Bubble Amplitude Research Articles

Rayleigh–Taylor instability in an arbitrary direction electrostatic field

Based on the potential flow theory, we carry out the nonlinear analysis for the inviscid incompressible Rayleigh–Taylor instability (RTI) in an arbitrary direction electrostatic field. The analytical expressions for the bubble amplitude and growth rate are presented. The effects of tangential and vertical electrostatic fields upon the bubble dynamics are opposite and depend on permittivity ratio. Agreements with recent simulations are found in the bubble amplitude. The direction of electrostatic field determines which (tangential or vertical) component plays the main role. The stability of the interface depends on whether the tangential and vertical components of the electrostatic field exceed the cut-off electrostatic field which is dependent of the permittivity ratio and the Atwood number. The results of this work demonstrate the importance of the direction of electrostatic field when considering the impact of electrostatic field on RTI.

Sound amplitude of discrete bubbles entrained by an impacting water stream.

Experiments were undertaken to develop a relationship between bubble size and acoustic-emission amplitude for a vertical stream of water impacting a water pool. A particular focus is the formation of the discrete bubbles. Although the relationship between bubble diameter and the natural frequency of sound emissions has been established through Minnaert's work, a comprehensive investigation into the amplitude of sound emissions is missing. Air bubbles were generated from the impact of falling-water streams of varying diameters on an underlying water pool and their acoustic emissions were recorded using a nearby hydrophone. Sound amplitude was found to increase monotonically with bubble size. A second-order polynomial relationship between logarithmic acoustic sound pressure level (L) and bubble diameter (Db) was found, L=-0.0401Db2+1.5781Db+110.7225 within the ±3 dB margin of error. The relationship between linear sound pressure level (P) and bubble diameter (Db) is expressed by the equation P=0.0059Db2+0.0505Db+0.3591, within the ±3 dB margin of error. Results demonstrate that larger bubbles (D > 4 mm) exhibit noise emissions similar to bubbles produced by other mechanisms, such as the underwater nozzle, while smaller diameters tend to produce higher noise levels compared to the same mechanism.

Analysis of single-mode Richtmyer–Meshkov instability using high-order incompressible vorticity—streamfunction and shock-capturing simulations

Two- and three-dimensional simulation results obtained using a new high-order incompressible, variable-density vorticity–streamfunction (VS) method and data from previous ninth-order weighted essentially nonoscillatory (WENO) shock-capturing simulations [M. Latini and O. Schilling, “A comparison of two- and three-dimensional single-mode reshocked Richtmyer-Meshkov instability growth,” Physica D 401, 132201 (2020)] are used to investigate the nonlinear dynamics of single-mode Richtmyer–Meshkov instability using a model of a Mach 1.3 air(acetone)/SF6 shock tube experiment [J. W. Jacobs and V. V. Krivets, “Experiments on the late-time development of single-mode Richtmyer–Meshkov instability,” Phys. Fluids 17, 034105 (2005)]. A comparison of the density fields from both simulations with the experimental images demonstrates very good agreement in the large-scale structure with both methods but differences in the small-scale structure. The WENO method captures the small-scale disordered structure observed in the experiment, while the VS method partially captures such structure and yields a strong rotating core. The perturbation amplitude growth from the simulations generally agrees well with the experiment. The simulation bubble and spike amplitudes agree well at early times. At later times, the WENO bubble amplitude is smaller than the VS amplitude and vice versa for the spike amplitude. The predictions of nonlinear single-mode instability growth models are shown to agree with the simulation amplitudes at early-to-intermediate times but underpredict the amplitudes at later times in the nonlinear regime. Visualizations of the mass fraction and enstrophy isosurfaces, velocity and vorticity fields, and baroclinic vorticity production and vortex stretching terms from the three-dimensional simulations indicate that, with the exception of the small-scale structure within the rollups, the VS and WENO results are in good agreement.

