Outer Interfaces Research Articles

Effects of reverberating waves and interface coupling on a divergent Richtmyer–Meshkov instability

Shock-tube experiments on Richtmyer–Meshkov (RM) instability at a perturbed SF $_6$ layer surrounded by air, induced by a cylindrical divergent shock, are reported. To explore the effects of reverberating waves and interface coupling on instability growth, gas layers with various shapes are created: unperturbed inner interface and sinusoidal outer interface (case US); sinusoidal inner and outer interfaces that have identical phase (case IP); sinusoidal inner and outer interfaces that have opposite phase (case AP). For each case, three thicknesses are considered. Results show that reverberating waves inside the layer dominate the early-stage instability growth, while interface coupling dominates the late-stage growth. The influences of waves on divergent RM instability are more pronounced than the planar and convergent counterparts, which are estimated accurately based on gas dynamics theory. Both the wave influence and interface coupling depend heavily on the layer shape, leading to diverse growth rates: the quickest growth for case AP, medium growth for case US, the slowest growth for case IP. In particular, for the IP case, there exists a critical thickness below which the instability growth is suppressed by both the reverberating waves and interface coupling. This provides an efficient way to modulate the growth of divergent RM instability. It is found that divergent RM instability involves weak nonlinearity and strong interface coupling such that the linear theory of Mikaelian (Phys. Fluids, vol. 17, 2005, 094105) can well reproduce the instability growth at late stages for all cases. This constitutes the first experimental confirmation of the Mikaelian theory.

Interfaces coupling deformation mechanisms of liquid–liquid–liquid three-phase flow in a confined microchannel

Interfaces coupling deformation mechanisms of liquid–liquid–liquid three-phase flow in a confined microchannel are ascertained by both experimental investigation and numerical simulation. The deformation behaviors of inner and outer interfaces of compound droplets mainly depend on the flow rate of continuous phase (Q) and the diameter ratio of core droplet to shell droplet (D*). Compared with that of single droplets, the outer interface deformation degree of compound droplets is always limited at large Q and D* because of the hindering effect of inner interface. However, the hindering effect can be weakened by decreasing the D*, and thus the outer interface deformations for both single and compound droplets remain almost consistent. Additionally, the interfaces coupling deformation mechanisms are also clarified, and the results show that due to the existence of outer interface, the differential pressure force and shearing force acting on the inner interface decrease, resulting in a low deformation coefficient of core droplet. The influence of inner interface on outer interface deformation is only reflected by the disturbance to the flow field structures. To achieve precise control over the outer interface deformation, a prediction correlation for aspect ratio with several dimensionless numbers is established with good precision. The results in this study provide valuable guidance for practical applications of liquid–liquid–liquid three-phase flow microsystems.

Evolution mechanism of double-layer heavy gas column interface with sinusoidal disturbance induced by convergent shock wave

Based on Navier-Stokes equations, combining the fifth-order weighted essentially non-oscillatory scheme with the adaptive structured grid refinement technique, the interactions between converging shock and annular SF<sub>6</sub> layers with different initial perturbation amplitudes and thickness are numerically investigated. The evolution mechanism of shock structure and interface are revealed in detail, and the variations of the circulation, mixing rate and turbulent kinetic energy are quantitatively analyzed. The dynamic mode decomposition method is used to analyze the dynamic characteristics of the vorticity. The results show that in the case with large initial perturbation amplitude, the transmitted shock wave forms Mach reflection structures both inside and outside of the inner interface of SF<sub>6</sub> layer, and multiple shock focusing phenomena occur in the center. After the transmitted shock wave penetrates the outer interface, the circulation increases faster, and the “spike” and “bubble” structure on inner interface develop faster, so that the amplitude of the inner and outer interfaces and the gas mixing rate increase. As for the case with larger thickness of the gas layer, the phase of the transmitted shock wave changes inside the layer, which forms “bubble” at the crest of the inner interface and “spike” at the trough. When the thickness of the gas layer decreases, the crest of the inner interface does not move inside after being impacted, and “spike” and “bubble” are generated in the late stage. The dynamic modes show that the main structure of vorticity and the exchange of positive and negative vorticity on the main structure are determined by the modes with weak growth and low frequency, but the modes with weak growth and high frequency determine rapid exchange of positive and negative vorticity at the interface in the cases with weak coupling effect.

