电场对协流式微流控装置中乳液液滴生成行为的调控机理

建立了直流电场作用下协流式微流控装置中单乳液液滴乳化生成过程的非稳态理论模型,并开展了数值模拟研究,揭示了电场对液滴乳化生成动力学行为的调控机理,阐明了流场/电场参数对液滴乳化生成特性的影响规律.研究结果表明:沿流体流动方向施加静电场可在电物性参数不同的两相流体界面法线方向上产生指向内相流体的电场力,进而强化了内相流体界面的颈缩和断裂,提升了液滴生成速率和形变程度,减小了液滴生成尺寸;在同一毛细数下,随着电毛细数的增大,乳液乳化流型由每周期仅有单一液滴生成的滴式流型转变为每周期有一个主液滴并伴随有卫星液滴生成的滴式流型;随着毛细数和电毛细数的增大,黏性拖曳力以及电场力作用增强,使内相流体颈缩过程后期更容易形成细长型液线,从而有助于诱发液线上产生Rayleigh-Plateau不稳定现象,继而促进卫星液滴的形成.     

Quantum field theoretical analysis on unstable behavior of Bose-Einstein condensates in optical lattices

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows an unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consistent with those given by the discrete nonlinear Schrödinger equation.     

Heat generation by impulse ultrasound

An original method allowing to get a system of nonlinear evolution equations for the interacting modes applies to a problem of the heat generation by non-periodic ultrasound, including impulse one. The basic idea and final equations for the thermoviscous plane flow are presented. The limit of periodic source is traced. The numerical calculations were based on the pulse solution of the Burgers equation as an ultrasound source. Some illustrations on temporal behavior of the medium expansion caused by the pulse ultrasound are presented.     

Heat generation by impulse ultrasound

An original method allowing to get a system of nonlinear evolution equations for the interacting modes applies to a problem of the heat generation by non-periodic ultrasound, including impulse one. The basic idea and final equations for the thermoviscous plane flow are presented. The limit of periodic source is traced. The numerical calculations were based on the pulse solution of the Burgers equation as an ultrasound source. Some illustrations on temporal behavior of the medium expansion caused by the pulse ultrasound are presented.     

Nonlinear dynamics of cell migration in anisotropic microenvironment

Cell migration in anisotropic microenvironment plays an important role in the development of normal tissues and organs as well as neoplasm progression, e.g., osteogenic differentiation of embryonic stem cells was facilitated on stiffer substrates, indicating that the mechanical signals greatly affect both early and terminal differentiation of embryonic stem cells. However, the effect of anisotropy on cell migration dynamics, in particular, in terms of acceleration profiles which is important for recognizing dynamics modes of cell migration and analyzing the regulation mechanisms of microenvironment in mechanical signal transmission, has not been systematically investigated. In this work, we firstly rigorously investigate and quantify the differences between persistent random walk and anisotropic persistent random walk models based on the analysis of cell migration trajectories and velocity auto-covariance function, both qualitatively and quantitatively. Secondly, we introduce the concepts of positive and negative anisotropy based on the motility parameters to study the effect of anisotropy on acceleration profiles, especially the nonlinear decrease and non-monotonic behaviors. We particularly elaborate and discuss the mechanisms, and physical insights of non-monotonic behaviors in the case of positive anisotropy,focusing on the force exerted on migrating cells. Finally, we analyze two types of in vitro cell migration experiments and verify the universality of nonlinear decrease and the consistence of non-monotonic behaviors with numerical results.We conclude that the anisotropy of microenvironment is the cause of the non-monotonic and nonlinear dynamics, and the anisotropic persistent random walk can be as a suitable tool to analyze in vitro cell migration with different combinations of motility parameters. Our analysis provides new insights into the dynamics of cell migration in complex microenvironment,which also has implications in tissue engineering and cancer research.     

Generation and amplification of magnetic islands by drift interchange turbulence

We investigate the multiscale nonlinear dynamics of a linearly stable or unstable tearing mode with small-scale interchange turbulence using 2D MHD numerical simulations. For a stable tearing mode, the nonlinear beating of the fastest growing small-scale interchange modes drives a magnetic island with an enhanced growth rate to a saturated size that is proportional to the turbulence generated anomalous diffusion. For a linearly unstable tearing mode the island saturation size scales inversely as one-fourth power of the linear tearing growth rate in accordance with weak turbulence theory predictions. Turbulence is also seen to introduce significant modifications in the flow patterns surrounding the magnetic island.     

