Brownian Motion Of Particles Research Articles

Molecular modelling of active oil droplet propulsion: Insights from dissipative particle dynamics simulation

This study employed dissipative particle dynamics (DPD) simulations to investigate the self-propelled motion of oil droplets in water–oil–surfactant systems. It is the first attempt to replicate self-propulsion models of oil droplets at the molecular level, contrasting previous simulations focused on Brownian motion and hydrodynamic behavior of colloidal particles. The DPD model reproduced droplet propulsion and visualized internal Marangoni flow, showing that larger droplet radii and greater interfacial tension differences increase propulsion speeds. Additionally, surfactants with stronger oil–oil repulsion enhanced propulsion speed, suggesting that surfactant-induced local structures are crucial for the self-propulsion mechanism.

The Variability of the Size Distributions of Submicron Particles in the Oceans

AbstractThe size distribution of submicron particles is essential for understanding their biogeochemical and optical roles, but it has seldom been measured. This study utilizes ViewSizer 3000, an instrument that tracks Brownian motions of particles, to measure the particle size distributions (PSD) from 250 to 1,050 nm in the North Pacific Ocean (NP) and the North Atlantic Ocean (NA) at depths from 5 to 500 m. The concentration of particles varies over one order of magnitude at any given size bin, with greater variations up to two orders of magnitude at sizes >600 nm. In both locations, concentrations decrease with depth. Bacterioplankton are a dominant component, accounting for 65%–90% of the submicron particles in the surface waters (<100 m) and approximately 30%–40% at depths >150 m at both sites. In the NP, the volume mean diameter increased approximately 5% from the morning to noon at the surface, probably resulting from the diurnal growth of bacterioplankton. In the NA, the concentration and mean size increased by >60% and ∼10% respectively after one storm that introduced a different particle population into the study area.

Quantum mechanics emerging from complex Brownian motions

The connection between the Schrödinger equation and Einstein's diffusion theory based on the Brownian motion of independent particles is well known. However, in contrast to diffusion theory, quantum mechanics theory has suffered controversial interpretations due to the counterintuitive concept of wavefunction. Here, while we confirm there is no difference in the mathematical form of these two equations, we derive the imaginary version of displacement. Using the diffusion theory of particles in a medium, as simple as it is, we describe that quantum mechanics is just an elegant and subtle equation to describe the probability of all the trajectories that a particle can take to propagate in time by a predictive wavefunction. Therefore, information on the position of particles through time in quantum theory is embedded in the wavefunction, which predicts the evolution of an ensemble of individual Brownian particles.

Programmable Crowding and Tunable Phases in a Binary Mixture of Colloidal Particles under Light-Driven Thermal Convection.

We employ photothermally driven self-assembly of colloidal particles to design microscopic structures with programmable size and tunable order. The experimental system is based on a binary mixture of "plasmonic heater" gold nanoparticles and "assembly building block" microparticles. Photothermal heating of the gold nanoparticles under visible light causes a natural convection flow that efficiently assembles the microscale building block particles (diameter 1-10 μm) into a monolayer. We identify the onset of active Brownian motion of colloidal particles under this convective flow by varying the conditions of light intensity, gold nanoparticle concentration, and sample height. We realize a crowded assembly of microparticles around the center of illumination and show that the size of the particle crowd can be programmed using patterned light illumination. In a binary mixture of gold nanoparticles and polystyrene microparticles, we demonstrate the formation of rapid and large-scale crystalline monolayers, covering an area of 0.88 mm2 within 10 min. We find that the structural order of the assembly can be tuned by varying the surface charge of the nanoparticles and the size of the microparticles, giving rise to the formation of different phases-colloidal crystals, crowds, and gels. Using Monte Carlo simulations, we explain how the phases emerge from the interplay between hydrodynamic and electrostatic interactions, as well as the assembly kinetics. Our study demonstrates the promise of self-assembly with programmable shapes and structural order under nonequilibrium conditions using an accessible setup comprising only binary mixtures and LED light.

Measuring the Adsorption Cross Section of YOYO-1 to Immobilized DNA Molecules.

