Many-body Dissipative Particle Dynamics Research Articles

Dynamics of Droplets Moving on Lubricated Polymer Brushes.

Understanding the dynamics of drops on polymer-coated surfaces is crucial for optimizing applications such as self-cleaning materials or microfluidic devices. While the static and dynamic properties of deposited drops have been well characterized, a microscopic understanding of the underlying dynamics is missing. In particular, it is unclear how drop dynamics depends on the amount of uncross-linked chains in the brush, because experimental techniques fail to quantify those. Here we use coarse-grained simulations to study droplets moving on a lubricated polymer brush substrate under the influence of an external body force. The simulation model is based on the many body dissipative particle dynamics (MDPD) method and designed to mimic a system of water droplets on poly(dimethylsiloxane) (PDMS) brushes with chemically identical PDMS lubricant. In agreement with experiments, we find a sublinear power law dependence between the external force F and the droplet velocity v, F ∝ vα with α < 1; however, the exponents differ (α ∼ 0.6-0.7 in simulations versus α ∼ 0.25 in experiments). With increasing velocity, the droplets elongate and the receding contact angle decreases, whereas the advancing contact angle remains roughly constant. Analyzing the flow profiles inside the droplet reveals that the droplets do not slide but roll, with vanishing slip at the substrate surface. Surprisingly, adding lubricant has very little effect on the effective friction force between the droplet and the substrate, even though it has a pronounced effect on the size and structure of the wetting ridge, especially above the cloaking transition.

Droplet bioprinting of acellular and cell-laden structures at high-resolutions

Advances in digital light projection(DLP) based (bio) printers have made printing of intricate structures at high resolution possible using a wide range of photosensitive bioinks. A typical setup of a DLP bioprinter includes a vat or reservoir filled with liquid bioink, which presents challenges in terms of cost associated with bioink synthesis, high waste, and gravity-induced cell settling, contaminations, or variation in bioink viscosity during the printing process. Here, we report a vat-free, low-volume, waste-free droplet bioprinting method capable of rapidly printing 3D soft structures at high resolution using model bioinks and model cells. A multiphase many-body dissipative particle dynamics model was developed to simulate the dynamic process of droplet-based DLP printing and elucidate the roles of surface wettability and bioink viscosity. Process variables such as light intensity, photo-initiator concentration, and bioink formulations were optimized to print 3D soft structures (∼0.4–3 kPa) with a typical layer thickness of 50 µm, an XY resolution of 38 ± 1.5 μm and Z resolution of 237 ± 5.4 µm. To demonstrate its versatility, droplet bioprinting was used to print a range of acellular 3D structures such as a lattice cube, a Mayan pyramid, a heart-shaped structure, and a microfluidic chip with endothelialized channels. Droplet bioprinting, performed using model C3H/10T1/2 cells, exhibited high viability (90%) and cell spreading. Additionally, microfluidic devices with internal channel networks lined with endothelial cells showed robust monolayer formation while osteoblast-laden constructs showed mineral deposition upon osteogenic induction. Overall, droplet bioprinting could be a low-cost, no-waste, easy-to-use, method to make customized bioprinted constructs for a range of biomedical applications.

Channel width-dependent viscosity and slip length in nanoslits and effect of surface wettability

The channel width-dependent behaviors of viscosity (μ) and slip length (ls) in nanoslits are investigated using many-body dissipative particle dynamics simulation in both Poiseuille and Couette flow systems. In both systems, the viscosity and slip length increase as the channel width (w) grows in smaller channels, while they reach bulk values in larger channels. Moreover, as the surface wettability decreases, the slip length is found to increase, while the viscosity remains the same. The channel width-dependent behavior in nanoslits can be explained by the unique structure of the confined fluid. As the channel width narrows, the uniform density profile in the central region diminishes, and an oscillation pattern appears throughout the system. The change in the microstructure with the channel width alters friction between layers of fluid in laminar flow and fluid-solid friction, leading to a w-dependent μ and ls. Nonetheless, the alteration of surface wettability influences only fluid–solid interactions but not the friction between layers of fluid.

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

The molten sand that is a mixture of calcia, magnesia, alumina and silicate, known as CMAS, is characterized by its high viscosity, density and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a parametric ordinary differential equation (ODE) that captures the spreading radius behaviour of the CMAS droplets. The ODE parameters are then identified based on the physics-informed neural network (PINN) framework. Subsequently, the closed-form dependency of parameter values found by the PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modelling and state-of-the-art machine-learning techniques.

