Force Balance Approach Research Articles

Prediction of the aggregation rate of nanoparticles in porous media in the diffusion-controlled regime.

The fate and aggregation of nanoparticles (NPs) in the subsurface are important due to potentially harmful impacts on the environment and human health. This study aims to investigate the effects of flow velocity, particle size, and particle concentration on the aggregation rate of NPs in a diffusion-limited regime and build an equation to predict the aggregation rate when NPs move in the pore space between randomly packed spheres (including mono-disperse, bi-disperse, and tri-disperse spheres). The flow of 0.2M potassium chloride (KCl) through the random sphere packings was simulated by the lattice Boltzmann method (LBM). The movement and aggregation of cerium oxide (CeO2) particles were then examined by using a Lagrangian particle tracking method based on a force balance approach. This method relied on Newton's second law of motion and took the interaction forces among particles into account. The aggregation rate of NPs was found to depend linearly on time, and the slope of the line was a power function of the particle concentration, the Reynolds (Re) and Schmidt (Sc) numbers. The exponent for the Sc number was triple that of the Re number, which was evidence that the random movement of NPs has a much stronger effect on the rate of diffusion-controlled aggregation than the convection.

Vascular adaptation model from force balance: Physarum polycephalum as a case study

Understanding vascular adaptation, namely what drives veins to shrink or grow, is key for the self-organization of flow networks and their optimization. From the top–down principle of minimizing flow dissipation at a fixed metabolic cost within flow networks, flow shear rate resulting from the flows pervading veins is hypothesized to drive vein adaptation. Yet, there is no proposed mechanism of how flow forces impact vein dynamics. From the physical principle of force balance, shear rate acts parallel to vein walls, and hence, naively shear rate could only stretch veins and not dilate or shrink them. We, here, resolve this paradox by theoretically investigating force balance on a vein wall in the context of the vascular network of the model organism Physarum polycephalum. We propose, based on previous mechanical studies of cross-linked gels, that shear induces a nonlinear, orthogonal response of the actomyosin gel making up vein walls, that can indeed drive vein dilatation. Furthermore, our force balance approach allows us to identify that shear feedback occurs with a typical timescale and with a typical target shear rate that are not universal properties of the material but instead depend smoothly on the vein’s location within the network. In particular, the target shear rate is related to the vein’s hydrostatic pressure, which highlights the role of pressure in vascular adaptation in this context. Finally, since our derivation is based on force balance and fluid mechanics, we believe our approach can be extended, giving attention to specific differences, to describe vascular adaptation in other organisms.

An updated force balance approach to investigate bubble sliding in vertical flow boiling at low and high pressures

An analysis of bubble sliding in vertical flow boiling is conducted using a reworked force balance including a recent formulation of the drag coefficient along with a proper derivation of added mass coefficients. The modeling strategy was further performed to avoid the use of too many empirical parameters.This offers the possibility to develop a non-dimensional approach that exhibits physical ranges of dominance for the detaching forces. Applied to experimental measurements, it shows that the main forces triggering departure by sliding at low and high pressures are respectively Added Mass and Drag forces. Predictions of bubble departure diameter using the force balance achieves good agreement over 122 measurements from several experimental data sets.Bubble sliding measurements from the literature at low and high pressures permitted to validate the model which was able to predict bubble velocity provided the use of a correct bubble growth rate.

An integrated modeling approach to predict critical flow rate for fines migration initiation in sandstone reservoirs and water-bearing formations

Fines migration causes formation damage in sandstone reservoirs and water-bearing subsurface formations. Several factors affect fines migration such as composition and salinity of permeating brine, flow rate, and system pH. Electrostatic forces of van der Waals attraction and electric double layer repulsion, gravitational force and hydrodynamic force all contribute to fines detachment and migration under certain conditions. The current research presents a new integrated model of electrostatic, gravitational, and hydrodynamic forces to estimate the critical injection rate of NaCl brine for fines migration initiation in subsurface formations.The DLVO modeling approach was modified by considering electrostatic, hydrodynamic, and gravitational forces. Parameters such as injection brine salinity, average fine particle size, and zeta potential of sand-brine systems were used, and effective forces were quantified. A microscopic force and torque balance approach was applied to model hydrodynamic forces to modify the DLVO model. The developed models were validated with experimental results.The profiles of injection velocity versus fine particle radius were generated and the models predicted critical flow rates of 0.9, 2.6, and 3.8 cc/min for 0.15 M, 0.2 M, and 0.25 M NaCl, respectively. For model validation, the coreflood experiments were performed on Berea sandstone core samples under given salinities and critical flow rates were determined. Comparable experimental results were obtained with critical flow rates of 1, 3, and 4 cc/min for 0.15 M, 0.2 M, and 0.25 M NaCl, respectively. In addition, sensitivity analysis assesses the impact of different forces on the fines migration phenomenon.Formation damage caused by fines migration is a well-documented problem in sandstone reservoirs and water-bearing formations. Regulating the injection/ permeating fluid rate and salinity can avoid fines migration and associated permeability impairment. Our study presents a novel approach incorporating electrostatic, gravitational, and hydrodynamic forces to accurately predict fines mobilization in fine-containing subsurface formations.

