Initial Separation Distance Research Articles

Pairwise interaction of in-line spheroids settling in a linearly stratified fluid

AbstractThis study investigates the transport of particles in density-stratified fluids, a prevalent natural phenomenon. In the ocean, particles and marine snow descend through fluids with significant density variations due to salinity and temperature gradients. Such heterogeneity in the background fluid affects the settling or rising rates of particles, often leading to accumulation at transitional density layers. Previous research has primarily focused on spherical particles, examining their isolated motion, pairwise interactions, and collective transport in stratified fluids. This work, however, extends the investigation to the interaction between two spheroidal particles settling in-line in a linearly stratified fluid. This study employs an immersed-boundary technique to perform particle-resolved numerical simulations in a three-dimensional Cartesian domain. The results showcase the effects of varying the stratification strength through the Froude number, the particles’ aspect ratios, and the initial separation distance between the particles on the interaction dynamics between the settling spheroids.

Controlling the initial separation distance between two electron plasma vortices in a Malmberg–Penning trap

This paper presents a novel method to continuously control the initial separation distance d between two plasma vortices of electrons. In this method, the two electron columns are initially confined individually in two coaxial Malmberg–Penning traps with different axial lengths. They rotate around the trap axis at different rotation frequencies due to the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{E}\ imes \\varvec{B}$$\\end{document} drift. Their different rotation rates cause periodic changes in their relative azimuthal positions. The initial conditions are established when the two columns are stretched along magnetic field lines of a unified Malmberg–Penning trap. This method precisely provides a simple and continuous adjustment of the initial d and facilitates efficient investigation of the interaction of the two plasma electron vortices.

Study of Soliton Interaction in Optical Fibers with Third Order Dispersion and Higher Order Nonlinear Effects

In this paper, we present a numerical approach to solve the GNLSE and analyze soliton interaction phenomena using COMSOL environment. By leveraging the capabilities of COMSOL's PDE module, we can accurately capture the dynamics of solitons and investigate their interactions. We analyze the impact of different parameters such as soliton power, initial separation distance, and dispersion characteristics on the soliton dynamics. Furthermore, we examine the role of higher-order dispersion terms in shaping the soliton interactions. Our findings demonstrate the effectiveness of the proposed numerical approach in accurately simulating and analyzing soliton interaction phenomena. The COMSOL-based methodology provides a flexible and efficient framework for studying complex nonlinear optical systems, enabling researchers to gain insights into the behavior of solitons in different media and design optimized communication systems. This paper contributes to the understanding of soliton dynamics and provides a practical tool for investigating the behavior of solitons in nonlinear dispersive media. The presented numerical approach using COMSOL opens avenues for further research in nonlinear optics and fiber optic communication systems.

Piezoresistive Theory and Numerical Calculation for Carbon Nanotube Polymer Composite.

A three-dimensional theory has been established for the piezoresistivity of carbon nanotube (CNT) polymer composites. Based on the Mori-Tanaka method in meso-mechanics theory and considering quantum tunneling effect between CNTs, an approach to calculate equivalent electrical conductivity of composites was proposed. On this basis, a piezoresistive theory, which incorporates the effect of composites' geometric nonlinearity, was developed for CNT polymer composites. The theory is dependent only on some basic physical parameters of the materials. A finite element formula of the theory for the numerical calculation of piezoresistivity was presented from the analysis of both elastic and electric fields. Numerical simulations demonstrated that the results predicted by the theory were in good agreement with those of the experimental tests. Parameter sensitivity analysis revealed that when both the potential barrier height of the matrix and the initial average separation distance between CNTs increased, the piezoresistivity obviously increased. However, with the increase in aspect ratio and CNT conductivity, the piezoresistivity decreased gradually. A practical engineering application of this theory is also provided.

Monomer and Excimer Emission in Electrogenerated Chemiluminescence of Pyrene and 2,7-Di-tert-butylpyrene Associated with Electron Transfer Distance.

