Ratio Of Force Research Articles

Forced motion modes of a patch of flexible rods in open channel flows

Flexible vegetation is common in riverine and coastal ecosystems. The patch of flexible vegetation is influenced by various factors, resulting in a series of characteristic modes of motion. This study aims to investigate the influence of the Cauchy number (Ca, the ratio of the hydrodynamic drag force to the bending rigidity, i.e., the inverse of the dimensionless bending rigidity) and the solid volume fraction (which reflects the distribution density of a patch of flexible rods) on the motion modes. Additionally, the induction mechanism of fluid and flexible vegetation interaction on motion modes is investigated. A semi-resolved coupling numerical model was employed to simulate the fluid and structure interaction. The results show that the Cauchy number and solid volume fraction influence the motion modes to different extents. Notably, the effect of Ca was significant within the designed range of the two parameters. The wavelength of the monami mode generally shows little variation compared to that observed in the Kelvin–Helmholtz (K-H) vortex, which results from the mixing layer flow instability. The physical mechanism that the motion mode of a patch of flexible rods is induced by the interaction between water flow and flexible rods is further validated and cognized. When the K-H vortex frequency, the natural frequency of the patch in water, and the motion frequency of the patch are close, the patch exhibits motion in the monami mode. Otherwise, the patch will exhibit motion in erect, swaying, and prone mode.

The lesser tuberosity C-block osteotomy for anatomical total shoulder arthroplasty has no negative impact on the volumetric ratio of the transversal force couple.

Mobilization of the subscapularis muscle (SSC) is crucial for optimal access to the glenohumeral joint during anatomical total shoulder arthroplasty (ATSA). However, the ideal mobilization technique remains controversial. This study aimed to assess the impact of the lesser tuberosity C-block osteotomy, a modified lesser tuberosity osteotomy, on the postoperative subscapularis (SSC) volume following anatomical shoulder arthroplasty and compare it to the volume of the infraspinatus/teres minor. All patients between 2006-2022 who received an anatomical total shoulder arthroplasty with the lesser tuberosity C-block osteotomy for primary shoulder osteoarthritis or avascular necrosis of the humeral head with a minimum follow-up of one year and received full scapulae CT scans postop were included in the study. Utilizing imaging software and a validated method established for healthy shoulders, we assessed the postoperative volume of the transversal force couple. 56 patients (59 shoulders) with an average follow-up of 5 years were included in the study. A strong correlation (rₛ=0.954) was observed between the volumes of the anterior and posterior parts of the transverse force couple, with no statistically significant difference (P=0.207) noted in muscle volumes. The mean transverse force couple ratio was 1.01±0.06, with similar values found across all age groups. Intraobserver and interobserver correlation coefficients were excellent. Using the lesser tuberosity C-block osteotomy during anatomical total shoulder arthroplasty does not disrupt the essential volumetric balance between the subscapularis and infraspinatus/teres minor, as observed in a well-functioning transverse force couple.

Effect of amplitude on resonance and propulsive characteristics of a pitching flexible panel

We present the effect of amplitude on resonance and propulsive characteristics of a pitching flexible panel in quiescent water. The first mode of the resonant frequency (fn1) of the fluid-panel system is determined based on the measured peak lateral excursion of the trailing-edge of the flexible panel at various input frequencies and pitch amplitudes. Both the resonant frequency and peak amplitude ratio a∗ are found to decrease with an increase in the pitch angle. The propulsive force ratio T∗ and power ratio P∗ are defined as the ratio of the mean propulsive force generated and the propulsive power required for the flexible panel to the rigid panel, respectively. The variation of T∗ and P∗ as a function of the frequency ratio f∗=f/fn1 shows that both the propulsive force and the required power are strongly interlinked to the peak lateral excursion of the trailing-edge of the flexible panel. The characteristic flapping velocity of the trailing edge governs the propulsive performance such that propulsive force generation and power required are found to increase with an increase in the characteristic flapping velocity. Moreover, the pitch amplitude can be considered as an input parameter to manipulate the resonance characteristics of a flexible panel, thereby achieving better propulsive performance for various cruise speeds.