Laser Measurement and Numerical Simulation of Elastomer Stopper Motion during High-Altitude Shipping of Pharmaceutical Syringes.

During high-altitude shipping of pre-filled syringes, pressure differentials can cause the elastomer stopper to move unintentionally. This motion represents a risk to container closure integrity and drug product sterility. To understand and quantitate this risk, we combined high-accuracy laser measurements and numerical simulations of stopper motion. We tested the effects of syringe barrel siliconization, stopper design, syringe orientation, and altitude rate on stopper displacement; only the siliconization factor had a significant effect. Our observations were compared with two mathematical models based on Boyle's Law and a force balance approach. For well-lubricated syringes, stopper motion was reasonably predicted by Boyle's Law (residual ≤ 10%). When the lubricant amount was reduced, Boyle's Law failed to accurately predict stopper motion (residual ≈ 40%). To simulate stopper motion more accurately, we developed a dynamic model in MATLAB-Simulink to incorporate the dry and viscous friction inherent to the lubricated interference fit. Using a Coulomb-viscous subroutine, deviations from Boyle's Law were successfully explained in terms of the displacement, but the system dynamics were not fully accurate. The combination of laser measurements and numerical simulation has yielded unique insight into stopper motion during high-altitude shipping. These tools can provide valuable input to a risk-based drug development strategy to enable global distribution of pre-filled syringes.

Width effect on contact angle hysteresis in a patterned heterogeneous microchannel

The width effect on contact angle hysteresis in a microchannel with patterned heterogeneous surfaces is systematically investigated. In the model, identical defects periodically appear on the background surface. To this end, a droplet's evaporation and condensation processes inside the microchannel are studied by theoretical analysis and numerical simulation based on a diffuse-interface lattice Boltzmann method. The microchannel width effect on the system's equilibrium properties is studied. The results demonstrate that the number of equilibrium configurations increases linearly with the microchannel width ( $b$ ), and has a quadratic relationship with the cosine of the reference contact angle and the heterogeneity strength ( $\varepsilon$ ). The average most stable contact angle is independent of $b$ and is always equal to the contact angle predicted by the Cassie–Baxter equation. For contact angle hysteresis ( $H$ ), when the microchannels are narrow and wide, there are individual-effect-dominated hysteresis (IDH) and collective-effect-dominated hysteresis (CDH), respectively. The IDH and CDH are hysteresis modes corresponding to the jumping behaviour of contact lines affected by individual defects and two neighbouring defects, respectively. Based on the graphical force balance approach, we establish a scaling law to quantify the connection between $H$ , $b$ and $\varepsilon$ . Specifically, in the IDH mode, $H\sim b \varepsilon ^2$ , while in the CDH mode, $H$ increases linearly with $\varepsilon$ but nonlinearly with $b$ .

Adhesion forces of radioactive particles measured by the Aerodynamic Method–Validation with Atomic Force Microscopy and comparison with adhesion models

Median adhesion forces of tritiated tungsten micro-particles deposited on a glass substrate were successfully determined using an aerodynamic method (AM) which is presented in this paper. The original aerodynamic device built for these experiments has been carefully characterized in terms of friction velocities allowing to quantify aerodynamic torque exerted on the particles and to deduce median adhesion forces thanks to a force balance approach. Using the same particle/surface systems (non-radioactive tungsten particles in contact with a glass substrate), distribution of adhesion forces were obtained using AFM for comparison with the AM. The results show a good agreement between the two techniques which allowed to validate the AM. Furthermore, a precise description of the root-mean square roughness (rms) distribution of the glass substrate made it possible to compare the experimental results with different analytical adhesion force models. Integrating the rms roughness distribution of the substrate into the model of Rabinovich et al. showed the best agreement with the present experiments capturing most of the adhesion forces of 10µm to 18µm diameter tungsten particles. Moreover, the method developed in this work made it possible to show that the electrostatic image force arising from the self-charging of tritiated tungsten particles has a negligible contribution in the adhesion of the particles for the studied configuration.