Electrogenerated chemiluminescence (ECL) is a light emission phenomenon caused by electrochemically generated radical anions (R•-) and cations (R•+), in which the ion annihilation results in the formation of a pair of excited (R*) and ground state (R) of a luminescent molecule. Here, the ECL properties of pyrene (Py) and 2,7-di-tert-butylpyrene (di-t-BuPy) are reported. It was found that at a commonly employed concentration (1 mM), the ECL spectra were time-dependent because of increasing the oligomer emission and increasing the concentration of R near R*, leading to an enhancement of the excimer emission. At a low concentration range (20-30 μM), the shape of the ECL spectra containing the monomer and excimer emission was determined by isolated pairs of R* and R, which were generated through ion annihilation of R•- and R•+. It was found that in the ECL of Py and di-t-BuPy originated from the isolated pairs of R•- and R•+, 58 and 48% of the excited states were the excimer states, respectively. Diffusion equation analysis indicates that the lower excimer formation in the case of di-t-BuPy is because of a farther initial separation distance between R* and R, i.e., a longer electron transfer distance between the radical ions. The Marcus model for the electron transfer kinetics suggests that the farther electron transfer distance is mainly caused by the larger molecular size, which resulted in a smaller reorganization energy of the solvent acetonitrile molecule. Taking advantage of the photophysical and electrochemical properties of Py and di-t-Bu Py, the monomer and excimer emission in ECL is discussed.

Analyzing of continuous and discontinuous contact problems of a functionally graded layer: theory of elasticity and finite element method

Contact mechanics analysis is crucial because such problems often arise in engineering practice. When examining contact mechanics, the material property of the contacting components is a crucially significant aspect. It is more complex to solve the contact mechanics of systems that are composed of materials that do not have a homogenous structure compared to materials that have homogeneous qualities throughout. While many studies on contact problems with homogeneous materials exist, those involving non-homogeneous materials are scarce in the literature. As material technology improves fast, there will be a greater need to solve such problems. In this respect, analytical and finite element method (FEM) solutions of the continuous and discontinuous contact problems of a functionally graded (FG) layer are carried out in this article. The FG layer in the problem rests on a rigid foundation and is pressed with a rigid punch. From the solutions, the contact length, contact stress, initial separation distance, and beginning and ending points of separation were determined, and the results were compared. It has been concluded that the FEM findings are consistent with the analytical results to a satisfactory degree. This study analyzes contact problem using different approaches and accounts for the influence of body force in a contact geometry that has yet to be reported.

Interaction of impinging marangoni fields

HypothesisSurface tension gradient driven Marangoni flows originating from multiple sources are important to many industrial and medical applications, but the theoretical literature focuses on single surfactant sources. Understanding how two spreading surfactant sources interact allows insights from single source experiments to be applied to multi-source applications. Two key features of multi-source spreading – source translation and source deformation – can be explained by transport modeling of a two-source system. ModelingNumerical simulations of two oleic acid disks placed at varying initial separation distances on a glycerol subphase were performed using COMSOL Multiphysics and compared to spreading of a single surfactant source. FindingsInteraction of two spreading sources can be split into three regimes: the independent regime – where each source is unaffected by the other, the interaction regime – where the presence of a second source alters one or more features of the spreading dynamics, and the quasi-one disk regime – where the two sources merge together. The translation of the sources, manifested as increasing separation distance between disk centers of mass, is driven by the flow fields within the subphase and the resultant surface deformation, while deformation of the sources occurs only once the surfactant fronts of the two sources meet.