Ecomorphology of South American Penguins.

A major goal of evolutionary ecology is to understand the interaction between ecological differences and the functional morphology of organisms. Studies of this type are common among flying birds but less so in penguins. Penguins (Spheniscidae) are the most derived extant underwater flying birds using their wings for swimming and beak when foraging. The Humboldt Penguin (Spheniscus humboldti) and Magellanic Penguin (S. magellanicus) occur along the coast of South America and their morphology was compared in allopatry and sympatry throughout their ranges. Measurements included: mass, tarsus length, four beak/head dimensions, bite force, wing loading, and aspect ratio. A thin-plate spline/relative warp analysis was also used to detect subtle differences in wing shape. Both species generally overlapped in trait morphology, but Magellanic Penguins showed greater trait diversity. Wing morphology was more homogenous between species than beak morphology indicating a similar mode of locomotion but potential differences in prey procurement. Morphological character displacement in sympatry was only evident in beak length. Local adaptation was common in other traits, and Punta Norte (Argentina) was often distinct in having high variation, notably in beak depth, wing loading, and wing shape (relative warp 1). This may be attributed to the fact that penguins here dive deep and forage farther from their colony; they also have a greater colony size that may contribute to greater intraspecific competition for resources. These results support a potentially optimal wing design for aquatic movement, which likely applies to other penguin species. Differences in morphology may also be related to differences between Atlantic and Pacific ecosystems.

Jazz dancing for improving cardiorespiratory fitness, body composition, muscle strength, and sleep quality in postmenopausal women: a randomized clinical trial with 6- and 12-month follow-ups.

The aim of the study was to analyze the effects of 16 weeks of Jazz Dance training compared to a control group in postmenopausal women, postintervention, and at the 6- and 12-month follow-ups, on cardiorespiratory fitness, body composition, muscle strength, and sleep quality. Two-arm randomized clinical trial with a total of 47 women (jazz dance intervention group [JDIG] [n = 23] and control group (CG) [n = 24]) with a mean age of 53.41 ± 2.8 y. Data collection was carried out at four times, baseline, postintervention, and 6- and 12-month follow-ups using the 6-minute walk test (cardiorespiratory fitness); bioimpedance (body composition); isokinetic dynamometry (muscle strength); and the Pittsburgh Sleep Quality Index (sleep quality). In the intention-to-treat analysis, the results showed positive differences for the JDIG in cardiorespiratory fitness at all time points (P = 0.034) and in the group x time interaction (P = <0.001). Lower limb muscle strength showed differences from baseline to postintervention and from baseline to the 12-month follow-up for the concentric force ratio (P = 0.021; P = 0.009). However, for peak extension and flexion, the results were not positive for the JDIG. There was a short-term improvement in sleep duration for the JDIG (P = 0.001) and significant intergroup differences in subjective sleep quality, where the JDIG showed better results compared to the CG (P = 0.041). Jazz Dance is effective for improving cardiorespiratory fitness (in the short, medium, and long term) and sleep quality (in the short and medium term); however, it does not seem to have presented sufficient intensity and duration for facilitating changes in body composition or increasing lower limb muscle strength in postmenopausal women.

Load-to-strength ratio as an estimate of wrist facture after gastric bypass vs gastric banding.