Many interactions between small molecules and particles occur in solutions. They are surrounded by other molecules that do not react, for example, biological processes in water, chemical reactions in gas or liquid solutions, and environmental reactions in air and water. However, predicting the rate of such diffusive interactions remains challenging, due to the random motion of molecules in solutions, as exampled by the famous Brownian motion of pollen particles. In this report, we experimentally confirmed that a disruptive rate equation we have published before can predict the association rate of typical adsorption at interfaces, which has a surprising fraction order of 4/3 that has not been considered before. This could be an important step toward a generalized method to predict the adsorption rate of many reactions.

Discovering dynamic laws from observations: The case of self-propelled, interacting colloids.

Active matter spans a wide range of time and length scales, from groups of cells and synthetic self-propelled colloids to schools of fish and flocks of birds. The theoretical framework describing these systems has shown tremendous success in finding universal phenomenology. However, further progress is often burdened by the difficulty of determining forces controlling the dynamics of individual elements within each system. Accessing this local information is pivotal for the understanding of the physics governing an ensemble of active particles and for the creation of numerical models capable of explaining the observed collective phenomena. In this work, we present ActiveNet, a machine-learning tool consisting of a graph neural network that uses the collective motion of particles to learn active and two-body forces controlling their individual dynamics. We verify our approach using numerical simulations of active Brownian particles, active particles undergoing underdamped Langevin dynamics, and chiral active Brownian particles considering different interaction potentials and values of activity. Interestingly, ActiveNet can equally learn conservative or nonconservative forces as well as torques. Moreover, ActiveNet has proven to be a useful tool to learn the stochastic contribution to the forces, enabling the estimation of the diffusion coefficients. Therefore, all coefficients of the equationof motion of Active Brownian Particles are captured. Finally, we apply ActiveNet to experiments of electrophoretic Janus particles, extracting the active and two-body forces controlling colloids' dynamics. On the one side, we have learned that the active force depends on the electric field and area fraction. On the other side, we have also discovered a dependence of the two-body interaction with the electric field that leads us to propose that the dominant force between active colloids is a screened electrostatic interaction with a constant length scale. We believe that the proposed methodological tool, ActiveNet, might open a new avenue for the study and modeling of experimental suspensions of active particles.

Boundary Layer Modelling of Flow Acceleration and Energy Transfer Effects in Smart Pavement Design

The integration of remote technology into the construction industry has advanced the emergence of smart, self-learning infrastructure across all levels of land transportation design and development. However, energy harvesting capabilities for smart road ventilation purposes have not yet been fully researched as the world gravitates towards energy sustainability. This study thus presents a mathematical investigation of the self-draining design potentials of road pavements, leveraging on energy absorption and conversion to accelerate conductive and convective ventilation of these pavements during wet conditions, as a means of ensuring the skid resistance and safety of such pavements are not compromised. Applying numerical methods with the aid of commercial software code MATLAB®, the classical physics of fluid-surface interaction was used to model accelerated drainage of microflood off paved surfaces through methodical modification of the thickness of the boundary layer associated with the flow regime over the flat road surface. Results indicate significant influences of energy exchange, thermal, and viscous diffusivity on flow acceleration. Alterations in parameters such as the slip factor, thermally induced Brownian motion or phoretic characteristics of the fluid particles at the boundary induce accelerated flow at the surface of the pavement. The findings contribute to the advancement of smart infrastructure by offering practical insights into the potential benefits of integrating energy-harvesting technologies into road pavement systems. By optimizing flow acceleration mechanisms, smart pavements can play a crucial role in improving road safety and sustainability in urban environments.

