Understanding ultrathin liquid-film dynamics is crucial for unraveling complex interfacial phenomena, yet deriving governing equations directly from experimental observations remains challenging. This study proposes a data-driven approach to model droplet dynamics, capturing liquid-film thickness on the nanometer scale in the form of a partial differential equation. As a challenging test case, we examine the superspreading wetting of surfactant-free nanofluids, a phenomenon whose physical mechanism defies standard theoretical explanations. We apply a sparse identification algorithm to spatiotemporal film-thickness profiles resolved at the nanometer scale using phase-shifting imaging ellipsometry. For a pure solvent, the discovered governing equation recovers classical lubrication physics driven by disjoining pressure and evaporation. In contrast, the nanofluid dynamics necessitates an additional, unique transport term scaling with the gradient of the inverse film thickness. Theoretical scaling analysis suggests this term represents a nanoparticle-induced bias flux, consistent with a hypothesized capillary wicking mechanism within the precursor film. The identification of the current nanofluid-specific term underscores the efficacy of integrating high-precision experimental measurements with data-driven modeling to discover hidden physics and generate testable hypotheses in complex wetting dynamics.
The thermophoretic migration of porous particles in confined environments is of considerable importance in microfluidic manipulation, filtration technologies, and targeted transport systems. In the present study, the steady thermophoretic motion of a porous spherical particle near a rigid planar wall is investigated within the Stokes-diffusion limit. The porous interior is modeled as a homogeneous Brinkman medium, thereby accounting for internal flow and permeability effects on thermophoretic transport. A uniform temperature gradient is imposed normal to the wall, inducing particle migration perpendicular to the boundary. A semi-analytical solution is developed using coupled spherical and cylindrical eigenfunction expansions. The wall boundary conditions are satisfied through Fourier-Bessel transform techniques, while the remaining interfacial conditions at the porous particle surface are enforced numerically using a boundary collocation method. The results demonstrate that wall confinement significantly suppresses thermophoretic migration owing to the combined effects of hydrodynamic resistance and thermal-field distortion within the narrow gap region. The reduction in migration velocity becomes more pronounced as the particle approaches the wall and depends strongly on both the permeability parameter and the thermal conductivity ratio. Comparisons with the impermeable-particle limit further clarify the role of internal permeability and show that the classical solid-particle behavior is recovered as a limiting case of the present formulation.
To address the limitation of the current decoupled parameter design approach between wind turbine blade airfoils and vortex generators (VGs), which often fails to achieve optimal aerodynamic performance after VGs are added, this study proposes an integrated optimization method for airfoil-VG configuration. First, a sensitivity analysis is conducted to investigate the influence of VG parameters on airfoil aerodynamic performance, revealing the sensitivity ranking as installation position, trailing-edge height, installation angle, and base length. Then, B-spline functions are employed to parameterize the geometry of the DU97W300 airfoil. An optimization model is established with the maximum lift coefficient and maximum lift-to-drag ratio of the airfoil with VGs as the objective functions. A MATLAB-based program coupled with a modified XFOILVG solver is developed to perform the integrated design and optimization, aiming to identify the optimal combination of airfoil shape and VG parameters for aerodynamic performance enhancement. The results show that, compared to the original airfoil with VGs, the integrated new airfoil with new VGs achieves a 10.5% improvement in the average lift-to-drag ratio over angle of attack (AOA) range of 0 degrees similar to 22 degrees, and a 6.6% increase in the maximum lift coefficient. Lastly, computational fluid dynamics (CFD) simulations are conducted to validate the theoretical results, demonstrating good agreement between theoretical and numerical predictions. Flow streamline plots, pressure coefficient distributions, and vorticity contours further confirm that the optimized airfoil with VGs effectively suppresses flow separation and delays stall. The proposed method is promising for the aerodynamic design of both utility-scale and small wind turbines to improve their power generation efficiency and operational stability.