Surfactant-laden liquid thread breakup driven by thermal fluctuations

The breakup of liquid threads into droplets is crucial in various applications, such as nanoprinting, nanomanufacturing, and inkjet printing, where a detailed understanding of the thinning neck dynamics allows for a precise droplet control. Here, the role of surfactant in the breakup process is studied by many-body dissipative particle dynamics, in particular, the various regime transitions and thread profiles, shedding light on molecular-level intricacies of this process hitherto inaccessible to continuum theory and experiments. Moreover, the role of surfactant in the most unstable perturbation, the formed droplet size, and surfactant distributions have been unraveled. As surfactant concentration rises, both the wavelength and time to breakup steadily increase due to the lowering of surface tension below the critical micelle concentration (CMC) and viscous effects introduced by micelles above the CMC. These changes prior to the breakup lead to larger droplets being formed in cases with higher surfactant concentration. We also compared the thinning dynamics to existing theoretical predictions, revealing that the surfactant-laden breakup starts at the inertial regime and transitions into the thermal fluctuation regime when the concentration is increased. Thus, we illuminate the hitherto poorly investigated and intricate breakup process of surfactant-laden liquid threads driven by thermal fluctuations, contributing to a deeper understanding of this process at molecular scales.

Many-body dissipative particle dynamics simulations of micellization of sodium alkyl sulfates.

We present a study of micelle formation in alkyl sulfate surfactants using the simulation method of many-body dissipative particle dynamics (MDPD). We parametrise our model by tuning the intermolecular interactions in order to reproduce experimental values for the chemical potential and density at room temperature. Using this approach, we find that our model shows good agreement with experimental values for the critical micelle concentration (CMC). Furthermore, we show that our model can accurately predict CMC trends, which result from varying properties such as surfactant tail length and the salt concentration. We apply our model to investigate the effect of aggregation number on various micellar properties, such as the shape of individual micelles and the fraction of bound counterions. We show that micelles become aspherical at large aggregation numbers, in line with experimental predictions, and that longer tail surfactants are generally more spherical at all aggregation numbers compared to those which are shorter. We find excellent agreement between our simulations and experimental values for the degree of counterion binding, a factor that is crucial to accurately studying micellar shape, but one that is typically overlooked in the existing literature.

Sliding motion of highly deformed droplets on smooth and rough surfaces: Shape oscillation, chaotic breakage, corner shape, and pearling

The sliding behavior of droplets on smooth and rough surfaces with various surface wettabilities is investigated by many-body dissipative particle dynamics simulations. On a smooth surface, as the driving force (Bo) increases, the droplet shape and velocity (Cac) before breakage can be classified into four distinct regimes: (I) nearly spherical cap with Cac∝Bo; (II) oval shape with negative deviation from the linear relation; (III) elongated shape without a neck, where Cac decreases with increasing Bo; and (IV) oscillation of an elongated shape with fluctuating sliding velocity. On rough surfaces, corner-shaped droplets, which are absent on a smooth surface, can be observed. A further increase in Bo leads to the formation of cusp and pearling. Different from pinching-off on rough surfaces, which produces a cascade of smaller droplets through groove-induced shedding, chaotic breakage of a droplet on a smooth surface is caused by an unsteady flow field. Finally, a universal linear relationship between the sliding velocity based on the surface velocity (Cas) and the modified driving force (Bo**) is derived to take into account the effects of surface wettability and roughness.

Criteria of Distribution Transitions in Dispersed Multiphase Systems Based on an Extended Lattice Model.

Dispersed multiphase systems are ubiquitous in biological systems, energy industries, and medical science. The distribution transition of the dispersed phase is critical to the properties and functions of the multiphase systems, among which the agglomeration, adsorption, and extraction processes are of most significance due to their impact on the colloidal stability, interface modification, and particle synthesis. To reveal fundamental correlations between the macroscopic particle distributions and the microscopic interactions, general thermodynamic models of the dispersed multiphase systems are needed. Here, based on Meyer's model, which is restricted to binary isotropic mixtures, we propose a novel extended lattice model that can be applied to multicomponent anisotropic mixtures with interfaces considered. For agglomeration, adsorption, and extraction processes, the approximate free energy differences between the initial distribution and the final distribution are obtained. Based on the minimum free energy principle, the above free energy differences are used to derive three criteria for the prediction of the preferable distribution of the system with given interparticle interaction potentials. While the quasi-uniform number density assumption is still required for all the previous lattice models, the long-range interactions neglected by previous lattice models are incorporated. The validity of our model and criteria is verified by many-body dissipative particle dynamics (mDPD) simulations. By tuning the interaction coefficients between mDPD particles, the simulated distribution transitions for all the agglomeration, adsorption, and extraction cases perfectly match the predictions from the three criteria. The good agreement between the theoretical predictions and the mDPD simulation results shows the great potential of our model for applications in various dispersed multiphase systems.