Importance of self‐induced vertical wind shear and diabatic heating on the Fujiwhara effect

AbstractThis study hypothesises that the motion of binary tropical cyclones (TCs) can be modified by diabatic heating (DH) asymmetry associated with self‐induced vertical wind shear. To demonstrate this hypothesis in the quiescent environment, a set of the idealised f‐plane numerical experiments such as identical (varied in the initial separation distance) and non‐identical (varied in TC intensity and size) experiments are conducted. Results show that the binary TC tracks are affected by the initial separation distance, and TC intensity and size, that is, TC influence radius. Identical experiments show that the critical distance for separating, merging or repelling motion is 8° (where 1° ≃ 111 km). The binary TC interaction shows that single large‐scale cyclonic and anticyclonic circulations can develop as a result of the superposition of the circulation of the binary TCs in the lower and upper troposphere. These two different large‐scale circulations result in a vertically sheared environment in each TC. Potential vorticity (PV) tendency diagnosis shows that the TC motion is consistent with a positive region of the local tendency of PV. To quantify the contribution of each PV diagnostic term to the TC motion, we calculate each vector of the PV tendency diagnostic equation. In the merger case, the horizontal advection vector (HADV) appears to be greater than the DH vector (DHV) due to attraction. In the repulsion case, the DHV is largely compensated by the HADV. Specifically, the strong shear‐induced DH generated in the lower troposphere and downshear or downshear‐left quadrant can modify the TC motion in collaboration with the transport of PV to the middle and upper troposphere by offsetting the PV imbalance via the HADV. Overall, these results validate our hypothesis, which we refer to as the three‐dimensional Fujiwhara effect.

Electrowetting-Induced Coalescence of Sessile Droplets in Viscous Medium

Manipulating the coalescence of microdroplets has recently gained enormous attention in digital microfluidics and biological and chemical industries. Here, coalescence between two sessile droplets is induced by spreading them due to electrowetting. The electrocoalescence dynamics is investigated for a wide range of operating parameters such as electrowetting number, Ohnesorge number, driving frequency, and drop to surrounding medium viscosity ratio. Here, the characteristic time scale from the classical lubrication theory is modified with an additional driving and resisting force due to the electrostatic pressure force and liquid-liquid viscous dissipation, respectively. With the revised characteristic time scale, a universal bridge growth is shown between the two merging droplets following a 1/3 power law during early coalescence followed by a long-range linear variation. To ensure precise control on droplet coalescence, a geometric analysis is also performed to define the initial separation distance.

Environmental Modulation of Mechanical and Thermodynamic Forcing from Cold Pool Collisions

Abstract Cold pools can initiate new convection by increasing vertical velocity (mechanical forcing) and locally enhancing moisture content (thermodynamic forcing). This study investigates the impact of the environment on mechanical and thermodynamic forcing from cold pool collisions. An ensemble of high-resolution numerical simulations was conducted that tested the sensitivity of cold pool collisions to three parameters: 1) the initial temperature deficit of cold pools, 2) the initial distance between cold pools, and 3) the static stability and moisture content of the environment. These parameters are tested in the absence of condensation, surface fluxes, radiation, and wind shear. Colder initial cold pools increase mechanical and thermodynamic forcing owing to greater horizontal winds during collisions. For all environments tested, mechanical forcing peaked robustly at an optimal initial distance between the cold pools due to a balance between the creation and dissipation of kinetic energy, and the different phases of density current evolution. Thermodynamic forcing peaked for greater initial cold pool distances than those associated with mechanical forcing. Decreased low-level static stability and an increased vertical gradient in low-level moisture enhanced mechanical and thermodynamic forcing, respectively. It is also shown that the initial temperature deficit had the greatest impact on mechanical and thermodynamic forcing, followed by the environment, and finally the initial separation distance. Finally, cold pool collisions are classified as “mechanically strong” or “mechanically weak,” where mechanically strong collisions increased mechanical forcing beyond that driven by the initial outward spreading of the cold pools. An analogous classification of “thermodynamically strong/weak” is also presented.

