Simulations of liquid nanocylinder breakup with dissipative particle dynamics

Local density dependent potentials for an underlying van der Waals equation of state: A simulation and density functional theory analysis

There is an ever increasing use of local density dependent potentials in the mesoscale modeling of complex fluids. Questions remain, though, about the dependence of the thermodynamic and structural properties of such systems on the cutoff distance used to calculate these local densities. These questions are particularly acute when it comes to the stability and structure of the vapor/liquid interface. In this article, we consider local density dependent potentials derived from an underlying van der Waals equation of state. We use simulation and density functional theory to examine how the bulk thermodynamic and interfacial properties vary with the cutoff distance, rc, used to calculate the local densities. We show quantitatively how the simulation results for bulk thermodynamic properties and vapor-liquid equilibrium approach the van der Waals limit as rc increases and demonstrate a scaling law for the radial distribution function in the large rc limit. We show that the vapor-liquid interface is stable with a well-defined surface tension and that the interfacial density profile is oscillatory, except for temperatures close to critical. Finally, we show that in the large rc limit, the interfacial tension is proportional to rc and, therefore, unlike the bulk thermodynamic properties, does not approach a constant value as rc increases. We believe that these results give new insights into the properties of local density dependent potentials, in particular their unusual interfacial behavior, which is relevant for modeling complex fluids in soft matter.

Rupture process of liquid bridges: The effects of thermal fluctuations

Rupture of a liquid bridge is a complex dynamic process, which has attracted much attention over several decades. We numerically investigated the effects of the thermal fluctuations on the rupture process of liquid bridges by using a particle-based method know as many-body dissipative particle dynamics. After providing a comparison of growth rate with the classical linear stability theory, the complete process of thinning liquid bridges is captured. The transitions among the inertial regime (I), the viscous regime (V), and the viscous-inertial regime (VI) with different liquid properties are found in agreement with previous work. A detailed description of the thermal fluctuation regime (TF) and another regime, named the breakup regime, are proposed in the present study. The full trajectories of thinning liquid bridges are summarized as I→V→VI→TF→ breakup for low-Oh liquids and V→I→ Intermediate →V→VI→TF→ breakup for high-Oh liquids, respectively. Moreover, the effects of the thermal fluctuations on the formation of satellite drops are also investigated. The distance between the peaks of axial velocity is believed to play an important role in forming satellite drops. The strong thermal fluctuations smooth the distribution of axial velocity and change the liquid bridge shape into a double cone without generating satellite drops for low-Oh liquids, while for high-Oh liquids, this distance is extended and a large satellite drop is formed after the breakup of the liquid filament occurs on both ends, which might be due to strong thermal fluctuations. This work can provide insights on the rupture mechanism of liquid bridges and be helpful for designing superfine nanoprinting.

Hydrodynamic behavior of the pseudopotential lattice Boltzmann method for interfacial flows

The lattice Boltzmann method (LBM) is routinely employed in the simulation of complex multiphase flows comprising bulk phases separated by nonideal interfaces. The LBM is intrinsically mesoscale with a hydrodynamic equivalence popularly set by the Chapman-Enskog analysis, requiring that fields slowly vary in space and time. The latter assumptions become questionable close to interfaces where the method is also known to be affected by spurious nonhydrodynamical contributions. This calls for quantitative hydrodynamical checks. In this paper, we analyze the hydrodynamic behavior of the LBM pseudopotential models for the problem of the breakup of a liquid ligament triggered by the Plateau-Rayleigh instability. Simulations are performed at fixed interface thickness, while increasing the ligament radius, i.e., in the "sharp interface" limit. The influence of different LBM collision operators is also assessed. We find that different distributions of spurious currents along the interface may change the outcome of the pseudopotential model simulations quite sensibly, which suggests that a proper fine-tuning of pseudopotential models in time-dependent problems is needed before the utilization in concrete applications. Taken all together, we argue that the results of the proposed paper provide a valuable insight for engineering pseudopotential model applications involving the hydrodynamics of liquid jets.

Effect of axial electric field on the Rayleigh instability at small length scales

The effect of an electric field along the longitudinal axis of a nanoscale liquid thread is studied to understand the mechanism of breakup. The Rayleigh instability (commonly known as the Plateau-Rayleigh instability) of a nanosized liquid water thread is investigated by using molecular dynamics simulations. The breakup mechanism of the liquid nanothread is studied by analyzing the temporal evolution of the thread radius. The influence of the temperature of the liquid nanothread and the electric-field strength on the stability and breakup is the major focus of the study. The results show that the axial electric field has a stabilizing effect even at nanoscale. The results from the simulations are in good agreement with the solutions obtained from the dispersion relation developed by Hohman et al. for the liquid thread. The critical electric-field strength necessary to avoid the breakup of the liquid thread is calculated and other effects such as the splaying and whipping instability are also discussed.

Hydrodynamic Interactions and Entanglements of Polymer Solutions in Many-Body Dissipative Particle Dynamics

Using many-body dissipative particle dynamics (MDPD), polymer solutions with concentrations spanning dilute and semidilute regimes are modeled. The parameterization of MDPD interactions for systems with liquid⁻vapor coexistence is established by mapping to the mean-field Flory⁻Huggins theory. The characterization of static and dynamic properties of polymer chains is focused on the effects of hydrodynamic interactions and entanglements. The coil⁻globule transition of polymer chains in dilute solutions is probed by varying solvent quality and measuring the radius of gyration and end-to-end distance. Both static and dynamic scaling relations for polymer chains in poor, theta, and good solvents are in good agreement with the Zimm theory with hydrodynamic interactions considered. Semidilute solutions with polymer volume fractions up to 0.7 exhibit the screening of excluded volume interactions and subsequent shrinking of polymer coils. Furthermore, entanglements become dominant in the semidilute solutions, which inhibit diffusion and relaxation of chains. Quantitative analysis of topology violation confirms that entanglements are correctly captured in the MDPD simulations.