Simulations and models for the Richtmyer–Meshkov instability with broadband perturbations

The Richtmyer–Meshkov instability (RMI) is shock driven and affects many phenomena from inertial fusion to supernova explosions. The behavior of single-modes in the RMI has been studied extensively but less is known with the broadband perturbations that occur in applications. Here, we describe extensive numerical simulations and modeling of the RMI with broadband perturbations with an initial power spectrum of the form P ∝ km, where k is the wavenumber. The hydrodynamic condition is the same as in the θ-Group Collaboration [Thornber et al., “Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer–Meshkov instability: The θ-group collaboration,” Phys. Fluids 29, 105107 (2017)] with a Mach ∼1.86 shock and gamma-law = 5/3 fluids with Atwood number A = −0.5. The bubble amplitude hB is found to grow in two stages. Initially, hB undergoes a phase-inversion and grows linearly in time (t) at a rate consistent with a linear theory. Asymptotically, hB grows as a power law ∼tθ when k|hB| > O(1), where k is the average wavenumber for the initial spectrum. The RMI behavior in simulations and modeling agree over a wide range of exponent m, spectral width, initial amplitude, and time. The agreement is quantified objectively using statistical analysis.

On Rayleigh–Taylor Dynamics

In this work, we theoretically and numerically investigate Rayleigh–Taylor dynamics with constant acceleration. On the side of theory, we employ the group theory approach to directly link the governing equations to the momentum model, and to precisely derive the buoyancy and drag parameters for the bubble and spike in the linear, nonlinear, and mixing regimes. On the side of simulations, we analyze numerical data on Rayleigh–Taylor mixing by applying independent self-similar processes associated with the growth of the bubble amplitude and with the bubble merger. Based on the obtained results, we reveal the constituents governing Rayleigh–Taylor dynamics in the linear, nonlinear, and mixing regimes. We outline the implications of our considerations for experiments in plasmas, including inertial confinement fusion.

Effects of ablation velocity on ablative Rayleigh–Taylor instability

The influence of the ablation velocity Va on the evolution of single-mode ablative Rayleigh–Taylor instability from the linear to the deeply nonlinear phases is investigated via two-dimensional numerical simulations. Linear growth rates from simulations agree well with the asymptotic theory except for larger discrepancies in the intermediate Froude number regime. The weakly nonlinear growth behavior of the bubble amplitude is found dependent on a critical perturbation wavenumber in a broad Froude number regime. For a linearly stable mode, its nonlinear excitation threshold is higher for larger Va and thus harder to be exceeded. For short-wavelength modes taking significant ablation effects, the bubble penetration velocity is found to reaccelerate after the first saturation and eventually saturate at a larger value with larger Va, due to stronger vortex-acceleration effects and more significant increase in g.

Richtmyer–Meshkov instability of a single-mode heavy–light interface in cylindrical geometry

Richtmyer–Meshkov (RM) instability of a single-mode SF6–air interface subjected to a convergent shock is investigated experimentally. The convergent shock tube is specially designed with an opening tail to weaken the Rayleigh–Taylor effect and eliminate the reflected waves' effect. The gas layer scheme is used to create a heavy gas environment at the upstream side of the interface. Before phase inversion is finished, the amplitude reduction is accelerated, but the Bell–Plesset (BP) effect in this process is found to be negligible. After phase inversion is completed, the linear growth rate is generally predicted due to small amplitude and the weak BP effect. In nonlinear regime, an existing nonlinear model is revised based on the Padé approximation to give a better prediction of amplitude growth. The spike amplitude grows almost linearly, whereas the bubble amplitude gradually saturates and even reduces. For a heavy-light interface in convergent geometry, although both the spike and bubble amplitude growths are promoted by the BP effect, the spike growth is more promoted than the bubble. The BP effect enhances generation of the second-order harmonic, which results in saturation and reduction of the bubble amplitude. The discrepancy in the BP effect between light-heavy and heavy-light interfaces is qualitatively demonstrated for the first time.

Effect of a modulated acoustic field on the dynamics of a vibrating charged bubble

We investigate the effect of amplitude-modulated acoustic irradiation on the dynamics of a charged bubble vibrating in a liquid. We show that the potential V(x) of the bubble, and the number and stability of its equilibria, depend on the magnitude of the charge it carries. Under high-frequency amplitude-modulation, a modulation threshold, Gth, was found for the onset of increased bubble amplitude oscillations. For some pressure field values, charge can facilitate the control of chaotic dynamics via reversed period-doubling bifurcation sequences. There is evidence for peak-shouldering and shock waves. The Mach number increases rapidly with the drive amplitude G. In the supersonic regime, for G>1.90Pa, the high-frequency modulation raises both Blake’s and the transient cavitation thresholds. We found a decrease in the bubble’s maximum charge threshold, and threshold modulation amplitude for the occurrence Vibrational resonance (VR). VR occurs due to the modulated oscillatory pressure field, and the influence on VR of the electrostatic charge, and other parameters of the system are investigated. In contrast to the cases of VR reported earlier, where the amplitude G of the high-frequency driving is typically much higher than the amplitude of the low-frequency driving (Ps), the VR resonance peaks occur here at relatively low G values (0<G<10Pa) compared to the acoustic driving pressure Ps∼105 Pa. The optimal parameter values for enhanced response could be useful in acoustic cavitation applications.