Continuous and discontinuous contact problem of a functionally graded orthotropic layer indented by a rigid cylindrical punch: Analytical and finite element approaches

AbstractIn this study, the continuous and discontinuous contact problems of a functionally graded (FG) orthotropic layer lying on a homogeneous and isotropic layer were investigated. The orthotropic layer was indented by a rigid cylindrical punch which was subjected to a concentrated normal force, and a homogeneous isotropic layer was firmly attached to a rigid substrate. For the analytical solution, the general expressions for the stresses and displacements were obtained in the presence of body forces by using elasticity theory and Fourier integral transforms. The continuous and discontinuous contact problems were reduced to the singular integral equations by means of boundary conditions. The system of the singular integral equations was solved using the Gauss‐Chebyshev integration formula. Then, the finite element solution of the two cases was also performed. Analytical results and numerical results (FEM) for critical load, initial separation distance, separation region in discontinuous contact, contact lengths under the punch, and contact stress distributions between the layer‐punch and layer‐layer were obtained for the dimensionless quantities.

Short-range repulsive force model for near-contact interactions of bubbles.

We introduce a short-range repulsive force model to tackle near-contact interactions when the collision occurs between bubbles. In contrast to the previous numerical method adopting the adaptive mesh refinement technique, such a mesoscale model can be applied to a relatively coarse mesh, which can prevent the nonphysical coalescence between bubbles without excessive mesh refinement. We assume that the repulsive force is inversely proportional to the third power of distance, as a reasonable approximation to the short-range phase interactions. The model is validated against two different experiments. In both experiments, two identical bubbles rising side by side were considered. First, the experiment performed in a water-glycerol mixture helps determine the model parameter K. Second, three typical combinations of bubble size and initial separation distance are simulated, presenting different types of interactions, i.e., coalescence, bouncing coalescence, and bouncing separation, agreeing well with the second experiment, which was performed in pure water. Owing to its simplicity, this model can be easily implemented into existing codes, and it can be extended to the case with multiple bubbles or droplets.

Clinical viability of magnetic bead implants in muscle.

Human movement is accomplished through muscle contraction, yet there does not exist a portable system capable of monitoring muscle length changes in real time. To address this limitation, we previously introduced magnetomicrometry, a minimally-invasive tracking technique comprising two implanted magnetic beads in muscle and a magnetic field sensor array positioned on the body's surface adjacent the implanted beads. The implant system comprises a pair of spherical magnetic beads, each with a first coating of nickel-copper-nickel and an outer coating of Parylene C. In parallel work, we demonstrate submillimeter accuracy of magnetic bead tracking for muscle contractions in an untethered freely-roaming avian model. Here, we address the clinical viability of magnetomicrometry. Using a specialized device to insert magnetic beads into muscle in avian and lagomorph models, we collect data to assess gait metrics, bead migration, and bead biocompatibility. For these animal models, we find no gait differences post-versus pre-implantation, and bead migration towards one another within muscle does not occur for initial bead separation distances greater than 3cm. Further, using extensive biocompatibility testing, the implants are shown to be non-irritant, non-cytotoxic, non-allergenic, and non-irritating. Our cumulative results lend support for the viability of these magnetic bead implants for implantation in human muscle. We thus anticipate their imminent use in human-machine interfaces, such as in control of prostheses and exoskeletons and in closed-loop neuroprosthetics to aid recovery from neurological disorders.

Investigation of droplet grouping in monodisperse streams by direct numerical simulations

Droplet grouping is important in technical applications and in nature where more than one droplet is seen. Despite its relevance for such problems, the fundamentals of the grouping processes are not yet fully understood. Initial conditions that expedite or impede the formation of droplet groups have been studied, but a thorough investigation of the temporal and spatial evolution of the forces at play has not been conducted. In this work, the grouping process in monodisperse droplet streams is examined in detail by direct numerical simulation (DNS), for the first time, using the multiphase code Free Surface 3D. The code framework is based on the volume-of-fluid method and uses the piecewise linear interface calculation method to reconstruct the interface. A method is established to quantify the development and evolving differences of pressure and shear drag forces on each droplet in the stream using the available DNS data. The results show a linear increase in the difference between the forces, where the drag force on the leading droplet is always larger than that on the trailing droplet. A comprehensive parametric study reveals that, on the one hand, large initial inter-droplet separation and small group distances increase grouping time due to reduced difference in the drag coefficients. On the other hand, higher initial Reynolds numbers and larger irregularities in the geometrical arrangement promote droplet grouping. The flow field shows stable wake structures at initial Reynolds numbers of 300 and the onset of vortex shedding at Reynolds numbers of 500, affecting the next pair of droplets, even for larger separation distances.