Numerical investigation of the effect of insoluble surfactant on drop formation in microfluidic device

Surfactants are commonly used in droplet-based microfluidics to stabilize the droplet interface. In this study, we investigate the effect of insoluble surfactant on drop formation in a capillary microfluidic device. We use a diffuse-interface method to describe the evolution of interface involving insoluble surfactant. The Navier-Stokes/Cahn-Hilliard equations and the surfactant conservation equation are solved by a finite element method along with a grid deformation method. As the surfactant has a non-uniform distribution during the drop formation in general, the surface tension has a gradient on the interface, which affects the flow field and interface evolution. The surfactant effect is discussed for dripping and jetting regimes.     

Nonlinear hydrodynamic phenomena in Stokes flow regime

We investigate nonlinear phenomena in dispersed two-phase systems under creeping-flow conditions. We consider nonlinear evolution of a single deformed drop and collective dynamics of arrays of hydrodynamically coupled particles. To explore physical mechanisms of system instabilities, chaotic drop evolution, and structural transitions in particle arrays we use simple models, such as small-deformation equations and effective-medium theory. We find numerical and analytical solutions of the simplified governing equations. The small-deformation equations for drop dynamics are analyzed using results of dynamical systems theory. Our investigations shed new light on the dynamics of complex fluids, where the nonlinearity often stems from the evolving boundary conditions in Stokes flow.     

Controlled cavitation in microfluidic systems

We report on cavitation in confined microscopic environments which are commonly called microfluidic or lab-on-a-chip systems. The cavitation bubble is created by focusing a pulsed laser into these structures filled with a light-absorbing liquid. At the center of a 20 microm thick and 1 mm wide channel, pancake-shaped bubbles expand and collapse radially. The bubble dynamics compares with a two-dimensional Rayleigh model and a planar flow field during the bubble collapse is measured. When the bubble is created close to a wall a liquid jet is focused towards the wall, resembling the jetting phenomenon in axisymmetry. The jet flow creates two counter-rotating vortices which stir the liquid at high velocities. For more complex geometries, e.g., triangle- and square-shaped structures, the number of liquid jets recorded correlates with the number of boundaries close to the bubble.     

Order-chaos-order transitions in electrosprays: the electrified dripping faucet

Electrosprays have diverse applications including protein analysis, electrospinning, and nanoencapsulation for drug delivery. We show that a variety of electrospray regimes exhibit fundamental analogy with the nonlinear dynamics of a dripping faucet. The applied voltage in electrosprays results in additional period doublings and temporal order-chaos-order transitions. Attractors in the return maps show logarithmic self-similarity in time, suggesting self-similar capillary waves on the meniscus. The bifurcations in ejection time can be explained by phase variations between capillary waves and pinch-off conditions and by ejection mode changes due to contact angle variations.     

A multiscale coupling method for the modeling of dynamics of solids with application to brittle cracks

We present a multiscale model for numerical simulations of dynamics of crystalline solids. The method combines the continuum nonlinear elasto-dynamics model, which models the stress waves and physical loading conditions, and molecular dynamics model, which provides the nonlinear constitutive relation and resolves the atomic structures near local defects. The coupling of the two models is achieved based on a general framework for multiscale modeling – the heterogeneous multiscale method (HMM). We derive an explicit coupling condition at the atomistic/continuum interface. Application to the dynamics of brittle cracks under various loading conditions is presented as test examples.     

Free surface flow between two horizontal concentric cylinders

Results are reported on a combined experimental and numerical investigation of a free surface flow at small Reynolds numbers. The flow is driven by the rotation of the inner of two horizontal concentric cylinders, with an inner to outer radius ratio of 0.43. The outer cylinder is stationary. The annular gap is partially filled, from 0.5 to 0.95 full, with a viscous liquid leaving a free surface. When the fraction of the annular volume filled by liquid is 0.5, a thin liquid film covers the rotating inner cylinder and reenters the liquid pool. For relatively low rotation speeds, the evolution of the film thickness is consistent with the theory for a plate being withdrawn from an infinite liquid pool. The overall liquid flow pattern at this condition consists of two counter-rotating cells: one is around the inner cylinder and the other with weaker circulation rate is in the bottom part of the annulus and nearly symmetric about the vertical axis. With increasing rotation rate, the free surface becomes more deformed, and the dynamics of the stagnation line and the cusp line dividing the cells are tracked as quantitative measures of the interface shape. In addition, the recirculating flow cells lose symmetry and the cusp deforms the free surface severely. A comparison of numerically computed flow which describes the interface by a phase-field method confirms the dynamics of the two cells and the interface deformation. For filling fraction 0.75, the liquid level is slightly above the inner cylinder and a significant decrease in size of the bottom cell with increasing rotation rate is found. For filling fractions approaching unity, the liquid flow consists of one single cell and the surface deformation remains small.     