The phenomenon of solid particles interacting with gas-liquid interfaces is ubiquitous in natural systems and numerous industrial processes. Owing to the intricate coupling between the gas, liquid, and solid phases, a comprehensive understanding of the underlying mechanisms remains elusive. This work presents a lattice Boltzmann model developed to simulate the traversal of gas-liquid interfaces by solid particles at a high liquid-gas density ratio. The numerical framework utilizes an enhanced cascaded lattice Boltzmann method to resolve the complex gas-liquid flow field and a finite difference method for tracking the particle motion. A robust two-way coupling among the three phases is achieved through moving boundary conditions and refilling algorithms. The model is validated by simulating a benchmark case of a stationary particle at a gas-liquid interface, with results consistent with existing studies. Furthermore, both qualitative and quantitative comparisons with earlier experiments further confirm its accuracy. Following validation, the effects of particle impact velocity and surface wettability are examined. The findings show that higher impact velocities lead to more distinct gas tails behind the particle and more intense oscillations at the gas-liquid interface. At the same time, increased surface hydrophobicity slows the particle's entry into the liquid and results in more distinct gas tails. Additionally, once the particle becomes fully immersed, both capillary and hydrodynamic forces decrease significantly, corresponding to a markedly slower decay in its settling velocity.
This work introduces the kinetic theory of particle flow (KTPF), a generalization of the classical kinetic theory of granular flow to systems composed of colliding, reactive, multicomponent, and mass-transferring particles such as gas bubbles, liquid droplets and solid particles. Built on a Boltzmann-like description in a joint physical-property space, the theory derives mass-weighted averaged transport equations that account for both individual particle dynamics and ensemble behavior. A key innovation is the structured decomposition of the property space into resolved and averaged-out components, enabling the derivation of statistically rigorous and computationally tractable moment equations. The resulting formulation unifies Lagrangian and Eulerian perspectives by embedding single-particle dynamics into an Eulerian ensemble framework. The KTPF systematically separates continuous particle-scale evolution from population-scale stochastic effects such as breakage, coalescence, and nucleation. Transport equations for mass, species, momentum, and energy are derived, including versions expressed in terms of enthalpy and temperature. A simplified model tailored to bubbly flow is presented along with closures and modeling assumptions. This hybrid approach bridges the gap between Euler-Euler and Euler-Lagrange methods, offering a flexible, extensible, and physically consistent basis for simulating complex multiphase flows.
This study presents numerical simulations on the vortex-induced vibration (VIV) of twin diamond-shaped cylinders in tandem at a low Reynolds number of 100. The investigation focuses on examining how the mass ratio (m*) affects vibration behavior, with the cylinders maintained at a fixed center-to-center distance of 4B (where B is the cylinder's characteristic length). The analysis employs reduced velocities (Ur) ranging from 3 to 18 and systematically examines three mass ratios (m* = 5, 10, and 20). The results reveal that this specific spacing exclusively produces co-shedding flow patterns, which manifest through five clearly distinguishable flow modes. The dominant vibration occurs in the transverse direction, with the downstream cylinder exhibiting the maximum amplitude. While the lock-in region (Ur approximate to 4-8) for the upstream cylinder shows no dependence on m*, the corresponding region for the downstream cylinder progressively contracts as the m* increases. Regarding frequency characteristics, the upstream cylinder demonstrates single-frequency vibrations at m* = 5 and 10, while the lift force transitions from single- to multi-frequency components within the lock-in region. But for m* = 20, the upstream cylinder's single-frequency vibration is driven by multi-frequency lift. Furthermore, due to vortex interactions caused by the upstream cylinder's wake, the downstream cylinder mostly experiences multifrequency lift forces.
Numerical analysis of the flow and heat transfer processes during the injection of a droplet-laden two-phase jet through an annular slit into a transverse flow of heated turbulent air, considering non-isothermal processes, is performed. Calculations of the averaged flow structure and local thermal efficiency are carried out using the axisymmetric RANS approach and the second-moment closure turbulence model. The transverse movement of droplets is controlled by the convection of momentum, viscosity, turbulent migration due to the heterogeneity of the turbulent energy of the dispersed phase, and the turbulent diffusion of the dispersed phase due to the gradient of its mass fraction. A simplified version of the droplet evaporation model, based on the assumption of small Spalding mass and heat transfer numbers, is used. An increase in the blowing parameter is shown to lead to an increase in the depth of secondary jet penetration into the main cross-flow (up to 50%). The highest level of turbulent kinetic energy is predicted in the layer of mixing of the radial jet with the cross-flow. The maximum turbulence level is predicted in the wall zone of the pipe. With an increase in the blowing parameter, an increase in the length of the separation region by up to 3.5 times is predicted. The presence of evaporating water droplets is shown to lead to an increase of up to 60% in the averaged thermal effectiveness of the radial jet in a cross-flow compared with a single-phase radial jet in a cross-flow. The numerical results are shown to be consistent with experimental data for the injection of a single-phase cross-flow into a single-phase main flow in a flat channel, injection of a single-phase transverse radial flow into a single-phase main flow in a pipe, and injection of a gas-droplet wall jet at an angle through circular openings into a single-phase main gas flow.