Bariatric surgeries such as Roux-en-Y gastric bypass (RYGB) and adjustable gastric banding (AGB) lead to long-term deficits in bone density but are also accompanied by decreased weight, which may lower the impact force with falls. The aim of this study was to compare the long-term skeletal impact of RYGB and AGB using a biomechanical evaluation of load-to-strength ratio at the distal radius as a surrogate for wrist fracture risk. We conducted a cross-sectional study evaluating bone microarchitectural parameters and bone turnover in adults who received either RYGB or AGB surgery ≥10yr ago (RYGB: n= 22; AGB: n= 23). Bone strength at the distal radius was estimated by microfinite element analysis from HR-pQCT. We used a single-spring biomechanical model to estimate impact force and then calculated load-to-strength ratio as a ratio of impact force to bone strength, with higher load-to-strength ratios representing a higher susceptibility to fracture. In multivariable analyses, the RYGB group had higher bone resorption marker C-telopeptide (CTX) levels, lower volumetric bone density, and worse cortical and trabecular microarchitectural parameters than the AGB group. Furthermore, estimated bone strength at the radius was lower in the RYGB group (3725 ± 139N vs 4141 ± 157N, p = .030), and the load-to-strength ratio was higher in RYGB group as compared with AGB (0.84 ± 0.04 vs 0.72 ± 0.05, p = .035), suggestive of higher propensity for wrist fracture. Taken together, these results indicate the long-term deleterious skeletal effects are more concerning with RYGB than AGB.

Stability and agility trade-offs in spring-wing systems.

Flying insects are thought to achieve energy-efficient flapping flight by storing and releasing elastic energy in their muscles, tendons, and thorax. However, 'spring-wing' flight systems consisting of elastic elements coupled to nonlinear, unsteady aerodynamic forces present possible challenges to generating stable and responsive wing motion. The energetic efficiency from resonance in insect flight is tied to the Weis-Fogh number (N), which is the ratio of peak inertial force to aerodynamic force. In this paper, we present experiments and modeling to study how resonance efficiency (which increases withN) influences the control responsiveness and perturbation resistance of flapping wingbeats. In our first experiments, we provide a step change in the input forcing amplitude to a series-elastic spring-wing system and observe the response time of the wing amplitude increase. In our second experiments we provide an external fluid flow directed at the flapping wing and study the perturbed steady-state wing motion. We evaluate both experiments across Weis-Fogh numbers from1<N<10. The results indicate that spring-wing systems designed for maximum energetic efficiency also experience trade-offs in agility and stability as the Weis-Fogh number increases. Our results demonstrate that energetic efficiency and wing maneuverability are in conflict in resonant spring-wing systems, suggesting that mechanical resonance presents tradeoffs in insect flight control and stability.

Comparing and optimizing different bio-inspired crash box designs

Abstract The use of bio-inspired structures in vehicles is promising. The crashworthiness performance of crash boxes inspired by honeycomb, bamboo, and horsetail structures was compared according to impact simulations. Results were compared regarding specific energy absorption (SEA), peak crushing force (PCF), and specific energy absorption to peak crushing force ratio. Single and multi-objective optimization studies were carried out with a horsetail crash box, which gave the best results. This crash box design can be used in vehicles to improve passive safety.

Dynamic similarity criteria for simple cases of buildings and structures aerodynamics

The work concerns dynamic similarity criteria of various phenomena occurring in hydraulics and fluid dynamics originally derived from ratios of forces and forces moments affecting these phenomena. The base of dynamic similarity criteria formulations and considerations is A.Flaga’s method and procedure for determining dynamic similarity criteria in different issues of fluid-solid interactions i.e. at different fluid-solid relative motions. The paper concerns the determination and analysis of dynamic similarity criteria for various practical problems encountered mainly in hydraulics and fluid dynamics at steady, smooth fluid onflow in front of a solid. Moreover, the cases of mechanically induced vibrations of a body in a stationary fluid moving with constant velocity in front of the body have been presented.

