Maximal Spreading Research Articles

Hydrodynamics during an immiscible compound droplet impact on a liquid pool

A numerical model based on the volume of fluid method is adopted to numerically study the hydrodynamics of an immiscible compound droplet impacting on a liquid pool. This numerical simulation achieves good agreement with the experimental results for both the evolutions of interface and cavity depth after droplet impact. By conducting the numerical simulation, three impact regimes are identified, namely, engulfment, bursting, and splashing, and a regime map with splashing threshold is plotted to quantitatively represent them. Under both bursting and splashing regimes, the inner and outer droplets have similar deformation behaviors during impact. The changes in impact velocity and inner droplet size have a greater effect on the hydrodynamic behaviors of the compound droplet under the bursting regime than that under the splashing regime. Larger inner droplet sizes can significantly reduce the deformation of the droplet and cavity. Moreover, to provide valuable guidance for controlling the compound droplet impacting on the liquid pool in the related real applications, a scaling correlation with a modified Weber number is proposed to predict the maximal spreading of the droplet.

Impact dynamics of compound drops of fluids with density contrast

The dynamics of compound drops impacting on a flat substrate is numerically investigated using a ternary-fluid diffuse-interface method, with the aim of assessing the effect of a density difference between the inner and outer droplets (denoted by $\lambda$ ) on the evolution of the interfaces. With the help of numerical simulations, we find that, at the intermediate stage of drop impact, the inner droplet exhibits a self-similar deformation at $\lambda =1$ and relatively high Weber number, and experiences more or less a uniform acceleration for various $\lambda$ . In particular, the acceleration magnitude at $\lambda \ne 1$ can be correlated with the acceleration at $\lambda =1$ and the Atwood number. When the inner droplet is denser than the outer one, a lamella occurs at the spreading front of the inner droplet. We present a scaling analysis of the thickness of the lamella, and the resultant theoretical prediction is in good agreement with numerical results. At the maximal spreading of the compound drop, a bulging structure is formed around the symmetry axis due to the presence of the inner droplet, thereby effectively reducing the liquid supply to the spreading front and leading to a decrease of maximal spreading ratio $\beta _{max}$ as compared with a pure drop. We proposed a corrected Weber number $We^*_\lambda$ by taking account of the combined effects of $\lambda$ , volume fraction of the inner droplet, Weber number and morphology of the compound drop. Integrating $We^*_\lambda$ with the universal model of $\beta _{max}$ for impacting pure drops, we successfully build up a new model for predicting the maximal spreading ratio of impacting compound drops with various $\lambda$ .

Emergence and competition of virus variants in respiratory viral infections.

The emergence of new variants of concern (VOCs) of the SARS-CoV-2 infection is one of the main factors of epidemic progression. Their development can be characterized by three critical stages: virus mutation leading to the appearance of new viable variants; the competition of different variants leading to the production of a sufficiently large number of copies; and infection transmission between individuals and its spreading in the population. The first two stages take place at the individual level (infected individual), while the third one takes place at the population level with possible competition between different variants. This work is devoted to the mathematical modeling of the first two stages of this process: the emergence of new variants and their progression in the epithelial tissue with a possible competition between them. The emergence of new virus variants is modeled with non-local reaction-diffusion equations describing virus evolution and immune escape in the space of genotypes. The conditions of the emergence of new virus variants are determined by the mutation rate, the cross-reactivity of the immune response, and the rates of virus replication and death. Once different variants emerge, they spread in the infected tissue with a certain speed and viral load that can be determined through the parameters of the model. The competition of different variants for uninfected cells leads to the emergence of a single dominant variant and the elimination of the others due to competitive exclusion. The dominant variant is the one with the maximal individual spreading speed. Thus, the emergence of new variants at the individual level is determined by the immune escape and by the virus spreading speed in the infected tissue.