Drop collision analysis by using many-body dissipative particle dynamics and machine learning

Droplet collisions are widely observed in daily life and industries. The study of droplet collision dynamics can guide engineering applications in, for examples, inkjet printing, fan cooling, and engine spraying. In this Letter, a numerical simulation method of droplet collision is proposed on the basis of the many-body dissipative particle dynamics. For the collision of two droplets of the same size, the post-collision morphology is analyzed in terms of two key factors: the initial eccentricity parameter and the Weber number. Then, the collision morphology is learned and classified in conjunction with a multilayer perceptron in order to quickly predict the collision morphology from the initial conditions. A machine learning model linking the initial conditions of collision with the post-collision droplet morphology is developed based on three typical morphologies generated by the collision of identical volume droplets. This study provides more insights into droplet dynamics and may benefit related engineering applications.

Multi-scale modelling of dilute viscoelastic liquids: Atomistic to mesoscale mapping of polymer solutions

A framework predicting the rheological (storage and loss moduli, first normal stress coefficient, and relaxation time) and transport (viscosity, diffusivity) properties of non-Newtonian dilute polymer solutions at mesoscales (e.g. ∼ns to μs) from the atomistic-scale molecular behaviour is presented. More specifically, the rheological behaviour differences of OCP and PMA polymer solutions in PAO-2 oil are simulated using both atomistic molecular dynamics (MD) and many-body dissipative particle dynamics (mDPD) within a temperature range of 313–373 K. The simulation methodology described is able to distinguish itself from the standard DPD model by accurately reproducing the shear-thinning with high sensitivity, as seen in the atomistic MD simulations at high shear rates (e.g. 108−1013 s−1). It is shown that the model is well-suited to compute properties such as first normal stress differences and relaxation times that are difficult to estimate at atomistic scales due to the low signal-to-noise ratio. Moreover, the Schmidt numbers (>103) are predicted with high accuracy when compared with the values from atomistic-scale simulations. The proposed model is able to predict relaxation times of dilute polymer mixtures that are difficult to be obtained using state-of-the-art rheometers. Finally, it is found that the terminal relaxation time of PMA polymer chain does not vary monotonically as a function of temperature, unlike in the case of OCP; this is significant for describing viscoelastic behaviour at macroscales where satisfactory constitutive equations are not available.

Entanglements via Slip Springs with Soft, Coarse-Grained Models for Systems Having Explicit Liquid-Vapor Interfaces.

Recent advances in nano-rheology require that new techniques and models be developed to precisely describe the equilibrium and non-equilibrium characteristics of entangled polymeric materials and their interfaces at a molecular level. In this study, a slip-spring (SLSP) model is proposed to capture the dynamics of entangled polymers at interfaces, including those between liquids, liquids and vapors, and liquids and solids. The SLSP model employs a highly coarse-grained approach, which allows for comprehensive simulations of entire nano-rheological characterization systems using a particle-level description. The model relies on many-body dissipative particle dynamics (MDPD) non-bonded interactions, which permit explicit description of liquid-vapor interfaces; a compensating potential is introduced to ensure an unbiased representation of the shape of the liquid-vapor interface within the SLSP model. The usefulness of the proposed MDPD + SLSP approach is illustrated by simulating a capillary breakup rheometer (CaBR) experiment, in which a liquid droplet splits into two segments under the influence of capillary forces. We find that the predictions of the MDPD + SLSP model are consistent with experimental measurements and theoretical predictions. The proposed model is also verified by comparison to the results of explicit molecular dynamics simulations of an entangled polymer melt using a Kremer-Grest chain representation, both at equilibrium and far from equilibrium. Taken together, the model and methods presented in this study provide a reliable framework for molecular-level interpretation of high-polymer dynamics in the presence of interfaces.