NONLINEAR FORCED OSCILLATIONS OF A BUBBLE IN A LIQUID

Forced nonlinear oscillations of a gas bubble in a liquid are investigated when the frequency of fluctuations in the external pressure of the liquid is equal to the natural frequency of the bubble (resonance). By the method of averaging, a simple formula is derived for the dependence of the oscillation amplitude of a gas bubble on the amplitude of the external pressure and the thermophysical characteristics of the gas and the viscosity of the liquid. Its good agreement with numerical calculations is shown up to the value of the oscillation amplitude of the bubble radius comparable to its equilibrium value.

Bubble Relaxation Dynamics in Homopolymer DNA Sequences.

Understanding the inherent timescales of large bubbles in DNA is critical to a thorough comprehension of its physicochemical characteristics, as well as their potential role on helix opening and biological function. In this work, we employ the coarse-grained Peyrard-Bishop-Dauxois model of DNA to study relaxation dynamics of large bubbles in homopolymer DNA, using simulations up to the microsecond time scale. By studying energy autocorrelation functions of relatively large bubbles inserted into thermalised DNA molecules, we extract characteristic relaxation times from the equilibration process for both adenine-thymine (AT) and guanine-cytosine (GC) homopolymers. Bubbles of different amplitudes and widths are investigated through extensive statistics and appropriate fittings of their relaxation. Characteristic relaxation times increase with bubble amplitude and width. We show that, within the model, relaxation times are two orders of magnitude longer in GC sequences than in AT sequences. Overall, our results confirm that large bubbles leave a lasting impact on the molecule's dynamics, for times between 0.5-500 ns depending on the homopolymer type and bubble shape, thus clearly affecting long-time evolutions of the molecule.

Effects of variable deceleration periods on Rayleigh-Taylor instability with acceleration reversals.

The dynamics of an interfacial flow that is initially Rayleigh-Taylor unstable but becomes statically stable for some intermediate period due to the reversal of the externally imposed acceleration field is studied. We discuss scenarios that consider both single and double-acceleration reversals. The accel-decel (AD) case consists of a single reversal imposed at an instant after the constant acceleration instability has entered a self-similar regime. The layer of mixed fluid ceases to grow upon acceleration reversal, and the dominant mechanics are due to internal wave oscillations. Variation of mass flux and the Reynolds stress anisotropy is observed due to the action of the internal waves. A second reversal of the AD case that is termed as accel-decel-accel, ADA is then explored; the response of the mixing layer is shown to depend strongly on the duration and the periodicity of the Reynolds stress anisotropy of the mixing layer during the deceleration period. We explore the effect of this variable deceleration period after the second acceleration reversal where the flow once again becomes Rayleigh-Taylor unstable based on metrics that include the integral mixing-layer width, bubble and spike amplitudes, mass flux, Reynolds stress anisotropy tensor, and the molecular mixing parameter.

Simulation of multi-point mixing concentration gradient generator

This paper proposes a new concentration gradient generator based on the principle and flow characteristics of solution mixing in the microchannel. This concentration gradient generator works with oscillating bubbles in the microchannel, which are excited with bulk acoustic wave. The oscillating bubbles are used to mix the solution in the microchannel. The volume of each bubble is controllable individually and the number of bubbles partaken mixing is adjustable. Therefore, the mixing position of the solution and the concentration gradient in the microchannel are adjustable. Therefore, the new concentration gradient generator has the advantages of fast response and high flexibility. Simulation software COMSOL 5.5 was used to simulate the influence of the inlet flow rate, the bubble amplitude, and the number of bubbles on the mixing result. The simulation result shows that the inlet flow rate and the bubble amplitude affect the mixing width of the solution in the microchannel. The simulation result also shows that the concentration distribution with different gradient can be generated by adjusting the number of bubbles located in the solution microchannel. The simulation has an important reference for the design of the concentration gradient generator.