The rebounding-coalescing behaviors in drop-on-drop impact on a superhydrophobic surface

The great anti-accumulation performance of drop-on-drop impact on a superhydrophobic surface is beneficial to self-cleaning and anti-icing. Hence, the rebounding-coalescing behaviors in drop-on-drop impingement with varying Weber number and offset ratio are studied experimentally in the present work. The complete regime map of rebounding states is proposed, which can be divided into no-coalesce, jug-like, pancake-like, and pendulum-like rebounding-coalescing behaviors. Subsequently, the increase in the contact time in pendulum-like rebounding-coalescing behaviors is captured and described by a linear model well. Finally, a theoretical prediction based on momentum conservation for the averaged maximal spreading radius of the coalesced droplet is provided. Our approach provides insight into a mechanism of the rebounding-coalescing behaviors, which is helpful for the improvement in related applications.

On the maximal spreading of drops impacting onto a no-slip substrate

We numerically study the impact of a liquid drop onto no-slip rigid substrates with different wettabilities using a diffuse interface method, aiming to obtain a universal model for the maximal spreading of the impacting drop at moderate Weber numbers. We find that the wettability plays an important role in the maximal spreading and that the ratio of the surface energy to the initial kinetic energy of the drop at the maximal spreading, η, follows η∼We−1/2 at high fixed Reynolds numbers, where We is the Weber number. Taking account of the wettability effect, we obtain a scaling law at high Reynolds numbers from an analysis of energy transformation. This scaling law is compatible with the one derived from the momentum balance at the high impact velocity by Clanet et al. [“Maximal deformation of an impacting drop,” J. Fluid Mech. 517, 199–208 (2004)]. Moreover, we attribute it to the presence of a viscous–capillary regime, in which the viscous dissipation of the kinetic energy from the substrate is as significant as the kinetic energy transformed into the surface energy. Accordingly, we identify a new impact parameter, which makes all the numerical results of maximum drop deformation (from the viscous regime to the viscous–capillary regime with Reynolds number up to 104) collapse onto a single curve. Finally, we propose a universal model, the predictions of which are shown to agree well with numerical results for a wide range of Weber and Reynolds numbers.

Two dimensional computational model coupling myoarchitecture-based lingual tissue mechanics with liquid bolus flow during oropharyngeal swallowing

Biomechanical relationships involving lingual myoanatomy, contractility, and bolus movement are fundamental properties of human swallowing. To portray the relationship between lingual deformation and bolus flow during swallowing, a weakly one-way solid-fluid finite element model (FEM) was derived employing an elemental mesh aligned to magnetic resonance diffusional tractography (Q-space MRI, QSI) of the human tongue, an arbitrary Lagrangian-Eulerian (ALE) formulation with remeshing to account for the effects of lingual surface (boundary) deformation, an implementation of patterned fiber shortening, and a computational visualization of liquid bolus flow. Representing lingual tissue deformation in terms of its 2D principal Lagrangian strain in the mid-sagittal plane, we demonstrated that the swallow sequence was characterized by initial superior-anterior expansion directed towards the hard palate, followed by sequential, radially directed, contractions of the genioglossus and verticalis to promote lingual rotation (lateral perspective) and propulsive displacement. We specifically assessed local bolus velocity as a function of viscosity (perfect slip conditions) and observed that a low viscosity bolus (5 cP) exhibited maximal displacement, surface spreading and local velocity compared to medium (110 cP, 300 cP) and high (525 cP) viscosity boluses. Analysis of local nodal velocity revealed that all bolus viscosities exhibited a bi-phasic progression, with the low viscosity bolus being the most heterogeneous and fragmented and the high viscosity bolus being the most homogenous and cohesive. Intraoral bolus cohesion was depicted in terms of the distributed velocity gradient, with higher gradients being associated with increased shear rate and bolus fragmentation. Lastly, we made a sensitivity analysis on tongue stiffness and contractility by varying the degree of extracellular matrix (ECM) stiffness through effects on the Mooney-Rivlin derived passive matrix and by varying maximum tetanized isometric stress, and observed that a graded increase of ECM stiffness was associated with reduced bolus spreading, posterior displacement, and surface velocity gradients, whereas a reduction of global contractility resulted in a graded reduction of obtainable accommodation volume, absent bolus spreading, and loss of posterior displacement. We portray a unidirectionally coupled solid-liquid FEM which associates myoarchitecture-based lingual deformation with intra-oral bolus flow, and deduce that local elevation of the velocity gradient correlates with bolus fragmentation, a precondition believed to be associated with aspiration vulnerability during oropharyngeal swallowing.