Application of the dissipative particle dynamics method to the instability problem of a liquid thread

We investigate the application of the dissipative particle dynamics method to the instability problem of a long liquid thread surrounded by another fluid. The dispersion curves obtained from simulations are compared with classic theoretical predictions. The results from standard dissipative particle dynamics (DPD) simulations at first have a tendency of gradually approaching to Tomotika's Stokes flow prediction when the Reynolds number is decreased. But they then abnormally deviate again when the viscosity is very large. The same phenomenon is also confirmed in droplet retraction simulations when also compared with theoretical Stokes flow results. On the other hand, when a hard-core DPD model is used, with the decrease of the Reynolds number the simulation results did finally approach Tomotika's predictions when Re≈0.1. A combined presentation of the hard-core DPD results and the standard DPD results, excluding the abnormal ones, demonstrates that they are approximately on a continuum when labeled with Reynolds number. These results suggest that the standard DPD method is a suitable method for investigation of the instability problem of immersed liquid thread in the inertioviscous regime (0.1<Re<10), which is relevant for microfluidics applications but there is currently no theory. It cannot reach the Re≈0.1 regime because of some irregular properties of highly viscous DPD fluid, while the hard-core DPD is suitable to overcome this inferiority with standard DPD.

Mesoscopic simulation of a thinning liquid bridge using the dissipative particle dynamics method

In this research, the dissipative particle dynamics method was used to investigate the problem of thinning and breakup in a liquid bridge. It was found that both the inertial-force-dominated thinning process and the thermal-fluctuation-dominated thinning process can be reproduced with the dissipative particle dynamics (DPD) method by varying the simulation parameters. A highly suspect viscous thinning regime was also found, but the conclusion is not irrefutable because of the complication of the shear viscosity of DPD fluid. We show in this article that the DPD method can serve as a good candidate to elucidate crossover problem in liquid bridge thinning from being hydrodynamics dominated to being thermal fluctuation dominated.

Rayleigh instability at small length scales

The Rayleigh instability (also called the Plateau-Rayleigh instability) of a nanosized liquid propane thread is investigated using molecular dynamics (MD). The validity of classical predictions at small length scales is verified by comparing the temporal evolution of liquid thread simulated by MD against classical predictions. Previous works have shown that thermal fluctuations become dominant at small length scales. The role and influence of the stochastic nature of thermal fluctuations in determining the instability at small length scale is also investigated. Thermal fluctuations are seen to dominate and accelerate the breakup process only during the last stages of breakup. The simulations also reveal that the breakup profile of nanoscale threads undergo modification due to reorganization of molecules by the evaporation-condensation process.

Bottom-up construction of interaction models of non-Markovian dissipative particle dynamics

We derive the equation of motion for non-Markovian dissipative particle dynamics (NMDPD) by introducing the history effects on the time evolution of the system. Our formulation is based on the generalized Langevin equation, which describes the motions of the centers of mass of clusters comprising microscopic particles. The mean, friction, and fluctuating forces in the NMDPD model are directly constructed from an underlying molecular dynamics (MD) system without any scaling procedure. For the validation of our formulation, we construct NMDPD models from high-density Lennard-Jones systems, in which the typical time scales of the coarse-grained particle motions and the fluctuating forces are not fully separable. The NMDPD models reproduce the temperatures, diffusion coefficients, and viscosities of the corresponding MD systems more accurately than the dissipative particle dynamics models based on a Markovian approximation. Our results suggest that the NMDPD method is a promising alternative for simulating mesoscale flows where a Markovian approximation is not valid.

Droplet formation and scaling in dense suspensions

When a dense suspension is squeezed from a nozzle, droplet detachment can occur similar to that of pure liquids. While in pure liquids the process of droplet detachment is well characterized through self-similar profiles and known scaling laws, we show here the simple presence of particles causes suspensions to break up in a new fashion. Using high-speed imaging, we find that detachment of a suspension drop is described by a power law; specifically we find the neck minimum radius, r(m), scales like near breakup at time τ = 0. We demonstrate data collapse in a variety of particle/liquid combinations, packing fractions, solvent viscosities, and initial conditions. We argue that this scaling is a consequence of particles deforming the neck surface, thereby creating a pressure that is balanced by inertia, and show how it emerges from topological constraints that relate particle configurations with macroscopic Gaussian curvature. This new type of scaling, uniquely enforced by geometry and regulated by the particles, displays memory of its initial conditions, fails to be self-similar, and has implications for the pressure given at generic suspension interfaces.

Multiscale modeling of emergent materials: biological and soft matter

In this review, we focus on four current related issues in multiscale modeling of soft and biological matter. First, we discuss how to use structural information from detailed models (or experiments) to construct coarse-grained ones in a hierarchical and systematic way. This is discussed in the context of the so-called Henderson theorem and the inverse Monte Carlo method of Lyubartsev and Laaksonen. In the second part, we take a different look at coarse graining by analyzing conformations of molecules. This is done by the application of self-organizing maps, i.e., a neural network type approach. Such an approach can be used to guide the selection of the relevant degrees of freedom. Then, we discuss technical issues related to the popular dissipative particle dynamics (DPD) method. Importantly, the potentials derived using the inverse Monte Carlo method can be used together with the DPD thermostat. In the final part we focus on solvent-free modeling which offers a different route to coarse graining by integrating out the degrees of freedom associated with solvent.