Magnetic field-induced control of a compound ferrofluid droplet deformation and breakup in shear flow using a hybrid lattice Boltzmann-finite difference method

The deformation and breakup dynamics of a compound ferrofluid droplet under shear flow and uniform magnetic field are numerically studied in this paper. Utilizing magnetic field provides the possibility to obtain better control over the compound droplet morphology and breakup in a simple shear flow. To solve the governing equations for interfaces motion and hydrodynamics, the conservative phase field lattice Boltzmann model is employed, and a finite difference approach is applied for calculating the magnetic field. To verify the accuracy of present simulations, the results are validated with those of four relevant benchmarks including liquid lens between two stratified fluids, three-phase morphology diagram, droplet under simple shear flow fluid flow, and ferrofluid droplet elongation under a uniform magnetic field. The magnetic field lines and magnetic force in the presence of ferrofluid are visualized. The effects of capillary and magnetic Bond numbers on the deformation and inclination angle of compound droplet under magnetic field at the angles of 45∘ and 135∘ are investigated when the inner or outer droplet is ferrofluid. The results show that by increasing capillary number, the shear force becomes greater and deforms the outer interface, whereas its effect on the inner interface is negligible and its small deformation is due to the squeezing force by the outer interface. As the magnetic Bond number increases, so does the magnetic force, and it leads to both of inner and outer interfaces elongation in the direction of the imposed magnetic field. Finally, the regime maps of compound droplet morphology and breakup in terms of capillary and magnetic Bond numbers are presented when the outer droplet is ferrofluid and the magnetic field is applied at the directions of 45∘ and 135∘, respectively. The border between breakup and non-breakup regions is illustrated, and according to the equilibrium shape of the compound droplet, donut-shaped, egg-shaped, eye-shaped, and peach-shaped regimes are observed in the non-breakup region.

Convergent Richtmyer–Meshkov instability on a light gas layer with perturbed inner and outer surfaces

The instability of an annular helium gas layer surrounded by air with sinusoidal inner and outer interfaces, formed by a novel soap-film technique, impacted by a cylindrically convergent shock is experimentally studied in a semi-annular shock tube. Detailed evolution of the interfaces and wave patterns is captured by a high-speed Schlieren system. The focus is placed on the influences of layer thickness and phase difference between the inner and outer interfaces on the instability development. It is found that the larger the layer thickness, the quicker the early stage development of the outer interface. This is because the layer thickness affects the arrival time of the reflected shock (RS) at the outer interface and further determines the direction of baroclinic vorticity deposited on the outer interface by RS; namely, RS inhibits or promotes the instability growth depending on the layer thickness. It is also found that phase difference between the inner and outer perturbations produces a negligible (an evident) influence on the early stage (late-stage) instability growth at the outer interface, whereas a considerable (weak) influence on the early stage (late-stage) instability growth at the inner interface. This finding suggests that the early stage development of the outer (inner) interface can be modulated by changing the layer thickness (perturbation phase difference). Empirical coefficient in the Charakhch'an model [J. Appl. Mech. 41, 23–31 (2000)] is calculated to be β=0.52 by comparing the prediction with the experimental results. The model with β=0.52 gives a reasonable prediction of the post-reshock growth rate for all the cases considered in this work.

Interfacial behavior of surfactant-covered double emulsion in extensional flow.

We analyze the interface-interface interactions of a surfactant-covered double emulsion using the lattice Boltzmann method and study the interaction of the inner and outer interfaces and the local surfactant distribution under a uniaxial extensional flow. First, the capillary effects are analyzed. Upon surfactant application, the outer droplet deformation increases and the inner droplet deformation decreases. The concentrated surfactants on the outer interface increase deformation, and the inner droplet is affected by the inner flow. At a fixed Péclet number (Pe), the surfactant concentration at the outer interface increases with an increase in capillary number (Ca); however, such a tendency is difficult to identify at the inner interface. Next, the Pe effects are analyzed. With an increase in Pe, the deformation of the inner droplet decreases significantly. The local distribution of the surfactant considerably affects the double emulsion stabilization, which is analyzed in terms of internal flow. The interfacial tension gradient induced by the surfactant generates vortices internally, which is verified by applying the surfactant to each interface independently. The radius ratio affects droplet deformation and surfactant transport. The compression of the inner flow region increases the viscous force and decreases the interface velocity. Therefore, with an increase in radius ratio, the deformation increases, and the surfactant transport becomes slow.