Distinct timing of neutrophil spreading and stiffening during phagocytosis

Phagocytic cells form the first line of defense in an organism, engulfing microbial pathogens. Phagocytosis involves cell mechanical changes that are not yet well understood. Understanding these mechanical modifications promises to shed light on the immune processes that trigger pathological complications. Previous studies showed that phagocytes undergo a sequence of spreading events around their target followed by an increase in cell tension. Seemingly in contradiction, other studies observed an increase in cell tension concomitant with membrane expansion. Even though phagocytes are viscoelastic, few studies have quantified viscous changes during phagocytosis. It is also unclear whether cell lines behave mechanically similarly to primary neutrophils. We addressed the question of simultaneous versus sequential spreading and mechanical changes during phagocytosis by using immunoglobulin-G-coated 8- and 20-μm-diameter beads as targets. We used a micropipette-based single-cell rheometer to monitor viscoelastic properties during phagocytosis by both neutrophil-like PLB cells and primary human neutrophils. We show that the faster expansion of PLB cells on larger beads is a geometrical effect reflecting a constant advancing speed of the phagocytic cup. Cells become stiffer on 20- than on 8-μm beads, and the relative timing of spreading and stiffening of PLB cells depends on target size: on larger beads, stiffening starts before maximal spreading area is reached but ends after reaching maximal area. On smaller beads, the stiffness begins to increase after cells have engulfed the bead. Similar to PLB cells, primary cells become stiffer on larger beads but start spreading and stiffen faster, and the stiffening begins before the end of spreading on both bead sizes. Our results show that mechanical changes in phagocytes are not a direct consequence of cell spreading and that models of phagocytosis should be amended to account for causes of cell stiffening other than membrane expansion.

Maximizing spreading in complex networks with risk in node activation

It is widely acknowledged that the initial spreaders play an important role in the spread of information in complex networks. Thus, a variety of centrality-based methods have been proposed for identifying the most influential spreaders. However, most existing studies overlook the fact that, in real social networks, it is more costly and difficult to convince influential individuals to act as initial spreaders, resulting in a high risk to maximal spreading. In this paper, we address this problem on the basis of the assumption that the activation of large-degree nodes carries a higher risk than that of small-degree nodes. We aim to identify the initial spreaders that most effectively maximize the spreading when considering both the activation risk and the outbreak size of the initial spreaders. Analysis of random networks reveals that the degree of the optimal initial spreaders does not correspond to the largest node degree in the network, but is instead determined by the infection probability and difference in activation risk among nodes with different degrees. We propose a risk-aware metric to identify the most effective spreaders in real networks. Numerical simulations show that this risk-aware metric outperforms the existing benchmark centralities in terms of maximizing the spreading.

Maximal spreading of droplet during collision on particle: Effects of liquid viscosity and surface curvature

This study uses the level contour reconstruction method to numerically investigate the maximum spreading due to droplet collision with a dry, stationary, spherical particle. We consider a broad range of impact conditions: Weber number 30–90, Ohnesorge number 0.0013–0.7869, and droplet-to-particle size ratio 1/10–1/2, and quantitatively and systematically analyze 120 collision cases to understand how liquid viscosity and surface curvature affect the maximum spreading. The maximum spreading increases on the smaller particles for both the capillary and viscous regimes, but the underlying physics clearly differ. The increase in maximum spreading is governed mainly by the surface deformation of the rim for the capillary regime and viscous dissipation for the viscous regime. An empirical correlation that can be applied to the droplet impact on both a particle and a flat surface is also presented. The model shows good agreement with existing experimental data as well as our simulation results within a deviation range of ±15%.