Theoretical Research on Suspension Bridge Cable Damage Assessment Based on Vehicle-Induced Cable Force

As one of the most critical load-bearing components in suspension bridges, cables require accurate damage assessments. Contemporary research methodologies primarily rely on cross-validation across multiple cables, which can present challenges in identifying damage under certain conditions. To address this limitation, this study proposes an evaluation method utilizing the cable force of individual cables. A damage index is introduced by the ratio of vehicle-induced cable tension (defined as the ratio of vehicle-induced cable force without weight to its baseline value), and the finite element model of a suspension bridge is used to verify this index. Initially, the finite element model of a suspension bridge is established, and a large number of datasets are generated using this model. These datasets include vehicle weight and vehicle-induced cable force. Subsequently, Gaussian Mixture Model (GMM) clustering is employed to categorize the dataset according to lanes, thereby establishing baseline values for each lane. Finally, damage assessments are conducted using data from individual cables and are validated against the outcomes obtained from the upstream–downstream cable force ratio method. The results show that the data trend of the damage index is clearly visible in six lanes, with the most pronounced trend occurring in the lane farthest from the cable (the sixth lane). The robustness of the index is also verified by adding 2% Gaussian white noise data, providing a research basis for related engineering projects.

Incorporating the Effect of Centrifugal Force into the Correlation for Saturated Flow Boiling Heat Transfer in a Helically Coiled Tube

The flow in a helically coiled tube exhibits a unique characteristic due to the centrifugal force acting on the fluid, which generates a secondary flow perpendicular to the main axial flow. This phenomenon is known to enhance convective heat transfer in both single- and two-phase flows. To account for this effect in a boiling heat transfer correlation, a new dimensionless number, defined by the ratio of centrifugal force to gravitational force, was introduced in a previous study. That study suggested a correlation incorporating this dimensionless number. This work aims to improve on the previous correlation. In deriving the dimensionless centrifugal force number, the pitch of the helical tube was not considered in the previous work. By properly incorporating both pitch and helical diameter into the dimensionless number, the coefficients of the heat transfer correlation must also be adjusted. The modified correlation was evaluated using 617 steam-water experimental data points for boiling heat transfer in helically coiled tubes. The results indicate that the modified correlation shows better results in comparison with the previous one and other existing correlations in terms of the root-mean-square errors of the calculated heat transfer coefficients.

The effect of fatiguing muscle contractions on kicking performance in experienced soccer players

ABSTRACT The objective of this study was to clarify the effects of fatiguing muscle contractions of the m. quadriceps femoris on kicking abilities of experienced soccer players. 16 male professional (n = 5) and amateur players (n = 11) performed kicking tests in two conditions (fatigue and control) on separate days in a randomised crossover design. The fatiguing protocol performed with the kicking leg consisted of 5 sets of 10 maximal voluntary concentric and eccentric knee extensions. Maximal voluntary isometric contraction force (MVIC), 15 hz/50 hz stimulation force ratio (force ratio), and kicking abilities were assessed before and after completion of the fatiguing protocol or rest (control). The fatiguing protocol successfully induced fatigue of 14.0 ± 2.7% (mean ± SE) reduced MVIC and 14.0 ± 3.7% reduced force ratio while no reductions occurred in the control condition. Between group difference showed ball speed declined 2.1 ± 0.95% more following the fatigue protocol compared to control condition. On the control day shooting accuracy improved by 13.3 ± 5.6% and was numerically impaired on the intervention day by 1.0 ± 9.2%. Despite this, no significant between group difference was observed in shooting accuracy (p = 0.18). The study demonstrated that fatigue induced by prior muscle contractions impairs maximal shooting speed, but we observed no significant impairment of shooting accuracy.

Stochastic Risk Assessment Framework of Deep Shale Reservoirs by a Deep Learning Method and Random Field Theory