Local entrainment velocity in a premixed turbulent annular jet flame

The local entrainment velocity of the enstrophy interfaces of a methane–air turbulent premixed turbulent annular jet flame stabilized on a bluff-body burner has been investigated using a high-fidelity flame-resolved three-dimensional simulation. The enstrophy (inner and outer) and the scalar interfaces have been defined and characterized by their propagation speeds, VE and Sd, relative to the fluid flow. Mean values (⟨Sd |c⟩ and ⟨VE |c⟩) conditioned on the reaction progress variable c have been obtained. A thin layer (near the enstrophy interfaces) has been used to compute mean values (⟨VE |E⟩, ⟨Sd |E⟩, and its different contributions) conditional upon enstrophy E. At the inner interface, results indicate that ⟨Sd |c⟩ > 0 and ⟨Sd |E⟩ > 0 (entrainment of fresh reactants into the flame front and hot products), while ⟨VE |c⟩ < 0 and ⟨VE |E⟩ < 0 (entrainment of hot products into the reacting jet across the inner enstrophy interface). The outer enstrophy interface displays ⟨VE |E⟩ > 0 (ambient gases are predominantly entrained into the jet of reactants), which implies a lean mixture in its neighborhood. These preliminary results aim at understanding the physical mechanisms of flame anchoring, in terms of entrainments of either hot products or fresh reactants into the diffusive-reactive region. Local geometries of the inner and outer interfaces have also been examined, through the computation of joint probability density functions of the mean curvature km and Gauss curvature kg of the iso-enstrophy surfaces, and through ⟨VE |km, kg⟩ at the inner and outer interfaces. This information has subsequently been used to discuss the physics of how the turbulent entrainment process affects premixed flames.

Dynamics of deformation and pinch-off of a migrating compound droplet in a tube

A computational fluid dynamic investigation has been carried out to study the dynamics of a moving compound droplet inside a tube. The motions associated with such a droplet is uncovered by solving the axisymmetric Navier-Stokes equations in which the spatiotemporal evolution of a pair of twin-deformable interfaces has been tracked employing the volume-of-fluid approach. The deformations at the interfaces and their subsequent dynamics are found to be stimulated by the subtle interplay between the capillary and viscous forces. The simulations uncover that when a compound drop composed of concentric inner and outer interfaces migrates inside a tube, initially in the unsteady domain of evolution, the inner drop shifts away from the concentric position to reach a morphology of constant eccentricity at the steady state. The coupled motions of the droplets in the unsteady regime causes a continuous deformation of the inner and outer interfaces to obtain a configuration with a (an) prolate (oblate) shaped outer (inner) interface. The magnitudes of capillary number and viscosity ratio are found to have significant influence on the temporal evolution of the interfacial deformations as well as the eccentricity of the droplets. Further, the simulations uncover that, following the asymmetric deformation of the interfaces, the migrating compound droplet can undergo an uncommon breakup stimulated by a rather irregular pinch-off of the outer shell. The breakup is found to initiate with the thinning of the outer shell followed by the pinch-off. Interestingly, the kinetics of the thinning of outer shell is found to follow two distinct power-law regimes-a swiftly thinning stage at the onset followed by a rate limiting stage before pinch-off, which eventually leads to the uncommon breakup of the migrating compound droplets.

On the selection of viscosity to suppress the Saffman–Taylor instability in a radially spreading annulus

We examine the stability of a system with two radially spreading fronts in a Hele-Shaw cell in which the viscosity increases monotonically from the innermost to the outermost fluid. The critical parameters are identified as the viscosity ratio of the inner and outer fluids and the viscosity difference between the intermediate and outer fluids as a fraction of the viscosity difference between the inner and outer fluids. There is a minimum viscosity ratio of the inner and outer fluids above which, for each azimuthal mode, the system is stable to perturbations of that mode at any flow rate. This condition is directly analogous to the result for a single interface. Below this minimum ratio, the system may be stable at any flow rate early in the flow. However, once the inner radius reaches a critical fraction of the outer radius, this absolute stability ceases to apply owing to the coupling of the inner and outer interfaces. We determine the maximum flow rate, as a function of time, in order that all modes remain stable due to the effects of interfacial tension. These criteria for stability are then used to select the viscosity of the intermediate fluid so that a fixed volume of the intermediate and then inner fluid can be added to the system in the minimum time with the system remaining stable throughout. The optimal viscosity for this intermediate fluid depends on the relative volume of the inner and intermediate fluid and also on the overall viscosity ratio of the innermost fluid and the original fluid in the cell, with the balance being to suppress the early time instability of the outer interface and the late time instability of the inner interface. We discuss application of this approach to a problem of injection of treatment fluid in an oil well.