Entropy generation on inclined magnetize double diffusive convective transportation of radiative Casson nanofluid in porous medium with source/sink

This research intends to investigate the entropy generation on the magnetized double diffusive heat and mass transfer flow of the Casson nanofluid under the influence of an inclined magnetic field in a porous medium. Additionally, the combined impact of heat absorption, chemical reaction, Brownian diffusion, source/sink, and thermophoresis phenomena is also taken care of. The fluid flow involves convective boundary conditions for both temperature and concentration instead of a constant value at the surface. The flow-regulating system involved nonlinear PDEs that are turned into nonlinear systems of ODEs by using scaling variables and then solved this system numerically in Matlab using the bvp4c strategy, which is a collocation technique based on the Lobatto 3-stage FDM algorithm. Graphical representations illustrate the behavior of fluid velocity, entropy generation, concentration, and temperature in response to changes in flow parameters. Physical quantities like skin friction coefficient, Nusselt number, and Sherwood number have been investigated using 2D and 3D plots. Here, we concluded that the inclined magnetic field decimates the flow velocity gradually and greater values of the magnetic field lead to an increased rate of entropy generation. Furthermore, it has been noted that the temperature profile improves as the Brownian motion of particles increases, and the distribution of energy also enhances with larger values of the thermophoresis. The obtained key findings are discussed in a physical manner using graphic representation.

Intelligent neural computing to investigate the heat and mass transmission in nanofluidic system between two rotating permeable disks: Supervised learning mechanism

The prime objective of the present study is to investigate the effectiveness and accuracy of a single-trained artificial neural network. The Levenberg-Marquardt Backpropagated networks are tested for heat and mass transmission in magnetized hybrid nanofluid flow between the rotating permeable system. The reference data to generate different cases for distinct scenarios has been obtained using the Adams method in Mathematica using the ND-Solver function. Additionally, the system of highly nonlinear PDE's is achieved and transformed into ODE's. The effect of body forces such as thermophoresis particle diffusion and Brownian motion are incorporated in the hybrid nanofluid system. Configuration under observation is permeable and under constant impact of the magnetic field. Rosseland thermal radiation approximation relation is utilized to investigate the linear impact of radiation on velocity and temperature profile. The accuracy and effectiveness of the proposed ANNLMB are depicted with performance demonstrations. Mean square error, histogram error, and regression plots are generated for all the scenarios to discuss the varying impact of different key study parameters on the performance of the proposed ANNLMB. Furthermore, the generated reference data is distributed in the following manner 82 %, 9 %, and 9 % for training, testing, and validation, respectively.

Enzymatic Reaction Enhanced Diffusion Accelerates Cargo Transport through Micro/Nano-Channels.

Energy conversion and transfer of enzyme-catalyzed reactions at molecular level are an interesting and challenging scientific topic that helps understanding biological processes in nature. In this study, it is demonstrated that enzyme-catalyzed reactions can enhance diffusion of surrounding molecules and thus accelerate cargo transport within 1D micro/nanochannels. Specifically, urease is immobilized on the inner walls of silica micro/nano-tubes to construct bio-catalytically active micro/nanochannels. The catalytic reaction inside the channels drives a variety of cargoes, including small dye molecules, polymers, and rigid nanoparticles (e.g., quantum dots, QDs), to pass through these micro/nanochannels much faster than they will by free diffusion. The enhanced diffusion of molecular species inside the channels is validated by direct observation of the Brownian motion of tracer particles, and further confirmed by significantly enhanced Raman intensity of reporter molecules. Finite element and Brownian dynamics simulations provide a theoretical understanding of these experimental observations. Furthermore, the effect of the channels' size on the diffusion enhancement is examined. The acceleration effect of the cargo transport through these enzymatically active micro/nanochannels can be turned on or off via chemical activators or inhibitors. This study provides valuable insights on the design of biomimetic channels capable of controlled and efficient transmembrane transport.

Theoretical derivation of Planck’s constant based on brownian motion model and uncertainty relation