Lattice Boltzmann simulation of three-dimensional fluid interfacial instability coupled with surface tension

In this paper, the development of three-dimensional fluid interfacial Rayleigh-Taylor (RT) instability coupled with the surface tension was numerically studied using the mesoscopic lattice Boltzmann method. We mainly analyzed the influence of surface tension on fluid interfacial dynamics and spike/bubble late-time growth. The numerical experiments show that there exists the critical surface tension (&lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$\sigma_{\rm{c}}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20212061_M3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20212061_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;) in the three-dimensional RT instability, above which the RT phenomenon does not appear and below which it would take place. It is found that the critical surface tension increases with the fluid Atwood number and the corresponding numerical predictions show good agreements with those of the theoretical analysis &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}${\sigma_{\rm{c}}}= {{({{\rho_{\rm{h}}}-{\rho_{\rm{l}}}})g}}/{{{k^2}}}$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20212061_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20212061_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. In addition, we can find that increasing surface tension reduces the roll-up of the interface and the complexity of interfacial structure, also preventing the breakup of the interface into the individual droplets. The late-time dynamics of phase interface change from the asymmetric development to the symmetry with respect to the middle axis. When the surface tension is sufficiently low, the spike and bubble amplitudes almost no longer change with it, and further increasing the surface tension can slow down the growth of the spike and bubble amplitudes. Furthermore, we can observe that the development of the high-Reynolds-number RT instability under different surface tensions can also be divided into four distinct stages, including the linear growth, saturated velocity growth, reacceleration, and chaotic mixing. The spike and bubble grow with approximately constant velocities at the saturated stage and their asymptotic values are consistent with those of the modified potential flow theory. In the following, the spike and bubble driven by the increasing Kelvin-Helmholtz vortices are accelerated such that their evolutional velocities exceed the solutions of the potential flow model at the reacceleration stage. The reacceleration stage cannot last infinitely and the spike and bubble velocities at the late time fluctuate with time, implying that the growth of the RT instability enters into the chaotic mixing stage. By numerical analysis, we demonstrate that the three-dimensional RT instability at the chaotic mixing stage has a quadratic growth and also report that the spike and bubble growth rates decrease with the surface tension in general.

Oscillation behavior of bubble pair in magnetic fluid tube under magneto-acoustic complex field

Based on the dynamic model of a single bubble in a magnetic fluid tube, the dynamic equation of a bubble pair system in a magneto-acoustic field is established by introducing the secondary sound radiation between bubbles and considering the magnetic field effect of the viscosity of the magnetic fluid. The effects of magnetic field intensity, bubble pair’s size, bubble interaction (including secondary Bjerknes force &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;B&lt;/sub&gt; and magnetic attraction &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt;) and fluid characteristics on the vibration characteristics of double bubbles are analyzed. The results show that magnetic field increases the amplitude of bubbles, and the influence of magnetic field on the large bubble is greater than on the small bubble. When the center distance between the two bubbles is constant and the relative size of two bubbles is larger, or when the size of the two bubbles is constant and the surface distance between two bubbles is small, the interaction between two bubbles is stronger. In the magneto-acoustic composite field, magnetic field can affect &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;B&lt;/sub&gt;, &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt;, magnetic pressure &lt;i&gt;P&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt; and viscosity resistance, and the influence degrees are different. There is competition between &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;B&lt;/sub&gt; and &lt;i&gt;F&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt; and between &lt;i&gt;P&lt;/i&gt;&lt;sub&gt;m&lt;/sub&gt; and viscosity resistance, and the forces acting on the microbubble jointly affect the movement of the bubbles. By studying the dynamic behavior of paired bubbles, it can provide a theoretical basis for improving the therapeutic effect of targeted regulation of microbubbles on biological tissues by adjusting the magneto-acoustic field in practical application.

