droplet reaches the hydrophilic surface, and a mechanism combining rolling and sliding dominates the transportation of the droplet. Another interesting finding is that the thermal fluctuation can accelerate the spontaneous motion of a liquid droplet under a wetting gradient. The effects of the steepness of wetting gradient and the size of droplet on the translation speed are studied as well.

Nonspherical bubble dynamics of underwater explosions in a compressible fluid
View Description Hide DescriptionThis paper is concerned with the bubble dynamics of underwater explosion in a compressible liquid flow whose Mach number, based on characteristic liquid velocities, is O(10−1). We will study this phenomenon based on weakly compressible theory using the method of matched asymptotic expansions. As a result, the inner flow near the bubble to second order is described by Laplace's equation with the compressible effects appearing only in the far field condition. The problem can thus be modelled approximately using the boundary integral method. Validations are performed against the Keller equation for spherical bubbles and available experimental data for “smallcharge” explosions for nonspherical bubbles under the action of buoyancy. The computation traces jet impact, the transition of the bubble from a singly connected to a doubly connected form, and the recombining of a doubly connected to a singly connected form, and the further repeated transitions. The computational result of the bubble shapes correlates well with experimental data to the end of the second oscillation. The first collapse, which we call the “principal collapse,” is the most severe in terms of energy loss. The damping of the bubble oscillation is alleviated by the buoyancy effects and reduced with the buoyancy parameter.