In stochastic mechanics, one of the interpretations of realistic quantum mechanics, the Schrödinger equation can be derived by assuming the Brownian motion (BM) of minute particles. In this study, we theoretically derive Planck’s constant (h), a fundamental constant of quantum physics, by assuming same BM. Einstein investigated the BM of a resonator caused by photons in a black body; meanwhile, in this study, BM is considered to be caused by the particle and wave natures of light. As a result, as the functional form of h,hN=4πe2cε01β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${h}_{N}=\\frac{4\\pi {e}^{2}}{c{\\varepsilon }_{0}}\\frac{1}{\\beta }$$\\end{document} (e: elementary charge, ε0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varepsilon }_{0}$$\\end{document}: permittivity, c: speed of light) was derived, where the undetermined coefficient β2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{\\beta }{2}$$\\end{document} represents the probability that the interaction between electrons and electromagnetic waves becomes particle-like absorption in one cycle of oscillation. The theoretical value of h was calculated to be 4πe2cε0π3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\frac{4\\pi {e}^{2}}{c{\\varepsilon }_{0}}\\pi \\sqrt{3}$$\\end{document} by obtaining β from the transition conditions of the BM model and uncertainty relation. This theoretical value is within 0.3% of the most recent value of h. Besides, Nelson’s assumed diffusion coefficient in the stochastic mechanics, which is essential in obtaining Schrödinger’s equation, was proved to be obtained from the BM model and the uncertainty relation. This finding and the conclusion that the Planck’s constant can be mathematically derived, provide support for Nelson’s stochastic mechanics.

Permanent fluidic magnets for liquid bioelectronics.

Brownian motion allows microscopically dispersed nanoparticles to be stable in ferrofluids, as well as causes magnetization relaxation and prohibits permanent magnetism. Here we decoupled the particle Brownian motion from colloidal stability to achieve a permanent fluidic magnet with high magnetization, flowability and reconfigurability. The key to create such permanent fluidic magnets is to maintain a stable magnetic colloidal fluid by using non-Brownian magnetic particles to self-assemble a three-dimensional oriented and ramified magnetic network structure in the carrier fluid. This structure has high coercivity and permanent magnetization, with long-term magnetization stability. We establish a scaling theory model to decipher the permanent fluid magnet formation criteria and formulate a general assembly guideline. Further, we develop injectable and retrievable permanent-fluidic-magnet-based liquid bioelectronics for highly sensitive, self-powered wireless cardiovascular monitoring. Overall, our findings highlight the potential of permanent fluidic magnets as an ultrasoft material for liquid devices and systems, from bioelectronics to robotics.

Simulating Brownian motion in thermally fluctuating viscoelastic fluids by using the smoothed profile method

To investigate the Brownian motion of individual particles suspended in viscoelastic fluids, the stochastic smoothed profile method (SPm) for direct numerical simulation is developed by extending deterministic SPm for suspensions in viscoelastic media. To simulate viscoelastic flow driven by thermal fluctuations in the suspending medium, the random stress in the fluid momentum equation as well as the random driving force for the conformation tensor in the Oldroyd-B model are incorporated according to the fluctuating hydrodynamics and fluctuating viscoelasticity formalisms. The thermal equilibrium and dynamical properties calculated by using numerical simulations successfully reproduce the analytic predictions, validating the direct simulation for the coupled fluctuating Navier–Stokes and Oldroyd-B equations and for the coupling between the stochastic viscoelastic medium and individual particles. As an application of the stochastic SPm, we investigate finite system-size effects under periodic boundary conditions (PBCs) on the passive microrheological relationship between the mean-square displacement (MSD) of a Brownian particle and the medium's dynamic modulus. Comparing the modulus that was microrheologically calculated from the MSD with the input modulus reveals that the effect of periodic image cell interaction appears not only in the long-time diffusive regime but also in the short-time region. A frequency-dependent finite system-size correction is implemented by phenomenologically extending the long-time diffusive regime correction, allowing passive microrheology analysis under PBCs. This result can be directly applied to other mesoscale numerical simulations including coarse-grained molecular dynamics and dissipative particle dynamics simulations.