In this work, a comprehensive analysis of scalar transport and dissipation behaviour in turbulent nonpremixed combustion was conducted using a spatially inhomogeneous zero-dimensional doubly conditional moment closure (DCMC) model. The study investigated a CH4/HQbluff-body flame and examined how the choice of progress variable definition and the modelling of the progress variable scalar dissipation rate influence predictions of reactive scalar fields in the DCMC framework. Two progress variable formulations based on HQO and COQ mass fractions were employed alongside two scalar dissipation rates of progress variable closures, referred to as Kolla and linear relaxation closure models. The doubly conditional distributions revealed that the definition of the progress variable strongly affects the structure and spread of the conditional space. The Kolla closure consistently yields accurate scalar dissipation rates localized at the flame front, whereas the linear relaxation closure overpredicted turbulent mixing, resulting in excessive variance damping. These modelling differences significantly influenced the predicted unconditional mean reactive scalars. The Kolla closure accurately reconstructed unconditional mean temperature, HQO, CO, and COQ fields for both progress variable definitions, while the linear relaxation model exhibited strong sensitivity to the progress variable choice and systematically underpredicted oxidation completeness. The results underscored the critical role of accurately modelling scalar dissipation of the progress variable in DCMC formulations. This study provided a physics-based foundation for improving DCMC closures for modelling complex turbulent flames arising in practical scenarios.
This study focuses on the nonlinear stability and dynamics of gravity-driven viscous films on a vertical rotating cylinder, considering both outer and inner surface flows with slip conditions at the cylinder wall. We develop an asymptotic model for the combined effects of rotation and wall slippage. Linear stability analysis indicates that wall slippage enhances instability on both surfaces, while rotation amplifies instability on the outer surface but reduces it on the inner surface. Weakly nonlinear stability analysis is then performed to examine the combined impact of rotation and wall slip on flow stability beyond the linear regime, yielding bifurcation diagrams for both surfaces. Traveling-wave solutions of the model and their stability are analyzed, showing how rotation affects the nonlinear wave characteristics in the presence of wall slip. Numerical simulations of the fully nonlinear evolution of the free surface reveal that increasing the slip length enhances the choke phenomenon in inner surface flow, while rotation can delay this effect. Additionally, for flow along the outer surface of a slippery rotating cylinder, the film tends to break up into droplets under the influence of rotation.
The finite difference method (FDM) is efficient but typically restricted to structured grids, limiting its use for complex geometries. This paper develops a DEER-based finite difference framework for unstructured grids using a relocated computational node strategy. By duplicating and directionally displacing original nodes, locally structured four-point stencils are constructed, restoring the pointwise formulation of classical FDM. Primitive variables at half-nodes are reconstructed using a weighted least-squares approach, and numerical fluxes are evaluated with an approximate Riemann solver under the DEER consistency condition. Numerical results for isentropic vortex propagation and cylinder flows demonstrate second-order accuracy, good robustness on irregular meshes, and stable shock capturing on the benchmark cases tested. The method provides a simple and effective finite difference approach for unstructured grid computations.