Enhancement of oscillation amplitude of cavitation bubble due to acoustic wake effect in multibubble environment

Acoustic cavitation occurs in ultrasonic treatment causing various phenomena such as chemical synthesis, chemical decomposition, and emulsification. Nonlinear oscillations of cavitation bubbles are assumed to be responsible for these phenomena, and the neighboring bubbles may interact each other. In the present study, we numerically investigated the dynamic behavior of cavitation bubbles in multi-bubble systems. The results reveal that the oscillation amplitude of a cavitation bubble surrounded by other bubbles in a multi-bubble system becomes larger compared with that in the single-bubble case. It is found that this is caused by an acoustic wake effect, which reduces the pressure near a bubble surrounded by other bubbles and increases the time delay between the bubble contraction/expansion cycles and sound pressure oscillations. A new parameter, called “cover ratio” is introduced to quantitatively evaluate the variation in the bubble oscillation amplitude, the time delay, and the maximum bubble radius.

Effect of Water Amount Intake before Scuba Diving on the Risk of Decompression Sickness.

Background and objective: The aim of this study was to investigate the influence of pre-hydration levels on circulating bubble formation for scuba divers and to evaluate the appropriate volume of water intake for reducing the risk of decompression sickness (DCS). Materials and Methods: Twenty scuba divers were classified into four groups according to the volume of water taken in before scuba diving as follows: no-water-intake group (NWIG), 30%-water-intake group (30WIG), 50%-water intake group (50WIG), and 100%-water-intake group (100WIG). We measured the circulating bubbles using movement status by Doppler on the right and left subclavian veins and precordial regions at pre-dive, post-dive, and 30 min after diving to a depth of 30 m for a duration of 25 min at the bottom. Results: Participants belonging to the 30WIG showed the lowest frequency, percentage, and amplitude of bubbles and consequently the lowest bubble grade in the left and right subclavian veins and precordial region at post-time and 30 min after diving. Conclusions: It can be inferred that pre-hydration with 30% of the recommended daily water intake before scuba diving effectively suppressed the formation of bubbles after diving and decreased the risk of DCS.

Enhancement of Oscillation Amplitude of Cavitation Bubble Due to Acoustic Wake Effect in Multibubble Environment

Acoustic cavitation occurs in ultrasonic treatment causing various phenomena such as chemical synthesis, chemical decomposition and emulsification. Nonlinear oscillations of cavitation bubble are assumed to be responsible for these phenomena. Therefore, bubble oscillations have been studied especially focusing on single bubble system while those in multi-bubble systems have not been analyzed yet despite their importance for the actual ultrasonic processing. In the present study, we numerically investigated the dynamic behavior of cavitation bubbles in multi-bubble systems. The results reveal that the oscillation amplitude of bubbles becomes larger in multi-bubble environment compared with that in the single-bubble case. It is found that this is caused by an acoustic wake effect, which reduces the pressure near a bubble surrounded by other bubbles and increases the time delay between the bubble contraction/expansion cycles and sound pressure oscillations. A new parameter, called “cover ratio” is introduced to quantitatively evaluate the variation in the bubble oscillation amplitude and time delay.

Dynamic characteristics of bubbles in spherical bubble group considering evaporation and condensation of water vapor

&lt;sec&gt;In order to explore the dynamic characteristics of bubbles in the cavitation bubble cluster in detail, the dynamic equation of a bubble with arbitrary location inside the bubble cluster is established in this paper, based on the interactions between bubbles inside the bubble cluster driven by ultrasound. The effects of evaporation and condensation of the water vapor are also taken into account in the derivation process. Based on the proposed equation, the influences of the bubble position, number of bubbles, and initial radius of bubbles on the dynamic characteristics of cavitation bubbles are studied, and the corresponding change laws of the bubble radius, energy, temperature, pressure, as well as the number of water vapor molecules in a bubble are investigated under ultrasound.&lt;/sec&gt;&lt;sec&gt; The calculation results are shown below. 1) Comparing with an isolated bubble, the oscillation of a bubble inside the bubble cluster is suppressed by its surrounding bubbles, which leads to the fact that the vibration amplitude of a bubble inside the bubble cluster is smaller, and that the internal energy, maximum temperature, maximum pressure and the number of water molecules in the bubble all become smaller. As the distance between the bubble and the center of the bubble cluster increases, the vibration amplitude of the bubble become larger. 2) The initial radii of the bubbles in the bubble cluster can significantly affect the normalized vibration amplitude, collapse time, internal energy, temperature, and pressure of bubbles, as well as the number of water vapor molecules in bubbles of the bubble cluster. 3) As the number of bubbles in the bubble cluster increases, the vibration amplitudes of the bubbles decrease. 4) The higher the ultrasonic frequency, the smaller the oscillation amplitude of the bubble; the smaller the maximum pressure and energy of the bubble, the larger the minimum value of the internal pressure and temperature of the bubble and the less the number of water molecules in the bubble. When the ultrasonic frequency increases, the cavitation effects of bubbles in the bubble cluster are suppressed. 5) As the ultrasonic sound pressure increases, the oscillation amplitudes of the bubbles in the bubble cluster increase, the maximum values of the bubbles' radii increase, the collapse times of the cavitation bubbles increase, and the number of oscillations of bubbles decreases after the cavitation bubbles have collapsed. Additionally, the maximum value of internal energy, temperature, pressure, and the number of water molecules in the bubble also increase as the ultrasonic sound pressure increases, while the minimum value of the pressure and temperature of the bubble decrease. Besides, when the ultrasonic sound pressure increases, the cavitation effects of the bubbles in the bubble cluster turn stronger.&lt;/sec&gt;&lt;sec&gt; This paper focuses on the dynamic characteristics of ultrasonic cavitation bubble cluster from the theoretical aspect and the results can be further applied to experimental analysis.&lt;/sec&gt;