Poly(o-aminophenol) Electrosynthesized onto Platinum at Acidic and Neutral pH: Comparative Investigation on the Polymers Characteristics and on Their Inner and Outer Interfaces

Poly(o-aminophenol) Electrosynthesized onto Platinum at Acidic and Neutral pH: Comparative Investigation on the Polymers Characteristics and on Their Inner and Outer Interfaces

Observation of an EPIR Effect in Nd1−xSrxMnO3 Ceramics with Secondary Phases

Nd1−xSrxMnO3 (x = 0.3, 0.5) ceramics containing a secondary phase are synthesized by high-energy ball milling and post heat-treatment method. The 4-wire and 2-wire measuring modes are used to investigate the transport character of the grain/phase boundary (inner interface) and electrode-bulk interface (outer interface), respectively, and the results indicate that there is a similar nonlinear I–V behaviour for both of the inner and outer interfaces, however, the electric pulse induced resistance change (EPIR) effect can only be observed at the outer interface.

Surface Chemistry and Annealing-Driven Interfacial Changes in Organic Semiconducting Thin Films on Silica Surfaces

Vibrational sum frequency generation (VSFG) spectroscopy was used in conjunction with steady-state IR spectroscopy, atomic force microscopy (AFM), and spectroscopic ellipsometry to characterize organic semiconductor thin films that were vapor deposited on silica- and trimethoxy(octadecyl)silane (ODTMS)-functionalized silica surfaces. The growth of perylene derivative N,N'-dioctyl-3,4,9,10-perylenedicarboximide (PTCDI-C(8)) was found to proceed differently on simple glass slides relative to that of native oxide on silicon and fused quartz slides. VSFG was applied to these samples to isolate structural changes that occurred specifically at the buried interface between the organic semiconductor and the silica dielectric upon thermal annealing. A model was introduced to globally fit the imide carbonyl symmetric and asymmetric interfacial spectra that included contributions from both inner and outer interfaces. The fits to the VSFG data and AFM topographic images revealed significant reordering at the outer interface on all substrates upon thermal annealing. Within the model, the spectroscopic data reported that the inner interfacial PTCDI-C(8) monolayer reoriented to a more reclined phase on bare substrates after annealing but remained essentially unchanged on ODTMS monolayers. Electrical characterization of PTCDI-C(8) field-effect transistors indicated that electron mobilities were higher on bare substrate devices but could be improved by a factor of 2 on both surface types by thermal annealing. The mobility effects were attributed to the annealing-driven coalescence of PTCDI-C(8) grain boundaries. Consistent with previous structural reports, the molecular rearrangements of the first monolayer of PTCDI-C(8) on bare substrates that were reported by VSFG spectroscopy had a noticeable impact on the device performance.

Theoretical study of the tunable second-harmonic generation (SHG) enhancement factor ofgold nanotubes

A theoretical calculation is performed to investigate the second-harmonic generationenhancement factor in gold nanotubes. The SHG at both inner and outer interfaces isgreatly enhanced by the surface plasmon resonance (SPR) which induces a local field effectand fluctuations of the density of oscillatory electrons in the gold wall. The outer interfacemode resulting from both basic and double frequency is more sensitive to the gold wallthickness. The coupling of the inner interface with outer interface makes theSHG enhancement factor increase greatly. Furthermore, the SPR frequency andlocal field intensity can be modulated by varying the dielectric constant, andconsequently the position and intensity of the SHG peaks can be tuned. Thiswork shows the potential of gold nanotubes for nonlinear optics at the nanoscale.