We propose a parametric model to reconstruct the energy spectrum of the streamwise velocity fluctuation within the logarithmic region of a high-Reynolds-number wall-bounded turbulent boundary layer, integrating mathematical fitting with logarithmic-region scaling relations. The model is based on the cumulative energy fraction (CEF), which quantifies the cumulative build-up of streamwise energy across wavenumbers in the spectrum Phi uu(kx), where Phi uu(kx) denotes the power spectral density of the streamwise velocity fluctuation u and kx is the streamwise wavenumber. The model can rapidly predict the spectral-shape characteristics of Phi uu(kx) using only the non-dimensional wall-normal coordinate z/S in the logarithmic region (with z the distance from the wall and S the boundary-layer thickness) as input. The CEF is modeled as a log-normal cumulative distribution function, with its location and scale parameters mu and a exhibiting an approximately linear dependence on log10(z/S), consistent with the empirical scaling characteristics of wall-attached structures in the logarithmic region. The reconstructed spectrum Phi recon uu(kx) can capture, over the inertial-range wavenumber interval, the k-5/3 x scaling anticipated by Kolmogorov's theory. To correct systematic deviations near the spectral peak, an empirical compensation function C(kx) calibrated from wind-tunnel data is introduced. The compensated spectrum Phi comp uu (kx) shows overall agreement with wind-tunnel experiments and near-neutral atmospheric surface-layer observations over friction Reynolds numbers ranging from O(104) to O(105). This method links turbulent structures and spectral characteristics, providing a compact and computationally inexpensive tool for spectral parameterization, remote sensing, and diagnostics of high-Reynolds-number inflows, and is applicable to wind-energy-relevant inflow characterization scenarios where broadband spectral information is limited by measurement bandwidth and sampling conditions.
This study investigates the non-equilibrium transport dynamics and macroscopic thermodynamic efficiency of a binary gas mixture traversing a tapering, selectively permeable cascade operating strictly within the Knudsen regime. By employing a Lagrangian test particle Monte Carlo framework alongside a Fokker-Planck formalism, discrete stochastic trajectories driven by particle-boundary interactions are coupled with ensemble macroscopic concentration profiles. The separation process is thermodynamically evaluated by balancing the separation work gain against two primary costs: the microscopic entropic penalty of momentum erasure via diffuse wall collisions, and the macroscopic transport penalty induced by geometric backscattering. To formalize this, the specific separation thermodynamic efficiency is introduced, a metric that normalizes overall performance against the intrinsic material transmission probability. The results reveal a critical morphological transition in optimal cascade architecture. It is demonstrated that low-affinity membranes fundamentally require moderate geometric constriction to mechanically force boundary collisions and maximize the integrated probability of permeation, optimally balancing permeation against induced backscattering. On the other hand, in high-affinity systems, the active species is rapidly extracted near the inlet, localizing maximum thermodynamic dissipation and rendering severe tapering physically detrimental. Consequently, highly selective membranes strictly favor uniform channel geometries to mitigate irreversible transport losses. Finally, this framework establishes that optimal geometric design is not static but must be dynamically tailored to the intrinsic surface affinity to maximize macroscopic thermodynamic efficiency.
Coordinated improvement of pressure recovery and flow recovery in the front stage of a deflector jet servo valve remains a key bottleneck for overall performance. Using numerical simulations, this study reveals how guide-slot length and deflector thickness jointly affect wall-attached jet stability, shear-layer spreading, and performance evolution. A multi-objective optimization framework combining a CNN surrogate model with an improved NSDBO algorithm is then developed. Results show that pressure recovery is mainly governed by wall-attachment stability and reattachment location, whereas flow recovery depends on shear-layer spreading and the effective inlet flow area of the receiving chamber. Their inconsistent responses to structural parameters create a non-convex conflict region in the design space. The Pareto front exhibits lower conflict in the medium-pressure range; the knee solution at a deflector displacement of 0.05mm achieves simultaneous gains of 12%-20% in pressure recovery and 13%-18% in flow recovery, without inducing pronounced shear separation.
Atomization of the injected bulk liquid in a confined environment is a widely studied phenomenon for its potential applications in industries ranging from chemical engineering to biomedical sciences. The present study conducts a second-order weakly nonlinear temporal instability analysis, while considering the fundamental varicose mode of initial disturbance at the first order. The study investigates the influence of confinement on the breakup dynamics of an injected planar viscous liquid sheet, emphasizing the roles of liquid viscosity and the gas-to-liquid velocity ratio. The results indicate that confinement significantly destabilizes the perturbed interface across all the considered gas-to-liquid velocity ratios (U = 2, 2.25, 2.50, and 3), with the effect being more pronounced at lower velocity ratios. Study also identifies the minimum (CH-1) and maximum (CH-2) confinement height. CH-1 value remains consistently low, ranging from 2 to 3 across all configurations. Furthermore, CH-2, the wall spacing beyond which confinement no longer influences interface disturbances, decreases with increasing gas-to-liquid velocity ratio and Weber number. Moreover, the present breakup model has been combined with the maximum entropy formalism (MEF) to predict the spray size distribution. For the varicose mode of initial disturbance, the confinement exhibited a dual effect on the droplet size, differing from the behaviour observed for the sinuous mode in our previous study.