Risk assessment of deep shale reservoirs is very important for subsurface energy development. However, due to complex geological environments and physicochemical interactions, shale reservoir fabric parameters exhibit variability. Moreover, the actual investigation and testing information is very limited, which is a typical small-sample problem. In this paper, the heterogeneity and statistical characteristics of deep shale reservoirs are clarified by the measured mechanical parameters. A deep learning method for deep shale reservoirs with limited survey data information is proposed. The variability of deep shale reservoirs is characterized by random field theory. A variable stiffness method and stochastic analysis method are developed to evaluate the risk of deep shale reservoirs. The detailed workflow of the stochastic risk assessment framework is presented. The frequency distribution and failure risk of deep shale reservoirs are calculated and analyzed. The risk assessment of deep shale reservoirs under different model parameters is discussed. The results show that a stochastic risk assessment framework of deep shale reservoirs, using a deep learning method and random field theory, is scientifically reasonable. The scatter plots of the elasticity modulus (EM), cohesive force (CF), and Poisson ratio (PR) distribute along the 45-degree line. The different distributed variables of EM, CF, and PR have a positive correlation. The statistical properties of the measurement data and deep learning data are approximately the same. The principal stress of deep shale follows the normal distribution with significance level 0.1. Under positive copula conditions, the maximum failure probability is 5.99%. Under negative copula conditions, the maximum failure probability is 4.58%. Different copula functions under positive and negative copula conditions have different failure probabilities. For the exponential correlation structure, the minimum failure probability is 3.46%, while the maximum failure probability is 6.19%. The mean failure probability of the EM, CF, and PR of deep shale reservoirs is 4.85%. Different random field-related structures and parameters have different influences on the failure risk.

A study on the mechanical strength of alfalfa seeds stimulated with continuous laser light.

The presented study explored the impact of He-Ne laser light stimulation on basic, selected mechanical properties of alfalfa seeds. The following parameters were considered: destructive force (F), destructive force work (W), and absolute longitudinal deformation (dL). Moreover, the single seed mass (m) was measured prior to the compression test, and the ratios of destructive force to absolute longitudinal deformation (F/dL) and destructive force work to single seed mass (W/m) were calculated. Subsequently, the mass of 1000 seeds was determined using RADWAG XA110.3Y scales, and the geometric dimensions of seeds were measured using a Keyence VHX-2000 microscope. Prior to the compression test, the seeds were subjected to laser light stimulation (λ = 632.8nm, surface force density = 6 mW·cm- 2) with the exposure time of, respectively: 0s (control - no stimulation - C), 30s (L30s), 1min (L1), 2min (L2), and 3min (L3). We observed an increase in most of the mechanical parameters measured under the influence of all the laser light stimulation variants. The only exception was the F/dL ratio, which decreased after 2 and 3-minute exposure, as compared to the control. The results evidenced increased mechanical strength of the stimulated seeds, which may prove significant to the cultivation of new, more resilient cultivars.

Aerodynamic instability of brush seals in gas turbine engines based on a fluid-structure interaction method

By brush seal, we mean a type of mechanical seal that uses a large number of closely packed, thin, and flexible bristles to create an outstanding seal between rotating and stationary components in gas turbine engines. However, at high levels of swirling and pressured environments in engines, bristles of brush seals tend to circumferentially slip, which leads to reduced sealing performance and seal failure. In this paper, the effects of upstream–downstream pressure differences Δp (0.2–0.5 MPa), downstream static pressure (0.1–1.0 MPa), and the coverage of bristles by a front plate (0%–90%) on the mechanical characteristics and deflections of bristles of a brush seal at highly swirling inlet were investigated based on a two-way fluid-structure coupling method. A key criterion for bristle instability, based on a simplified two-dimensional (2D) theoretical analysis, is obtained from the fluid-structure coupling simulations. The results indicate that a fundamental reason for the bristle circumferential slip is the ratio of the normal to the axial aerodynamic forces (Fn/Fax) acting on the first row of bristles. When this ratio exceeds 0.9, the bristles will slip circumferentially. The effects of the pressure differential across the seal, the downstream pressure, inlet swirl velocity, and front plate coverage of the bristles on bristle stability can all be explained through their influences on this force ratio. At relatively low outlet static pressure of 0.1 MPa, upstream bristles slip when the inlet swirl is in the range of 230–300 m/s and the bristle slip instability is more likely to occur at higher pressure difference conditions. However, at high downstream pressures, Fn/Fax declines with the growth of Δp, contributing to the stability tendency. With the constant Δp, the value of Fn/Fax significantly increases as the downstream pressure rises, and the critical swirl velocity required to trigger bristle slip is considerably reduced. Additionally, the front plate shields a part of the bristles away from pressure gradient in axial direction but leads to outward radial flow upstream of the bristle pack, thereby increasing the Fn/Fax. Thus, front plate does not offer protection to bristles under high inlet swirl conditions, on the contrary, it may cause early slip of the bristles.