Imbibition Dynamics in a U-Groove Microchannel with Sudden Enlargement.

Imbibition dynamics in a rectangular U-groove that is connected to a sudden enlargement and complicated by the presence of Concus-Finn (CF) filaments is investigated using many-body dissipative particle dynamics. For open-ended sudden enlargement, four flow types are identified and depend on the contact angle θy, the critical angle θf associated with the occurrence of CF filaments, and the critical angle θc associated with the occurrence of main flow. First, for θy > θf and θy > θc, the corner flow is absent, and the main flow stops at the end of the small U-groove. Second, for θc > θy > θf, the corner flow vanishes, but the main flow occurs. Third, for θf > θy > θc, the corner flow takes place in the large U-groove, but the main flow is still absent. Fourth, for θy < θf and θy < θc, both the corner and main flows appear in the large U-groove. Additionally, the flow dynamics is greatly influenced by the length of the large U-groove (le). For closed-ended sudden enlargement, similar findings can be obtained. However, the outcome of the third case is altered for sufficiently small le, and the sudden enlargement can eventually be filled.

Temperature-dependent surface tension model in many-body dissipative particle dynamics with energy conservation

As a hybrid method, many-body dissipative particle dynamics with energy conservation (MDPDe), promises to simulate heat transport process with free surface fluids. However, the temperature-dependent surface tension cannot be modelled accurately in MDPDe so far, which greatly limits its further applications. In the present study, semi-empirical relationships between the attractive coefficient and temperature obtained by mapping with real liquids (i.e., water, ethylene glycol and benzaldehyde) are introduced into MDPDe. The simulation results are validated by comparing with the relevant experimental, theoretical and numerical results, respectively. The improved MDPDe model in the present work opens the door to study various thermocapillary phenomena with free surface fluids at mesoscopic scale.

Whether contact time can evaluate the anti-icing properties of superhydrophobic surface - A research based on the MDPDE method

Impact freezing of droplets on a cold surface has attracted the attention of scholars. This process is vital for practical problems such as the anti-icing of aircraft wings and cables. Researchers have found that superhydrophobic surfaces can reduce the contact time of droplets and delay nucleation. However, whether contact time can evaluate the anti-icing properties of superhydrophobic surface needs further study. Considering the change in droplet temperature, we vary the dissipative force term of the conservative force in the many-body dissipative particle dynamics with the energy conservation (MDPDE) method. Then combined with the experimental results, a nucleation model of the recalescence rate related to the degree of undercooling is achieved. Finally, we obtain a droplet impact freezing model based on the MDPDE method for the first time, and the impact processes of supercooled droplets on the superhydrophobic surface with three different topological microstructures are explored. Effect of Weber number We on the critical adhesion temperature T* of micropillar surface is reversed when the solid fraction φ is different, and φ is the main factor affecting T*of the microcavity surface. When other conditions are the same, T* of the microridge surface is the lowest. And surprisingly, we observed that the contact time of droplets did not fully measure the anti-icing ability of the superhydrophobic surface.

Liquid thread breakup and the formation of satellite droplets

The breakup of liquid threads into smaller droplets is a fundamental problem in fluid dynamics. In this study, we estimate the characteristic wavelength of the breakup process by means of many-body dissipative particle dynamics. This wavelength shows a power-law dependence on the Ohnesorge number in line with results from stability analysis. We also discover that the number of satellite droplets exhibits a power-law decay with exponent 0.72 ± 0.04 in the product of the Ohnesorge and thermal capillary numbers, while the overall size of main droplets is larger than that based on the characteristic wavelength thanks to the asynchronous breakup of the thread. Finally, we show that the formation of satellite droplets is the result of the advection of pinching points toward the main droplets in a remaining thinning neck, when the velocity gradient of the fluid exhibits two symmetric maxima.

Accurate and scale-free pressure prediction for many-body dissipative particle dynamics

We have developed a generalized mean-field equation of state suitable for many-body dissipative particle dynamics method in a homogeneous system, which is accurate and valid at arbitrary level of coarse-graining in pressure prediction. Specifically, the truncation influences caused by finite cutoff radius have been mitigated to satisfy with the assumption of mean-field theory, and the so-called local density has been replaced with global one in the frame of homogeneous system. Our present work represents an advancement toward establishing a robust and reliable one-to-one parameter mapping protocol based on mean-field theory.