Hydrodynamic Interaction of Two Self-Propelled Fish Swimming in a Tandem Arrangement

Collective locomotion in biological systems is ubiquitous and attracts much attention, and there are complex hydrodynamics involved. The hydrodynamic interaction for fish schooling is examined using two-dimensional numerical simulations of a pair of self-propelled swimming fish in this paper. The effects of different parameters on swimming speed gain and energy-saving efficiency are investigated by adjusting swimming parameters (initial separation distance d0, tail beat amplitude A, body wavelength λ, and period of oscillation T) at different phase difference δϕ between two fish. The hydrodynamic interaction performance of fish swimming in a tandem arrangement is analyzed with the help of the instantaneous vorticity contours, pressure contours, and mean work done. Using elementary hydrodynamic arguments, a unifying mechanistic principle, which characterizes the fish locomotion by deriving a scaling relation that links swimming speed u to body kinematics (A, T, and λ), arrangement of formation (d0), and fluid properties (kinematic viscosity ν), is revealed. It is shown that there are some certain scaling laws between similarity criterion number (Reynolds number (Re) and Strouhal number (St)) and energy-consuming coefficient (CE) under different parameters (Δ). In particular, a generality in the relationships of St–Re and CE–(Re ·Δ) can emerge despite significant disparities in locomotory performance.

Behavior Evolution of Droplets Suspended in Castor Oil under Alternating Current Electric Field.

Electric fields, which can promote the approach of droplets and break the liquid film, are extensively used in the separation of the water phase in water-in-oil emulsions. However, there is an evolution of droplet behavior under an electric field. After the two droplets meet with each other, the electric force becomes undesirable, which would even cause breakup of the merged droplet. When the electric field strength E reaches a particular value, the final behavior of droplets is made, which goes against coalescence, and there are lots of behavior evolution types. Several research studies have studied on whether droplets coalesce and the critical condition, but few works have focused on the classification and mechanism of non-coalescence behaviors. In this paper, the behavior evolution of two single droplets suspended in castor oil under an alternating current electric field is studied by a high-speed camera. Six distinct behavior evolution modes are observed and summarized: coalescence, bounce, partial coalescence, partial rupture, coalescence-rupture, and rupture. The behavior evolution mode is influenced by the initial separation distance s0 between droplets and the electric field strength. Moreover, there exist critical electric field strengths among different behavior evolution modes. As E gradually increases, two water droplets go through coalescence, partial coalescence, and coalescence-rupture in sequence when s0 is small and coalescence, bounce, partial rupture, and rupture when s0 is large. The mechanisms of behavior evolution are revealed by investigating the confrontation between electric force and capillary force in the condition with liquid bridge or pressure difference from the surrounding fluid and electric force in the condition without a liquid bridge. In addition, a cone-dimple mode of water droplets in castor oil is found, demonstrating the rationality of electric force theory.

Prediction and measurement of leaky dielectric drop interactions

The electrohydrodynamic interactions between multiple and dissimilar drops are measured experimentally, and a pairwise electrohydrodynamic theory to describe the drop interactions is presented. The trajectories of three and four interacting drops are shown to be qualitatevly predicted by the theory. Drops with distinct electrical properties exhibit nonreciprocal interactions, and the same drop pair can undergo opposite trajectories with different initial separation distances.