The role of oscillation in ellipsoidal drop impact on a solid surface

Ellipsoidal shapes of drops can significantly modify the impact dynamics and suppress the rebound by inducing symmetry breaking in the mass and momentum distributions compared to the axisymmetric dynamics of typical drops. However, the previous works have assumed that the drop oscillation at the moment of impact only slightly affects the post-dynamics although the oscillation must be involved in the spreading. Here, we study the impact dynamics of the oscillating ellipsoidal drops on non-wetting surfaces as a function of the ellipticity, oscillation phase, and Weber number (We) experimentally and numerically. The spreading dynamics show notable hysteretic features in the maximal spreading diameters at the four regions of the oscillation phase. The hysteresis appears more prominently in prolate drops than in oblate drops and becomes remarkably suppressed at the four phases as We increases. Momentum analysis shows that the phases for shaping the drops spherically can drive higher asymmetry in the horizontal momenta than the other phases for shaping the drops ellipsoidally. The momentum asymmetry in the horizontal axes indicates that the oscillation phase as well as the ellipticity can play an important role in altering the hydrodynamics and reducing the bounce magnitude.

Biomechanical Analysis of Sagittal Plane Pin Placement Configurations for Pediatric Supracondylar Humerus Fractures

Anterior to posterior (AP) pinning is the recommended sagittal pin configuration in divergent lateral entry coronal pinning of pediatrics supracondylar fractures. However, there was still a lack of evidence regarding alternative sagittal pins configurations. We aimed to compare the construct stiffness of alternative sagittal pin configurations by using synthetic bone models. Sixty synthetic pediatric humeri were osteotomized to create a supracondylar fracture. After the fracture reduction, all specimens were fixed in the coronal plane with divergent lateral entry pin configurations in four different patterns in the sagittal plane: AP, crossed, divergent and parallel sagittal pin configuration. Each configuration was tested with five loading patterns. The AP sagittal pin had significantly lower construct stiffness than the divergent (p = 0.003) and the parallel sagittal pin configuration (p = 0.005) in external rotation loading tests. The divergent sagittal pin had the highest construct stiffness in extension, valgus, and external rotation loads, but the parallel sagittal pin had lower construct stiffness under extension load than the divergent and crossed sagittal pin configurations. The divergent sagittal pin configuration provides greater construct stiffness than other sagittal pin configurations due to the maximal pin spreading distance at the fracture site and the pin angle lock mechanism.

Head-on collision of two immiscible droplets of different components

We numerically study the head-on collisions of two immiscible droplets of different components and focus on the effects of droplet inertia and interfaces, which are expected to play a crucial role in the interaction between the two droplets. A ternary-fluid diffuse-interface method is used here after being validated by comparing against experiments of the collision between an aqueous droplet and a silicone oil droplet. In order to figure out how the droplet inertia and interfaces affect the dynamic behavior after the collision, axisymmetric simulations are performed with various Weber number We and surface tension ratio λ, i.e., the ratio of the surface tension coefficient of the liquid–liquid to the liquid–gas interfaces. Their effects on the film thickness, maximal deformation of the colliding droplets, and the corresponding contact time are investigated. To describe the collision dynamics, we propose an equivalent surface tension σ* based on the analysis of the energy conservation and morphology of the colliding droplets. Using the equivalent surface tension σ*, we theoretically predict the film thickness, maximal spreading time, and deformation of the colliding droplets. The theoretical predictions are in good agreement with the numerical results.