An Updated Force Balance Approach to Investigate Bubble Sliding in Vertical Flow Boiling at Low and High Pressures

An Updated Force Balance Approach to Investigate Bubble Sliding in Vertical Flow Boiling at Low and High Pressures

Characterization and Analysis of Extensile Fluidic Artificial Muscles

Extensile fluidic artificial muscles (EFAMs) are soft actuators known for their large ranges of extension, low weight, and blocked forces comparable to those of pneumatic cylinders. EFAMs have yet to be studied in a way that thoroughly focuses on their manufacturing, experimental characterization, and modeling. A fabrication method was developed for production of two EFAMs. The quasi-static axial force response of EFAMs to varying displacement was measured by testing two specimens under isobaric conditions over a pressure range of 103.4–517.1 kPa (15–75 psi) with 103.4 kPa (15 psi) increments. The muscles were characterized by a blocked force of 280 N and a maximum stroke of 98% at 517.1 kPa (75 psi). A force-balance model was used to analyze EFAM response. Prior work employing the force-balance approach used hyper-elastic constitutive models based on polynomial expressions. In this study, these models are validated for EFAMs, and new constitutive models are proposed that better represent the measured stress values of rubber as a function of strain. These constitutive models are compared in terms of accuracy when estimating pressure-dependent stress–strain relationships of the bladder material. The analysis demonstrates that the new hyper-elastic stress models have an error 5% smaller than models previously employed for EFAMs for the same number of coefficients. Finally, the analysis suggests that the new stress functions have smaller errors than the polynomial stress model with the same number of coefficients, guarantee material stability, and are more conservative about the stress values for strains outside of the testing range.

The not-so-subtle flaws of the force balance approach to predict the departure of bubbles in boiling heat transfer

We present a critical evaluation of the force balance approach in predicting the departure of rapidly growing bubbles from a boiling surface. To this end, we conduct separate effect bubble growth experiments in a carefully controlled environment. We use high-speed video to quantify experimentally all the external forces acting on a growing bubble through the profile of the liquid–vapor interface. Our experimental data show that the momentum conservation equation is always rigorously satisfied, as it should, if the various forces are precisely quantified. However, based on our analysis and our observations, we come to the conclusion that force balance models cannot be either robust or accurate for the purpose of predicting bubble departure. They are not robust because the rate of change of the bubble momentum, i.e., the key quantity that force balance models aim at evaluating as the sum of the external forces, is orders of magnitude smaller than each of the force terms in the momentum conservation equation throughout the entire bubble life cycle. Thus, the slightest error on one of the external forces leads to very different predictions for bubble departure. The approach is also not accurate because the analytical expressions used to estimate the external forces are riddled with questionable assumptions (e.g., on the bubble growth rate, added mass coefficient, contact line length, and contact angle) and uncertainties that are, once again, orders of magnitude larger than the rate of change of the bubble momentum itself.

How particle-particle and liquid-particle interactions govern the fate of evaporating liquid marbles.

Liquid marbles refer to droplets that are covered with a layer of non-wetting particles. They are observed in nature and have practical significance. These squishy objects bounce, coalesce, break, inflate, and deflate while the liquid does not touch the substrate underneath. Despite the considerable cross-disciplinary interest and value of the research on liquid marbles, a unified framework for describing the mechanics of deflating liquid marbles-as the liquid evaporates-is unavailable. For instance, analytical approaches for modeling the evaporation of liquid marbles exploit empirical parameters that are not based on liquid-particle and particle-particle interactions. Here, we have combined complementary experiments and theory to fill this gap. To unentangle the contributions of particle size, roughness, friction, and chemical make-up, we investigated the evaporation of liquid marbles formed with particles of sizes varying over 7 nm-300 μm and chemical compositions ranging from hydrophilic to superhydrophobic. We demonstrate that the potential final states of evaporating liquid marbles are characterized by one of the following: (I) constant surface area, (II) particle ejection, or (III) multilayering. Based on these insights, we developed an evaporation model for liquid marbles that takes into account their time-dependent shape evolution. The model fits are in excellent agreement with our experimental results. Furthermore, this model and the general framework can provide mechanistic insights into extant literature on the evaporation of liquid marbles. Altogether, these findings advance our fundamental understanding of liquid marbles and should contribute to the rational development of technologies.