The motion of Brownian particles suspended in a non-uniform fluid flow

The effect of the type of fluid flow velocity profile on the motion of a Brownian particle in a circular tube has been studied using a Monte Carlo technique to simulate particle trajectories. Three types of fluid flow were studied: uniform (UF), parabolic (PF), and an initial uniform flow which evolves and may eventually attain the parabolic velocity profile, i.e. transient flow (TF). For UF and PF, radial and axial particle diffusion were simultaneously considered in some cases; for TF, where fluid dynamics equations had to be solved in addition to the Monte Carlo simulations, axial diffusion was neglected for fluid and particles, so that calculations had to be restricted to tube aspect ratios (radius/length) smaller than 0.1, a common scenario in most practical aerosol applications. A first series of simulations were performed to determine the overall particle penetration through the tube. For fixed tube geometry and particle diffusion coefficient, penetration in TF lied between those in PF (highest) and UF (lowest), in such a manner that, for a given value of the diffusion coefficient, the larger the degree of flow development (i.e., the smaller the values of the tube aspect ratio and the Reynolds number), the larger the penetration. These findings are coherent with those found in a former investigation dealing with the particle residence time in the tube. In a second series of simulation runs, calculations were done for selected initial locations of the particle within the tube entrance cross section, to examine the effect that the proximity of the particle starting position to the tube wall or to the tube axis has on variables such as penetration, mean first hitting time and length, mean first exit time, and mean axial velocity of lost and survived particles. When the fluid flow is not uniform but varies from place to place, the mean particle axial velocity is larger than that of the fluid. This counterintuitive fundamental result allows interpretation of the trends observed in penetration and residence time.

Brownian motion based multi-objective particle swarm optimization methodology and application in binary classification

The particle swam optimization (PSO) method has been widely applied in evolutionary computation and related industrial areas. However, the optimization performance of traditional PSO is usually influenced by particle updating displacement and velocity, which is randomly distributed and makes the solution solving process inefficient. To deal with this challenge, a Brownian particle motion and Euler-Maruyama (EM) methodology-based model is proposed to improve the performance of the multi-objective PSO. The EM based PSO principles and algorithm framework are introduced by theoretical analysis and mathematical modeling, and then the optimization performance of four comparing PSO models is tested, while the feasibility of the new PSO4 is verified by typical benchmark problems. Afterwards, the characterizations of the EM based PSO method are investigated from the perspective of particle motion mechanism analysis, binary classification application and various optimization performance comparison. The result manifests that the new PSO4 features higher accuracy and less running time among 24 related optimization methods for 4 typical standard datasets of Ionosphere, Breast, Diabetes and Wine. Finally, the multi-objective optimization and classification application potential of the Brownian motion and EM based PSO4 is demonstrated, and the future work regarding the new PSO model is discussed.

Pattern formation in dense populations studied by inference of nonlinear diffusion‐reaction mechanisms

SummaryReaction‐diffusion systems have been proposed as a model for pattern formation and morphogenesis. The Fickian diffusion typically employed in these constructions model the Brownian motion of particles. The biological and chemical elements that form the basis of this process, like cells and proteins, occupy finite mass and volume and interact during migration. We propose a Reaction‐Diffusion system with Maxwell‐Stefan formulation to construct the diffusive flux. This formulation relies on inter‐species force balance and provides a more realistic model for interacting elements. We also present a variational system inference‐based technique to extract these models from spatiotemporal data for these processes. We show that the inferred models can capture the characteristics of local Turing instability that instigates the pattern formation process. Moreover, the equilibrium solutions of the inferred models form similar patterns to the observed data.

Investigating the Impact of Magnetohydrodynamic (MHD) and Radiation on the Casson-Based Nanofluid Flow over a Linear Stretching Sheet in a Porous Medium with Heat Source or Sink