This study numerically investigates the thermocapillary-driven transport and coalescence dynamics of two tandem compound droplets within a sinusoidally constricted microchannel. By employing a front-tracking method, we systematically examine the influence of key dimensionless parameters, including the Marangoni number (Ma = 5-80), initial axial location of the leading droplet (H-0L = 4.5R(o)-8.0R(o)), inner-to-outer radius ratio (R-io = 0.4-0.8), and constriction depth (d/R-c = 0.56-0.60). Our results reveal a distinct regime transition between droplet coalescence and non-coalescence, primarily governed by the competition between thermocapillary driving forces and hydrodynamic resistance at the channel throat. It is found that lower Marangoni numbers and larger inner cores (specifically within the range of 0.4 <= R-io <= 0.6) facilitate earlier coalescence, driven by pronounced interfacial stretching and diminished thermal convective interference. Furthermore, we identify a critical initial separation threshold (H-0L approximate to 7.8R(o)), beyond which the leading droplet escapes the constriction's influence before the trailing one can bridge the gap. Increasing the constriction depth significantly decelerates the leading droplet, thereby promoting rapid convergence and reducing the total coalescence duration. These findings provide fundamental insights into the precise control of multi-layered droplets in microfluidic systems.
Flow cytometry enables rapid, quantitative analysis of individual cells and selective separation of target biological particles. Accurate single-file analysis requires the sample stream to be hydrodynamically compressed to dimensions comparable with the particle diameter so that particles traverse the detection region sequentially. Conventional microfluidic focusing strategies typically employ sequential, two-stage constriction and often position the focused stream close to channel walls, which can induce particle-wall interactions, fouling, sample loss, and degraded measurement fidelity. Here, we propose a novel microfluidic device that achieves true onestep, 3D hydrodynamic focusing by symmetrically compressing the sample stream about the channel centerline in both the horizontal and vertical directions. Coupled numerical simulations performed in COMSOL Multiphysics and an analytical solution for the core-stream dimensions show that the device produces a narrow, centrally aligned cylindrical core in which particles are subjected to minimal shear variability, a uniform optical path, and a consistent axial velocity; conditions that improve the reproducibility of scattering and fluorescence signals. The core stream height/width decreases monotonically with increasing sheath-to-sample velocity ratio and attains a stable confinement regime for velocity ratios greater than 60, beyond which additional increases in this value provide negligible refinement. Comparative analysis using Newtonian and shear-thinning rheology indicates that viscosity exerts only a secondary influence on core size. Finally, analytical predictions and numerical results exhibit excellent agreement across the full range of velocity ratio, validating the analytical assumptions of fully developed flow and negligible axial diffusion for this geometry.
The triggering mechanisms and interfacial dynamics of vapor explosions during droplet impact on molten metal surfaces remain inadequately understood, posing significant challenges to safety assessments in nuclear and metallurgical industries. This study systematically investigates the interaction modes between water droplets and molten tin, with particular focus on vapor explosion triggering conditions and the resulting macroscopic hydrodynamic response, characterized by crown width. A high-speed visualization experimental system was employed to characterize droplet-melt interactions over wide ranges of Weber number (We = 109-914) and molten tin temperature (Tm = 232-520 degrees C). Four distinct regimes were identified: spherical state, splashing, vapor explosion, and bubble entrainment. The vapor explosion regime boundaries are governed by the coupled effects of We and Tm, with a critical transition in the lower temperature boundary observed at We approximate to 400. This transition is attributed to a shift in the dominant interfacial instability from Rayleigh-Taylor to Kelvin-Helmholtz, which alters the controlling thermodynamic parameter from the instantaneous contact temperature to the melt pool temperature. The presence of a surface oxide layer was shown to narrow the vapor explosion region while enhancing the macroscopic hydrodynamic response (crown width), owing to a confinement effect that facilitates greater pressure accumulation before oxide layer rupture. The addition of cloud-point additives-polyethylene glycol (PEG), fatty acid methyl ester ethoxylate (FMEE), and Poloxamer 407-significantly suppressed both the occurrence and the macroscopic hydrodynamic response of vapor explosions in a concentration-dependent manner. These findings provide critical insights into the thermohydrodynamic mechanisms governing vapor explosion initiation and present potential pathways for its suppression in practical scenarios.