Computational contact mechanics for a medium consisting of functionally graded material coating and orthotropic substrate

This paper presents a semi-analytical method to investigate the frictionless contact mechanics between a functionally graded material (FGM) coating and an orthotropic substrate when the system is indented by a rigid flat punch. From the bottom, the orthotropic substrate is completely bonded to the rigid foundation. The body force of the orthotropic substrate is ignored in the solution, while the body force of the FGM coating is considered. An exponential function is used to define the smooth variation of the shear modulus and density of the FGM coating, and the variation of Poisson’s ratio is assumed to be negligible. The partial differential equation system for the FGM coating and the orthotropic substrate is solved analytically through Fourier transformations. After applying boundary and interface continuity conditions to the mixed boundary value problem, the contact problem is reduced to a singular integral equation. The Gauss–Chebyshev integration method is then used to convert the singular integral equation into a system of linear equations, which are solved using an appropriate iterative algorithm to calculate the contact stress under the rigid flat punch. The parametric analyses presented here demonstrate the effects of normalized punch length, material inhomogeneity, dimensionless press force, and orthotropic material type on contact stresses at interfaces, critical load factor, and initial separation distance between FGM coating and orthotropic substrate. The developed solution procedures are verified through the comparisons made to the results available in the literature. The solution methodology and numerical results presented in this paper can provide some useful guidelines for improving the design of multibody indentation systems using FGMs and anisotropic materials.

Experimental analysis of overtaking behavior in disks falling in a low-density particle bed

Cooperative behavior displayed by five steel disks falling in a low-density particle bed involves the formation of upward and downward convex configurations, which resembles the flying pattern of a flock of birds. In this study, we focused on overtaking behavior in two falling disks, which causes the cooperative behavior, and we investigated the effects of differences in the disk release time and the initial disk separation distance on the falling behavior of the disks experimentally. Expanded polystyrene (EPS) particles (diameter 5.08 mm, mass 1.45 mg) were used as the bed particles and steel disks (diameter 25.4 mm, thickness 5.22 mm, mass 20.2 g) were used as the falling disks. We released one to five disks with various disk release time differences (0–0.154 s) and initial separation distances (0–100 mm). We recorded the disk falling behavior in the particle bed with a high-speed video camera (500 fps) and analyzed the behavior with image analysis software. Five-disk cooperative behavior similar to that reported in the literature occurred in our experimental setup. In the two-disk experiments, we observed overtaking behavior for an initial separation distance of 10 mm and release time difference of ≤ 0.076 s, and for an initial separation distance of ≤ 60 mm and release time difference of 0.02–0.03 s. The overtaking behavior arose from the decrease in the falling velocity of the first disk released. The EPS particle packing fraction in the area above the disk one disk diameter wide and a quarter of the disk diameter high determined the disk falling velocity. This mechanism was explained by the displacement behavior of EPS particles around the disks as the disks fell.

Observation of a different type of splitting solitons induced by interaction of second order spatial solitons

In this work the behavior of the split solitons derived from the interaction between two (1 + 1)- Dimensional second-order bright spatial solitons, is numerically investigated. Each individual interaction occurs when the two second-order solitons are initially propagating in the parallel way, while the variety of relative phases and the different initial transversal separation are adjusted. When the initial separation distance is on the appropriate distance where they feel the presence of other soliton, both second-order solitons breakup into a couple of first order (fundamental) low- and high-amplitude solitons, and consequently their initial parallel path suffers a lot. Although the propagation path of high- amplitude solitons receive low effects due to interaction and consequently almost follow their initial propagation path, the propagation path of the low-amplitude solitons suffers based on their initial relative phase. The derived low-amplitude fundamental solitons interact with each other and their propagation path also, as usual of their basic interaction properties, while the high-amplitude fundamental solitons, do not show the interaction, and almost continue their own parallel paths. As the initial separation distance decreases, and almost the initial overlap occurs, the propagation paths suffer for both (high and low amplitude) fundamental solitons. Behavior of the broken solitons induced by the interaction between the second order spatial solitons are investigated by solving the Nonlinear Schrodinger equation (NLSE), and it is simulated numerically by MATLAB program by using the well-known Split-Step Fourier Transform method.