Characteristic evolution and energy variation during the generation of water droplet

Understanding water droplet characteristic is an important prerequisite for improving wet dust removal efficiency. Using the high-speed camera system, the process of water droplet generation under the different Ca2+ concentrations and injecting velocities was studied. The width and length of water droplet increased, whereas the ratio of droplet width and length decreased with generation time. The water droplet generation time decreased with injecting velocity increasing, whereas kept almost unchanged with Ca2+ concentration. The equivalent diameter of droplet decreased with injecting velocity, whereas presented first a slight decrease and then a slight increase with Ca2+ concentration. This result suggested that the injecting velocity effect was stronger than the Ca2+ effect on the water droplet generation time and size. Furthermore, the effective injecting force and capillary force were mainly forces to influence the droplet generation in force analysis. RF (ratio of capillary force and effective pressure force) was first used to evaluate the synergistic effect of capillary force and effective injecting force. The greater RF, the water droplet generation time was longer and water droplet diameter was larger. Furthermore, the relationship between surface energy per unit (E/S) of water droplet and RF was a negative correlation. Those results can provide valuable suggestions to the development theory of dust removal.

Research on magnetic force of magnetic seal in aero-engine

Aiming at the magnetic seal in an aero-engine accessory, the range of magnetic force required for the normal operation of the magnetic seal is analyzed. The finite element analysis method based on the Maxwell stress tensor method is used to calculate the magnetic force between the dynamic ring and the magnetic static ring in the magnetic sealing system. The magnetic force under different magnetization modes and gaps is tested by the magnetic measuring test bench, which verifies the correctness of the magnetic calculation method. The effects of permanent magnet material, permanent magnet magnetization direction, magnetic seal structural parameters, and working conditions on the magnetic force between the dynamic ring/magnetic static ring in the magnetic seal are analyzed. Under the same structure, the magnetic force of NeFeB35, SmCo28, Alnico5, and Ferrite as magnetic static rings is compared. The results show that NdFeB35 has the largest magnetic force, SmCo28 is second, Alnico5 and Ferrite are relatively small, and their magnetic forces are about 1/4 to 1/5 of the first two materials. When the rotor or the casing is moving axially, NeFeB35 and SmCo28 materials with large magnetic force should be selected to meet the normal working requirements. Under the same material, the magnetic forces of axial, radial, and radiative magnetization modes are compared. the ratio of magnetic force under axial, radiative, and radial magnetization is about 2.3:1.1:1. If NeFeB35 and SmCo28 materials are axially magnetized, their magnetic forces will exceed the allowable range, which will increase the seal wear. The increase in the inner diameter of the dynamic ring and the gap between the dynamic ring and the magnetic static ring causes a decrease in the magnetic force. The increase in temperature affects the magnetic properties of permanent magnetic material, which leads to the decline of magnetic force between the dynamic ring and the magnetic static ring. The increase in rotor speed leads to the acceleration of the fluctuation frequency of the magnetic force. Still, the maximum and minimum values of the magnetic force under different speeds remain unchanged, and the maximum fluctuation rate is less than 3%. According to the analysis results, the fitting formula of magnetic force calculation is presented by the orthogonal test and the least squares method.