Effective Navier-slip in non-Newtonian fluid flows over corrugated surfaces

In this study, we show that complex local flow fields, particularly those near corrugated surfaces, can be accurately reproduced with effective Navier-slip boundary conditions over an imaginary smooth surface, in which the normalized slip length can be considered as a surface property even for non-Newtonian fluid flows. The expression for the normalized slip length was derived analytically using the effective viscosity and effective shear rate in a pressure-driven channel flow with a corrugated surface, based on the two-parameter model by separating geometrical and rheological factors with the effective viscosity concept. Our framework was established on the combination of the force balance approach for slip length characterization and the flow quantification method based on the energy dissipation rate. Effects of corrugated patterns with various aspect ratios were investigated. For verification, an example stick–slip–stick flow problem was tested and the results were compared with those of direct simulations. We report that the dimensionless normalized slip length appears to be almost constant and independent of the flow rate (or pressure drop). This implies that the normalized slip length is nearly independent of rheological properties. In addition, the dimensionless slip length of non-Newtonian fluids was found to be close to that of a Newtonian fluid, and it depends on the flow geometry itself.

An improved mechanistic model for predicting bubble characteristic size in subcooled flow boiling

Bubble nucleation and its life cycle in subcooled flow boiling follows a sequence of processes known as bubble ebullition cycle, where the nucleating vapor bubble grows, followed by sliding and departure from the heated surface before the cycle is repeated. In the present work an analytical model has been developed to predict bubble departure and lift-off diameter in subcooled flow boiling. Present model is based on mechanistic force balance approach and it considers few unresolved issues of existing analytical models. Wall contact diameter and relative velocity of sliding bubble with respect to coolant flow have been identified as key parameters which have been either ignored or used as constants in existing analytical models. In the force balance approach dominant forces responsible for bubble departure have been considered while others are ignored. Relative velocity of the vapor bubble is premeditated during bubble lift off predictions and its value is used for optimizing the wall contact diameter while predicting the departure diameter. Present model has been validated with reported experimental data of subcooled flow boiling for a wide range of operating conditions. Compared to available analytical models, present model further reduces the prediction error in estimating bubble characterisctic size.

Force balance approach for advanced approximations in density functional theories.

We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead, it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent settings. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density functional theories that for a homogeneous system and no external vector potential reduce to the exchange-only local-density and Slater Xα approximations.

Modeling Bubble Collisions at Liquid?Liquid and Compound Interfaces.

The collision of a bubble at liquid?liquid, solid?liquid?liquid, and gas?liquid?liquid interfaces, the latter two of which are referred to as compound interfaces, is modeled to predict the bubble?s velocity profile and the pressure buildup and drainage rate of the film(s) formed at impact. A force balance approach, previously outlined for bubble collisions at solid and free surfaces, is employed, which takes into account four forces acting on the bubble: buoyancy, drag, inertia of the surrounding liquid through an added mass force, and a film force resulting from the pressure buildup in the liquid film formed between the bubble and the interface upon impact. The augmented Young?Laplace equation is applied to define the pressure buildup in the film(s), while lubrication theory is employed to define the film drainage rate(s) through the use of the Stokes?Reynolds equation. This is the first time this modeling technique has been implemented for bubble collisions with these interface types as all previous models have relied only on grid-based simulations. The models were validated through experiments conducted here with water and silicone oils of various viscosities and from data found in literature. A reasonable agreement is observed between the theoretical and experimental velocity profiles found for these liquid combinations under varying conditions of impact velocity and top film thickness. The spatiotemporal film thickness and pressure profile evolution, features not yet able to be captured through experiment, are also presented and discussed.

Prediction of Bubble Departure in Forced Convection Boiling with a Mechanistic Model That Considers Dynamic Contact Angle and Base Expansion

A mechanistic model for bubble dynamics in flow boiling that is based on a force balance approach for a growing bubble is introduced. It considers the evaporation of the microlayer underneath the bubble, thermal diffusion and condensation around the bubble cap as well as dynamic inclination and contact angles between the bubble and the heating wall. It requires no recalibration of parameters to predict the bubble growth. Validation against different experimental flow boiling data was carried out with no case-dependent recalibration and yielded good agreement. The simulations confirmed the dependency of bubble departure and lift-off diameters on different parameters such as heat flux, liquid properties, subcooling temperature, system pressure, inclination angle of channel, channel geometry and mass flow rate.