Taylor dispersion analysis (TDA) in a viscous fluid flow through an annular pipe has been crucial for studying mixing processes in many areas of science and technology. Transport of solutes in blood flow is an important area of application of TDA, which can be effectively modeled using a two-fluid approach due to the complex rheology of blood in microvessels. In the present study, a two-fluid (Casson-Newtonian) model is considered, where the Casson fluid occupies the core region, which is surrounded by a Newtonian region. To account for hematocrit effects, the viscosity of the Casson fluid is assumed to be variable. The solute is considered chemically active and performs an irreversible absorptive-type reaction with the outer wall of the annulus. The statistical moments method is employed to solve the two-dimensional unsteady transport model. Further, using the significance of various moments, the transport process is explained in terms of the exchange coefficient, advection coefficient, dispersion coefficient, skewness, and kurtosis. Also, using the Hermite polynomial representation of central moments, the distribution of solute concentration is evaluated. The purpose of this study is to examine the effects of wall absorption, yield stress, radius ratio, and variable viscosity on the transport processes. It is found that the magnitude of all transport coefficients decreases with an increase in the radius ratio. Convection and dispersion coefficients are decreased by the variable viscosity parameter, but the exchange coefficient is independent. The spreading process is accelerated by the presence of wall absorption as well as peripheral layer thickness. One of the major uses for this model is the analysis of blood flow through arteries with plaque deposits.
This article presents an experimental characterization of the behaviour of the free surface of a liquid contained in a horizontal cylindrical tank with flat end walls and an aspect ratio of L/D=1.14. The cylinder is subjected to forced oscillations in the horizontal plane with fixed amplitude and frequency, followed by a second stage in which the cylinder is held stationary and the liquid undergoes free damped oscillations. An additional parameter in these experiments was the liquid filling level in the tank. Time-resolved measurements of the lateral forces acting on the cylinder and of the axial moment were acquired, along with video recordings for each test case. The free-surface characterization is derived from the experimental video recordings, comprising both a detailed qualitative assessment of the different sloshing regimes and a quantitative analysis through image post-processing.Within the range of excitation frequencies allowed by the experimental setup, the two dominant frequencies controlling the response of the fluid free surface were identified. These frequencies agree with the theoretical and experimental values predicted for the first two antisymmetric modes for all filling levels. When the driving frequency approaches either of these natural frequencies, intense fluid motion develops, generating jets and splashes that disrupt the continuity of the free surface. For our particular excitation amplitude range, each of these resonance bands is flanked by relaxation regions in which the free surface remains compact. The spectra of the force signal with and without external excitation were compared, and the occurrence of a beating phenomenon was observed. The study systematically maps the sloshing regimes as a function of excitation parameters and filling levels, providing practical insights for predicting free-surface behaviour in industrial and cryogenic tank applications, and supporting the validation of numerical models.
Numerical simulations of the two-dimensional oscillatory flow generated by a uniform, oscillating pressure gradient over a wavy wall are made and the results show that simulations, carried out for the same geometrical characteristics of the bottom waviness and the same hydrodynamic parameters, can converge to different states and can generate different steady streaming. Indeed bifurcations, that occur when the Reynolds number becomes larger than critical values, cause the flow to converge towards different states. Although the numerical simulations are made for moderate values of the Reynolds number so that a laminar flow is expected to provide reliable results, the numerical simulations of Sishah and Vittori (2022) and the experimental measurements of Ridler and Sleath (2000) suggest that a similar phenomenon is present even when the flow regime is turbulent and the Reynolds averaged flow field is considered. Hence, it is likely that the differences observed by Ciri et al., (2024) when comparing (i) the oscillatory flow generated over a rippled bed by an external uniform pressure gradient that oscillates in time (pressure-driven flow) and (ii) the flow generated by the oscillations of a rippled bed in a still fluid (shear-driven flow) are due to the growth of different initial perturbations of very small amplitudes that make the flow to converge to different states.