Wetting dynamics of a droplet impact on target-like chemically heterogeneous substrates: The determinations of contact angle

Wetting is a common natural phenomenon with many useful applications. However, some fundamental aspects of wetting theory, such as determining the contact angle, remain unresolved. Two mainstream options are debated: whether the contact angle depends on the contact area or the contact line. To understand this, the present work used many-body dissipative particle dynamics to simulate wetting on chemically heterogeneous substrates. The simulations show that there is a ratio that separates contact angles into two regimes: a stable regime where the contact angles follow the contact-area-based Cassie-Baxter equation, and a fluctuating regime where contact angles are mainly determined by the contact line. The ring/droplet ratio, initial impact velocity, and wettability pair all play a role in the formation of the contact angle. This brief communication provides clear and sound observations to shed light on the determinations of the contact angle.

Insights into Waterflooding in Hydrocarbon-Bearing Nanochannels of Varying Cross Sections from Mesoscopic Multiphase Flow Simulations

Waterflooding is one of the geotechniques used to recover fuel sources from nanoporous geological formations. The scientific understanding of the process that involves the multiphase flow of nanoconfined fluids, however, has lagged, mainly due to the complex nanopore geometries and chemical compositions. To enable the benchmarked flow of nanoconfined fluids, architected geomaterials, such as synthesized mesoporous silica with tunable pore shapes and surface chemical properties, are used for designing and conducting experiments and simulations. This work uses a modified many-body dissipative particle dynamics (mDPD) model with accurately calibrated parameters to perform parametric flow simulations for studying the influences of waterflooding-driven power, pore shape, surface roughness, and surface wettability on the multiphase flow in heptane-saturated silica nanochannels. Remarkably, up to an 80% reduction in the effective permeability is found for water-driven heptane flow in a baseline 4.5-nm-wide slit channel when compared with the Hagen-Poiseuille equation. In the 4.5-nm-wide channels with architected surface roughness, the flow rate is found to be either higher or lower than the baseline case, depending on the shape and size of cross sections. High wettability of the solid surface by water is essential for achieving a high recovery of heptane, regardless of surface roughness. When the solid surface is less wetting or nonwetting to water, the existence of an optimal waterflooding-driven power is found to allow for the highest possible recovery. A detailed analysis of the evolution of the transient water-heptane interface in those nanochannels is presented to elucidate the underlying mechanisms that impact or dictate the multiphase flow behaviors.

A many-body dissipative particle dynamics study of droplets impacting on fiber

Collisions between droplets and fibers are a common phenomenon in nature and daily life, such as raindrops on the surface of spider webs and the surface of transmission cables. We present a numerical model to study the droplets impacting on fibers with the many-body dissipative particle dynamics (MDPD) method. The droplets impact on neutral fiber at different velocities and diameters is simulated. The diffusion trend of droplets is affected by the velocities and diameters. According to the morphologies of droplets, the results of impacting could be divided into three types, stick to the fiber, merge and split into parts. The spreading factors and internal velocity distributions are obtained and analyzed. And the determination of regimes at these states is found. In addition, the droplets impact on hydrophobic fiber is also investigated.

Diverse wetting behavior of a binary mixture of antagonist liquids: Nanodroplet with finite precursor film and leak-out phenomenon

The binary mixtures containing the partial and total wetting liquids corresponding to a specified substrate are commonly seen. However, studies of their wetting behavior, particularly the leak-out phenomenon, are very scarce. The wetting state of a nanodroplet of the binary mixture on a smooth substrate is investigated by Many-body dissipative particle dynamics. The influences of the molecular size of the partial wetting liquid and the affinity between the two liquids on the leak-out phenomenon are examined. Dependent on the mixture composition (ϕp), three wetting regimes of the nanodroplet can be identified: (I) total wetting, (II) partial wetting with precursor film, and (III) partial wetting. The binary droplet always spreads spontaneously in regime (I), while its contact angle (CA) changes with the composition monotonously in regime (III). However, in regime (II), the CA remains constant regardless of the composition. The droplet morphology exhibits the fried-egg shape, a spherical cap surrounded by a precursor film. The compositions in both egg yolk and egg white regions remain unaltered for varying ϕp in the plateau regime (II). Although the affinity between the two liquids is strong, some of the total wetting liquid always escape from the spherical cap to precursor film in regime (II), the so-called leak-out phenomenon. The outcome can be beneficial to the application of nanotechnologies such as lithography and microfluidics.