Modelling of bubble departure in flow boiling using equilibrium thermodynamics

To improve the closure relations employed for component-scale Computational Fluid Dynamics simulation of boiling flows, a first-principles method for predicting bubble departure diameters in flow boiling has been developed. The proposed method uses minimisation of the free energy of a system in thermodynamic equilibrium to predict the contact angle and the resistance to sliding of a vapour bubble attached to a surface in the presence of a forced liquid flow. Predictions of the new method are compared with measurements from existing experimental databases, and agreement with data is shown to be comparable or superior to that obtained with previous bubble departure models that have generally used a force-balance approach. The main advantages of the energy-based method over the previous force-based methods are that its formulation is simpler, and that the new model does not require the use of ad hoc tunable parameters to define force terms, or geometrical characteristics of the attached bubble such as its base area, which cannot be confirmed experimentally. This increases confidence in the validity of the new approach when applied outside the rather limited range of current test data on bubble departure in flow boiling.

Evaluation of Particle Resuspension and Single-layer Rates with Exposure Time and Friction Velocity for Multilayer Deposits in a Turbulent Boundary Layer

The present work deals with the resuspension of small nondeformable particles from multilayer deposits in a turbulent boundary layer. A kinetic force-balance approach was adopted to model particle motion at the point of detachment, whereby intermolecular interactions were modeled by the Lennard-Jones potential. The rate of change of the number of particles was estimated for each discrete layer based on existing kinetic models. In particular, the kinetic equations of Lazaridis and Drossinos (1998), LD, and Friess and Yadigaroglu (2001), FY, were implemented and compared using lattice arranged deposits. The influence of exposure time and friction velocity was investigated through the obtained resuspension rates. It was found that the single-layer resuspension rates were substantially affected by the layer position within the deposit as well as considerably influenced by both the exposure time and the friction velocity. Moreover, the numerical results demonstrate that the LD kinetic estimates higher resuspension rates compared to the FY kinetic only for short exposures to the flow, predominantly due to a different expression for the fraction of exposed particles. In addition, the present study recognized the time dependence (i.e., a short-term vs. long-term regime) of the resuspension rate observed both experimentally (Wu et al., 1992; Wang et al., 2012) and by model predictions (Lazaridis and Drossinos, 1998; Friess and Yadigaroglu, 2001; Reeks and Hall, 2001) and confirmed the inverse dependence of the resuspension rate with time in long-term regime. Two regimes were also identified while evaluating the resuspension rate for a range of friction velocities, viz., a low-friction regime in which the resuspension rate increases with friction and a high-friction regime in which the opposite behaviour was observed.

Heat transfer and force balance approaches in bubble dynamic study during subcooled flow boiling of water–ethanol mixture

ABSTRACTIn this paper, the subcooled flow boiling heat transfer coefficient of pure water, water–ethanol mixture and pure ethanol is determined experimentally in horizontal rectangular channels for various parameters like heat flux, mass flux and channel inlet temperatures. Flow visualization is carried out using high speed camera. The bubble departure diameter, growth period and waiting period of bubbles are determined. Correlations are developed for subcooled flow boiling Nusselt number of water–ethanol mixture based on force balance approach and heat transfer approach. The parameters considered for correlation are grouped as dimensionless numbers by Buckingham π-theorem. The significance of each dimensionless number on heat transfer coefficient is discussed. The correlations developed for subcooled flow boiling heat transfer coefficient are validated with the experimental data. They are found to be in good agreement with the experimental data. It is found that the correlation based on force balance approach predicts the subcooled flow boiling Nusselt number well when compared with that of heat transfer approach correlation.

Physical theory for near-bed turbulent particle suspension capacity

Abstract. The inability to capture the physics of solid-particle suspension in turbulent fluids in simple formulas is holding back the application of multiphase fluid dynamics techniques to many practical problems in nature and society involving particle suspension. We present a force balance approach to particle suspension in the region near no-slip frictional boundaries of turbulent flows. The force balance parameter Γ contains gravity and buoyancy acting on the sediment and vertical turbulent fluid forces; it includes universal turbulent flow scales and material properties of the fluid and particles only. Comparison to measurements shows that Γ = 1 gives the upper limit of observed suspended particle concentrations in a broad range of flume experiments and field settings. The condition of Γ > 1 coincides with the complete suppression of coherent turbulent structures near the boundary in direct numerical simulations of sediment-laden turbulent flow. Γ thus captures the maximum amount of sediment that can be contained in suspension at the base of turbulent flow, and it can be regarded as a suspension capacity parameter. It can be applied as a simple concentration boundary condition in modelling studies of the dispersion of particulates in environmental and man-made flows.