The formation of liquid bridge in different operating modes of AFM

The liquid bridge is one of the principal factors that cause artifacts in ambient-pressure atomic force microscope (AFM) images. Additionally, it is the main component of the adhesion force in ambient conditions. To understand the AFM imaging mechanism and the sample characteristics, it is essential to study the liquid bridge. This study interprets the physical mechanism involved in liquid bridge formation, which is composed of three different physical processes: the squeezing process, capillary condensation, and liquid film flow. We discuss the contributions of these three mechanisms to the volume and the capillary force of the liquid bridge in different AFM operation modes.     

Nonlinear dynamics of a flow-focusing bubble generator: an inverted dripping faucet

We describe the rich dynamic behavior--including period-doubling and period-halving bifurcations, intermittency, and chaos--observed in the breakup of an inviscid fluid in a coflowing, viscous liquid, both confined in a microfabricated flow-focusing geometry. Experimental observations support inertia-dominated dynamics of the interface, and suggest the possible similarity to the dynamics of a topologically inverted counterpart of this system, that is, a dripping faucet.     

The effects of surface tension and temperature on the nonlinear dynamics of the dripping faucet

The effects of surface tension and temperature on the nonlinear dynamics of the dripping faucet were investigated, through the introduction of high-resolution timing, temperature and continuously variable flow rate controls, and the addition of surfactant of the water. The continuously variable flow rate allows the recording of the novel “dripping spectrum” (drop intervals {t_i} versus flow rate) over a wide range of flow rate in a single experiment. Lowering the surface tension dramatically changes the dynamics, sharpens the familiar dripping patterns previously found for water, and reveals the existence of novel single and multiple closed-loop patterns. Using dripping spectra, time-delay and time-series representations, the closed-loop patterns are shown to correspond to quasiperiodic states. Lowering the temperature reduces random noise and shifts the occurrence of characteristic patterns to higher flow rates.     

Non-quantum liquefaction of coherent gases

We show that a gas-to-liquid phase transition at zero temperature may occur in a coherent gas of bosons in the presence of competing nonlinear effects. This situation can take place in atomic systems like Bose-Einstein condensates in alkali gases with two-body and three-body interactions of opposite signs, as well as in laser beams which propagate through optical media with Kerr (focusing) and higher order (defocusing) nonlinear responses. The liquefaction process takes place in the absence of any quantum effect and can be formulated in the framework of a mean field theory, in terms of the minimization of a thermodynamic potential. We study from a thermodynamic point of view all the stationary solutions of the cubic-quintic nonlinear Schrödinger equation which describes our system. We show that solitonic localized solutions connect the gaseous and liquid phases. Furthermore, we also perform a numerical simulation in the presence of linear gain and three-body recombination where a rich dynamics, including the emergence of self-organization behavior, is found.     

Accumulation of particles in time-dependent thermocapillary flow in a liquid bridge. Modeling of experiments

The study addresses the phenomenon of accumulation of rigid tracer particles suspended in a time-dependent thermocapillary flow in a liquid bridge. We report the results of the three-dimensional numerical modeling of recent experiments [1,2] in a non-isothermal liquid column. Exact physical properties of both liquids and particles are used for the modeling. Two liquids are investigated: sodium nitrate (NaNO₃) and n-decane (C₁₀H₂₂). The particles are modeled as perfect spheres suspended in already well developed time-dependent thermocapillary flow. The particle dynamics is described by the Maxey-Riley equation. The results of our simulations are in excellent agreement with the experimental observations. For the first time we reproduced numerically formation of the particle accumulation structure (PAS) both under gravity and under weightlessness conditions. Our analysis confirms the experimental observations that the existence of PAS depends on the strength of the flow field, on the ratio between liquid and particle density, and on the particle size.     

Nonlinear dynamics of an interface between shear bands

We study numerically the nonlinear dynamics of a shear banding interface in two-dimensional planar shear flow, within the nonlocal Johnson-Segalman model. Consistent with a recent linear stability analysis, we find that an initially flat interface is unstable with respect to small undulations for a sufficiently small ratio of the interfacial width l to cell length L(x). The instability saturates in finite amplitude interfacial fluctuations. For decreasing l/L(x) these undergo a nonequilibrium transition from simple traveling interfacial waves with constant average wall stress, to periodically rippling waves with a periodic stress response. When multiple shear bands are present we find erratic interfacial dynamics and a stress response suggesting low dimensional chaos.