Bearing behaviors of rock-socketed piles in layered dynamically compacted soil-rock mixtures: A case study

After layered dynamic compaction (DC) treatment in a mountainous area with deep backfill in Chongqing, China, a series of pile tests and analyses were conducted to evaluate the vertical bearing capacity of rock-socketed piles and to investigate their mechanical characteristic and load-bearing behavior. Static pile load tests (SPLT) were carried out on three types of rock-socketed piles with different diameters (800 mm, 1000 mm, and 1200 mm). Based on the test data of pile reinforcement stress, the pile axial force, frictional resistance, and load-sharing ratio were calculated and analyzed. The results indicate that load-settlement curves of static load tests for all piles change progressively, and the S-lgt curves are relatively straight lines without obvious downward bending. The pile axial force exhibits the characteristics of “large at the top and small at the bottom”, resulting in stress concentration at the pile top, especially prominent in longer piles (lengths of 33.2–37.1 m). Additionally, the overall frictional resistance increases with the increase of pile top load. In shorter piles (lengths of 16.5–22.6 m), the frictional resistance presents a C-type curve with depth, while in longer piles, it presents an S-type curve distribution. Comparatively, the test pile bears the upper load mainly by the side friction resistance, which is more prominent in the longer pile. With the increase of pile top load, the load-sharing ratio of side friction decreases and the load-sharing ratio of pile tip resistance increases.

Active curling of epithelial monolayers dominated by actin cytoskeleton mechanics.

Active curling of epithelial tissues, as an indispensable component of developmental morphogenesis, occurs frequently both in vivo and in vitro microenvironments. Deciphering the mechanisms underlying the active curling of epithelial monolayers is crucial for understanding many physiological and pathological processes. Here, a multiscale structure-based cell monolayer model and an active constitutive relation are established to characterize this spontaneous curling of the epithelial tissue. It is shown that the asymmetric distribution of Myosin II along the apicobasal axis generates an active moment that drives spontaneous curling of the suspended epithelial tissue. The time-dependent deflection and rotation angle of the active curling are analytically solved, proving that the curling is driven by the active bending moment directly associated with the apicobasal asymmetric contractile force. Moreover, we demonstrate that the rotation angle is proportional to the apicobasal force ratio and inversely proportional to the thickness of epithelial tissues. In addition, we derive an approximate analytical relation between the out-of-plane curling behavior and in-plane stress, in good agreement with the experimental data and our simulation results. This study provides a pathway to elucidate the mechanical mechanism underlying complex morphological development as well as the physiological and pathological phenomena of epithelial tissues.

Direct numerical simulation of bubble rising in turbulence

We describe the rising trajectory of bubbles in isotropic turbulence and quantify the slowdown of the mean rise velocity of bubbles with sizes within the inertial subrange. We perform direct numerical simulations of bubbles, for a wide range of turbulence intensity, bubble inertia and deformability, with systematic comparison with the corresponding quiescent case, with Reynolds number at the Taylor microscale from 38 to 77. Turbulent fluctuations randomise the rising trajectory and cause a reduction of the mean rise velocity $\tilde {w}_b$ compared with the rise velocity in quiescent flow $w_b$ . The decrease in mean rise velocity of bubbles $\tilde {w}_b/w_b$ is shown to be primarily a function of the ratio of the turbulence intensity and the buoyancy forces, described by the Froude number $Fr=u'/\sqrt {gd}$ , where $u'$ is the root-mean-square velocity fluctuations, $g$ is gravity and $d$ is the bubble diameter. The bubble inertia, characterised by the ratio of inertial to viscous forces (Galileo number), and the bubble deformability, characterised by the ratio of buoyancy forces to surface tension (Bond number), modulate the rise trajectory and velocity in quiescent fluid. The slowdown of these bubbles in the inertial subrange is not due to preferential sampling, as is the case with sub-Kolmogorov bubbles. Instead, it is caused by the nonlinear drag–velocity relationship, where velocity fluctuations lead to an increased average drag. For $Fr &gt; 0.5$ , we confirm the scaling $\tilde {w}_b / w_b \propto 1 / Fr$ , as proposed previously by Ruth et al. (J. Fluid Mech., vol. 924, 2021, p. A2), over a wide range of bubble inertia and deformability.