Drops retracting while forming a rim

HypothesisSurfactant laden droplets may spread faster on a substrate and, subsequently, retract (spontaneously reversing the drop’s direction). We hypothesize that this Marmur-Lelah type retraction can be explained by a de Gennes-type triple line fluctuation expression that is modified to represent our anisotropic surfactant adsorption. This explanation requires that the retraction originates inner to the triple line (not at the triple line itself). ExperimentsDrops of oil with surfactant (mainly tetradecane with octadecylamine) were allowed to spread on freshly cleaved mica surfaces at various concentrations and recorded with a high-speed camera. FindingsAt low concentrations, the subsequent retraction left a rim of liquid at the triple line location of maximal spreading whose thickness was inversely related to the surfactant concentration.This indeed agrees with de Gennes’ triple line fluctuation expression that is modified to fit the anisotropic adsorption of the surfactant during the spreading period, which induces a solid–liquid interfacial energy gradient. According to this explanation, the rim may exist also at high surfactant solution concentrations, however, there can be a limit at which the surfactant solution concentration is so high that the rim’s thickness is practically zero.

Numerical simulation of droplet impact on wettability-patterned surfaces

Numerical simulations have unexplored potential in the study of droplet impact on nonuniform wettability surfaces. In this paper, we compare numerical and experimental results to investigate the application potential of a volume-of-fluid method utilized in OpenFOAM. The approach implements the Kistler model for the dynamic contact angle of impacting droplets. We begin with an investigation into the influence of the most important solver parameters to optimize the computational setup and reach the best compromise between computational cost and solution errors, as assessed in comparison to experimental results. Next, we verify the accuracy of the predictions for droplet impact on uniformly hydrophilic or superhydrophobic surfaces. Benchmarking the maximal spreading factor, contact, and spreading times, as well as contact-line behavior, we show strong agreement between the present numerical results and the models of Pasandideh-Fard et al., Phys. Fluids 8, 650 (1996) and Clanet et al., J. Fluid Mech. 517, 199 (2004). Lastly, we demonstrate the capability of the model to accurately predict outcome behaviors of droplets striking distributed-wettability surfaces, which introduce 3D outcome characteristics, even in orthogonal impact. The model successfully predicts droplet splitting and vectoring, as reported in the experiments of Schutzius et al., Sci. Rep. 4, 7029 (2014). Finally, we demonstrate a configuration wherein a droplet centrally strikes a circular disk of different wettability than its surrounding domain. The main contribution of the present paper is a numerical model capable of accurately simulating droplet impact on spatially nonuniform wettability patterns of any foreseeable design.

Biphasic mechanosensitivity of T cell receptor-mediated spreading of lymphocytes.

Mechanosensing by T cells through the T cell receptor (TCR) is at the heart of immune recognition. While the mechanobiology of the TCR at the molecular level is increasingly well documented, its link to cell-scale response is poorly understood. Here we explore T cell spreading response as a function of substrate rigidity and show that remarkably, depending on the surface receptors stimulated, the cellular response may be either biphasic or monotonous. When adhering solely via the TCR complex, T cells respond to environmental stiffness in an unusual fashion, attaining maximal spreading on an optimal substrate stiffness comparable to that of professional antigen-presenting cells. However, in the presence of additional ligands for the integrin LFA-1, this biphasic response is abrogated and the cell spreading increases monotonously with stiffness up to a saturation value. This ligand-specific mechanosensing is effected through an actin-polymerization-dependent mechanism. We construct a mesoscale semianalytical model based on force-dependent bond rupture and show that cell-scale biphasic or monotonous behavior emerges from molecular parameters. As the substrate stiffness is increased, there is a competition between increasing effective stiffness of the bonds, which leads to increased cell spreading and increasing bond breakage, which leads to decreased spreading. We hypothesize that the link between actin and the receptors (TCR or LFA-1), rather than the ligand/receptor linkage, is the site of this mechanosensing.

Efficient Design Method of Segmented Lenses for Lighting Applications with Prescribed Intensity and Low Peak Luminance

ABSTRACT Light emitting diodes (LEDs) that are used today in general lighting applications provide high luminous flux from small packages, which can result in high peak luminance and glare. The use of diffusors allows reducing peak luminances, but these components do not allow accurate control over the resulting intensity pattern as is possible with nonimaging lenses for low-étendue sources such as LEDs. In this article, a new design method is presented to create a rotational or transverse symmetric segmented lens that results in a reduced peak luminance but still allows excellent control over the resulting intensity distribution. Each segment of the lens spreads out the light in a certain angular range, but the different contributions of each lens segment result together in the desired target intensity distribution. The design method is based on the iterative optimization of a linear transformation of a source intensity distribution into a target intensity distribution, starting from a transformation that yields maximal light beam spreading.