This study delves into the magnetohydrodynamic (MHD) flow of Casson-based nanofluids over a linear stretching sheet, accounting for multiple influencing factors. These findings offer significant real-time applications across a spectrum of fields, including energy generation, environmental engineering, and materials science. The acquired insights into Casson-based nanofluid behaviour within magnetohydrodynamic contexts can foster efficiency improvements, energy conservation, and enhanced overall system and process performance. Furthermore, the current study aims at Casson-based nanofluid's magnetohydrodynamic flow across a linear stretching sheet considering effects of thermal radiation, heat source/sink, and porosity. The governing equations are converted to ordinary differential equations by using similarity transformations. The Runge-Kutta-4 method, along with the shooting technique, is used to solve the reduced equations. The effects of dimensionless parameters, magnetic, Casson, thermophoresis, thermal radiation, and Brownian motion on velocity, thermal, and concentration profiles are considered in the study. As the magnetic and Casson parameters are increased, the findings indicate a reduction in the thickness of the momentum boundary layer. Moreover, the fluid temperature intensifies with the enhancement of thermophoresis and Brownian motion of particles. Finally, for various combinations of applied parameters, the values of skin friction coefficient, Nusselt number, and Sherwood number are obtained and are shown in the tables. The research is unique in a way that incorporates the impacts of heat source/sink and porosity as well as a more precise description of Casson nanofluid flow when compared to earlier findings. The novelty of the investigation lies in the implementation of a heat source/sink and porosity to obtain refined Casson nanofluid flow.

Brownian motion in a viscous fluid of particles with constant and time-dependent friction

The Brownian motion (BM) of particles in a fluid under the influence of a moving harmonic potential is described analytically. It is assumed that the bath is viscous and particles constituting it experience Stokes' force with friction coefficients that can depend on time. The generalized Langevin equation (GLE) is derived from the equations of motion for the bath and Brownian particles. It has a familiar form, but its memory kernel generalizes the expressions known from the literature even in the case of constant friction. Analytical solutions of the found GLE are obtained for the mean and mean squared displacements of the Brownian particle, assuming the overdamped character of its motion and both the overdamped and underdamped dynamics of bath particles. In the case of constant friction, the model well describes the BM when the external potential does not move so that the system is in equilibrium. The results determined by the time-dependent friction of the bath particles must be specified for concrete fluids. An example of Lennard–Jones atomic liquid is considered with the recently proposed exponential time dependence of the friction coefficient.

Brownian motion of soft particles near a fluctuating lipid bilayer.

The dynamics of a soft particle suspended in a viscous fluid can be changed by the presence of an elastic boundary. Understanding the mechanisms and dynamics of soft-soft surface interactions can provide valuable insights into many important research fields, including biomedical engineering, soft robotics development, and materials science. This work investigates the anomalous transport properties of a soft nanoparticle near a visco-elastic interface, where the particle consists of a polymer assembly in the form of a micelle and the interface is represented by a lipid bilayer membrane. Mesoscopic simulations using a dissipative particle dynamics model are performed to examine the impact of micelle's proximity to the membrane on its Brownian motion. Two different sizes are considered, which correspond to ≈10-20nm in physical units. The wavelengths typically seen by the largest micelle fall within the range of wavenumbers where the Helfrich model captures fairly well the bilayer mechanical properties. Several independent simulations allowed us to compute the micelle trajectories during an observation time smaller than the diffusive time scale (whose order of magnitude is similar to the membrane relaxation time of the largest wavelengths), this time scale being hardly accessible by experiments. From the probability density function of the micelle normal position with respect to the membrane, it is observed that the position remains close to the starting position during ≈0.05τd (where τd corresponds to the diffusion time), which allowed us to compare the negative excess of mean-square displacement (MSD) to existing theories. In that time range, the MSD exhibits different behaviors along parallel and perpendicular directions. When the micelle is sufficiently close to the bilayer (its initial distance from the bilayer equals approximately twice its gyration radius), the micelle motion becomes quickly subdiffusive in the normal direction. Moreover, the temporal evolution of the micelle MSD excess in the perpendicular direction follows that of a nanoparticle near an elastic membrane. However, in the parallel direction, the MSD excess is rather similar to that of a nanoparticle near a liquid interface.

Two-dimensional Brownian motion of active particle on superfluid helium surface

We report an experimental study of the 2D dynamics of active particles driven by quantum vortices on the free surface of superfluid helium at T = 1.45 К. The particle motion at short times (< 25 ms) relates to anomalous diffusion mode typical for active particles, while for longer times it corresponds to normal diffusion mode. The values of the rotational and translational kinetic energies of the particle allow to determine for the first time the intensity of the particle-vortex interaction and the dissipation rate of the vortex bundle energy. Strong bonding between a particle and a vortex is explained by coupling of normal and superfluid components.