Nonlinear dynamics and breakup of compound jets

Finite-amplitude deformation and breakup of a compound jet, whose core and shell are both incompressible Newtonian fluids, that is surrounded by a passive gas are analyzed computationally by a temporal analysis. The means is a method of lines algorithm in which the Galerkin/finite element method with elliptic mesh generation is used for spatial discretization and an adaptive finite difference method is employed for time integration. The dynamics are initiated by subjecting the inner and the outer interfaces of a quiescent compound jet to axially periodic perturbations that are either in phase (ω=0) or π radians out phase (ω=π), where ω is the phase shift between the disturbances imposed on the two interfaces. The initial growth rates of disturbances obtained from computations are compared and demonstrated to be in excellent agreement with predictions of linear theory [Chauhan et al., J. Fluid Mech. 420, 1 (2000)]. Computations reveal that recirculating flows occur commonly during the deformation and pinch-off of compound jets, and hence render inapplicable the use of slender-jet type approximations for analyzing the dynamics in such cases. Moreover, as the deformations of one or both of the interfaces of the compound jet grow, the resulting shapes at the incipience of pinch-off are asymmetric and lead to the formation of satellite drops. Calculations are carried out over a wide range of Reynolds numbers of the core fluid, ratios of the viscosity and density of the shell fluid to those of the core fluid, ratio of the surface tension of the outer interface to the interfacial tension of the inner interface, the ratio of the unperturbed radius of the outer cylindrical interface to that of the inner cylindrical interface, wavenumber, and perturbation amplitudes to determine their effects on breakup time and whether both interfaces pinch at the same instant in time to result in the formation of compound drops. Conditions are also identified for which the dynamical response of compound jets subjected to initial perturbations with ω=0 differ drastically from those subjected to ones with ω=π.

Instability analysis of a coaxial jet under a radial electric field in the nonequipotential case

The linear temporal stability analysis of a coaxial jet model under the radial electric field is carried out on the assumption that all free charges are “frozen” on the outer interface of the conducting liquid (i.e., the nonequipotential case) in the present paper. The analytical dimensionless dispersion relation is derived and solved numerically. Three unstable modes, namely the paravaricose, parasinuous, and transitional modes, are found in the Rayleigh regime and they change into the other two unstable modes, namely mode 1 and mode 2, in the wind induced and atomization regimes if the dimensionless electrostatic force or Weber number is sufficiently amplified. The numerical results show that the dimensionless electrostatic force as well as the Weber number inhibits the jet instability in the long wavelength region while enhances it in the short wavelength region. The relative dielectric constant of the outer liquid alters the behaviors of the nonequipotential case significantly, whereas the electrical permittivity of the inner liquid does not affect the jet instability much. Besides, the relatively small diameter ratio may make the inner and outer interfaces decouple from each other. And the critical diameter ratio is calculated crudely. The differences between the equipotential and nonequipotential cases are clarified step by step.

Local Dielectric and Polarization Properties of Inner and Outer Interfaces in PZT Thin Films

We report on novel approaches using scanning force methods [i.e. piezoresponse force microscopy (PFM), Kelvin probe force microscopy (KPFM) and pull-off force spectroscopy (PFS)] in order to deduce the local dielectric and polarization properties of PZT thin films both at outer and inner interfaces with a lateral resolution <50 nm. We show that the polarization profile into the depth of the PZT sample varies dramatically being built up at the bottom Pt electrode over a transition layer of more than 200 nm in thickness. The results are explained both in the view of negatively charged defects pinned at the PZT/Pt interface as well as the possible variation in the local dielectric properties across the film thickness. Investigating the latter made the quantitative deduction of values such as the effective dielectric polarization P z , the deposited charge density σ, and the surface dielectric constant ϵsurface in thin ferroelectric PZT films necessary. We illustrate that such measurements in fact are possible on the nanometer scale revealing quantitative data when combining PFM and PFS.

Heat and mass transfer in annular liquid jets: II. g-jitter

The effects of g-jitter on heat and mass transfer in underpressurized, annular liquid jets are analyzed numerically as a function of the amplitude and frequency of the gravitational modulation by means of a mapping technique that transforms the time-dependent geometry of these jets into a unit square and a conservative finite difference method. It is shown that the pressure coefficient, gas concentration at the jet's inner interface, heat fluxes at the jet's inner and outer interfaces and interfacial temperature are periodic functions of time whose amplitudes increase as the amplitude of the g-jitter is increased, but decrease as the jitter frequency is increased. The pressure coefficient is almost in phase with the heat flux at the jet's outer interface, and out of phase with the mass transfer rate at the jet's inner interface. It is also shown that the temperature field adapts itself rapidly to the imposed gravity modulation, and thermal equilibrium is reached quickly. However, mass transfer phenomena are very slow and require a very long time to become periodic.