Effect of surface tension on late-time growth of high-Reynolds-number Rayleigh-Taylor instability

In this paper, we numerically investigate the late-time growth of high-Reynolds-number single-mode Rayleigh-Taylor instability in a long pipe by using an advanced phase-field lattice Boltzmann multiphase method. We mainly analyze the influence of surface tension on interfacial dynamic behavior and the development of the bubble front and spike front. The numerical experiments indicate that increasing surface tension can significantly reduce the complexity of formed interfacial structure and also prevents the breakup of phase interfaces. The interface patterns in the instability process cannot always preserve the symmetric property under the extremely small surface tension, but they do maintain the symmetries with respect to the middle line as the surface tension is increased. We also report that the bubble amplitude first increases then decreases with the surface tension. There are no obvious differences between the curves of spike amplitudes for low surface tensions. However, when the surface tension increases to a critical value, it can slow down the spike growth significantly. When the surface tension is lower than the critical value, the development of the high-Reynolds-number Rayleigh-Taylor instability can be divided into four different stages, i.e. the linear growth, saturated velocity growth, reacceleration, and chaotic mixing. The bubble and spike velocities at the second stage show good agreement with those from the modified potential flow theory that takes the surface tension effect into account. After that, the bubble front and spike front are accelerated due to the formation of Kelvin-Helmholtz vortices in the interfacial region. At the late time, the bubble velocity and spike velocity become unstable and slightly fluctuate over time. To determine the nature of the late-time growth, we also measure the bubble and spike normalized accelerations at various interfacial tensions and Atwood numbers. It is found that both the spike and bubble growth rates first increase then decrease with the surface tension in general. Finally, we deduce a theoretical formula for the critical surface tension, below which the Rayleigh-Taylor instability takes place and above which tension it does not occur. It is shown that the critical surface tension increases with the Atwood number and also the numerical predictions by the lattice Boltzmann method are also in accord well with the theoretical results.

Base pair opening in a damped helicoidal Joyeux-Buyukdagli model of DNA in an external force field.

Upon the Joyeux-Buyukdagli model of DNA, the helicoidal interactions are introduced, and their effects on the dynamical behaviors of the molecule investigated. A theoretical framework for the analysis is presented in an external force field, taking into account Stokes and hydrodynamics viscous forces. In the semi-discrete approximation, the dynamics of the molecule is found governed by the cubic complex Ginzburg-Landau (CGL) equation. By choosing an appropriate decoupling ansatz, the cubic CGL equation is transformed into a nonlinear differential equation whose analytical solitary wave-like solutions can be explored by means of the direct method, which is more tractable in case where the form of soliton solutions is known. Based on this, a dissipative bright-like soliton solution is obtained. Numerical experiments have been done, and relevant results were brought out, such as the quantitative and qualitative influences of the helical interactions on the parameters of the traveling bubble. The important role-played by these interactions in the DNA biological processes is brought out, showing that depending on the wave number, their effects can increase, decrease, or keep constant the bubble angular frequency, velocity, amplitude, and width, as well as the energy involved by enzymes in the initiation of DNA biological processes. This can prevent some coding or reading errors and resulting genetic damages. Analytical predictions and numerical experiments were in good agreement.