Empirical paths to the spread of information in location-based social networks

Spreading phenomena in complex networks have attracted much attention in recent years. However, most of the previous works only concern the critical thresholds and final states of the spread. In this paper, we investigate the empirical spreading paths in real location-based networks and find an abnormal phenomenon that the transferring probability of an epidemic between users varies with time, which violates the classical spreading models with a constant transferring probability. Besides, we observe an interesting delay gap between the maximal spreading velocity and the maximal transferring probability, where the spreading velocity refers to the fraction of newly infected nodes, and transferring probability represents the probability that a susceptible individual gets infected by one of its infected neighbors. Then we propose an advanced SI (susceptible-infected) model to analyze the problem, which could analytically explain the delay gap between the spreading velocity and the transferring probability. Experiments in BA and ER model networks demonstrate the effectiveness of our model. Thus, our work provides a deep understanding of the dynamics of the spreading problems.

Optimizing MDS Coded Caching in Wireless Networks With Device-to-Device Communication

We consider the caching of content in the mobile devices in a dense wireless network using maximum distance separable (MDS) codes. We focus on an area, served by a base station (BS), where mobile devices move around according to a random mobility model. Users requesting a particular file download the coded packets from caching devices within a communication range using device-to-device communication. If additional packets are required to decode the file, these are downloaded from the BS. We analyze the device mobility and derive a good approximation of the distribution of caching devices within the communication range of mobile devices at any given time. We then optimize the MDS codes to minimize the network load under a cache size constraint and show that using optimized MDS codes results in significantly lower network load compared to when caching the most popular files. We further show, numerically, that caching coded packets of each file on all mobile devices, i.e., maximal spreading, is optimal.

On the maximal spreading of impacting compound drops

We numerically study the impact of a compound drop on a hydrophobic substrate using a ternary-fluid diffuse-interface method, aiming to understand how the presence of the inner droplet affects the spreading dynamics and maximal spreading of the compound drop. First, it is interesting to see that the numerical results for an impacting pure drop agree well with the universal rescaling of maximal spreading ratio proposed by Lee et al. (J. Fluid Mech., vol. 786, 2016, R4). Second, two flow regimes have been identified for an impacting compound drop: namely jammed spreading and joint rim formation. The maximal spreading ratio of the compound drop is found to depend on the volume fraction of the inner droplet $\unicode[STIX]{x1D6FC}$, the surface tension ratio $\unicode[STIX]{x1D6FE}$, the Weber number and the flow regime. Moreover, we propose a universal rescaling of maximal spreading ratio for compound drops, by integrating the one for pure drops with a corrected Weber number that takes $\unicode[STIX]{x1D6FC}$, $\unicode[STIX]{x1D6FE}$ and the flow regime into account. The predictions of the universal rescaling are in good agreement with the numerical results for impacting compound drops.

Anisotropic drop spreading on superhydrophobic grates during drop impact.

We study the influence of geometric anisotropy of micro-grate structures on the spreading dynamics of water drops after impact. It is found that the maximal spreading diameter along the parallel direction to grates becomes larger than that along the transverse direction beyond a certain Weber number, while the extent of such an asymmetric spreading increases with the structural pitch of grates and Weber number. By employing grates covered with nanostructures, we exclude the possible influences coming from the Cassie-to-Wenzel transition and the circumferential contact angle variation on the spreading diameter. Then, based on a simplified energy balance model incorporating slip length, we propose that slip length selectively enhances the spreading diameter along the parallel direction, being responsible for the asymmetric drop spreading. We believe that our work will help better understand the role of microstructures in controlling the drop dynamics during impact, which has relevance to various engineering applications.