Approach Velocity Research Articles

Evaluation of gait termination strategy in individuals with Essential Tremor and Parkinson's disease

IntroductionGait termination (GT) is a challenging transitory task involving converting from a dynamic state of motion to a static state. These transitional locomotor tasks are particularly troublesome for populations with postural deficits, i.e., Parkinson’s disease (PD) and Essential Tremor (ET). They demand greater postural control and intricate integration of the neuromuscular system. The mechanisms involved in GT in these populations have not been well studied despite the safety concerns and potential risk for falls. The purpose of this investigation was to examine the different control strategies utilized during GT between individuals with ET and PD. MethodsTwenty-four individuals with ET (66 ± 8 yrs), twenty-four individuals with PD (64 ± 8 yrs), and twenty healthy older adults (HOA: 63 ± 9 yrs) participated in this study. Average self-selected gait velocity for each group was collected during the GT trial walking portion. Ground reaction force (GRF) data were used to calculate braking and propulsive forces from the last two steps during GT. GRF data measured the dynamic postural stability index (DPSI), defined as an individual’s ability to maintain balance while transitioning from a dynamic to a stable state. ResultsPersons with ET had a significantly slower approach velocity (0.63 m/s) when compared to HOA (0.92 m/s) and PD (0.77 m/s). Persons with PD had significantly slower approach velocity when compared to HOA. Examination of GRF data found that those with ET generated significantly smaller propulsive and braking forces (p < .05). Forces increased in those with PD and then even more in the HOA group. Postural stability analysis revealed that ET had significantly worse stability scores than PD and HOA (p < .05). ConclusionIndividuals with PD and ET utilize different control strategies for planned GT, which suggests both the cerebellum and the basal ganglia play central yet potentially different roles in anticipatory control during self-directed activities.

Effect of Intermittent Traveling Water Screen Operation on Fish Survival

AbstractThe U.S. Environmental Protection Agency’s final rule for complying with section 316(b) of the Clean Water Act states that cooling water intakes withdrawing &gt;7.6 million liters per day must use one of seven alternatives to reduce fish impingement mortality. Fish‐friendly traveling water screens (TWSs) are expected to be frequently utilized because of relative ease of retrofit. The final rule requires “continuous or near continuous screen rotation” to facilitate recovery of collected fish as soon as practical. However, intermittent TWS operation could be advantageous for operators because reductions in screen system operating time will extend equipment life and reduce operating costs. A laboratory evaluation was conducted with Golden Shiner Notemigonus crysoleucas, Bluegill Lepomis macrochirus, Largemouth Bass Micropterus salmoides, and Common Carp Cyprinus carpio (42–106 mm TL) to determine whether intermittent rotation would optimize TWS operation and maintain biological performance. A preliminary evaluation was conducted with three approach velocities (0.30, 0.45, and 0.60 m/s) at four stationary screen durations (2, 4, 6, 12 h) in small test flumes to select parameters for a larger‐scale evaluation. The full‐scale evaluation tested two approach velocities (0.30 and 0.45 m/s) at two stationary durations (2 and 4 h at 0.45 m/s; 6 and 12 h at 0.30 m/s) and continuous screen operation. Fish avoided impingement at 0.30 m/s, and approach velocity was the primary determinant of survival probability, with increased velocity leading to increased mortality. Severe injuries occurred more frequently during stationary screen trials than with continuous operation; over 50% of fish had &gt;40% scale loss at 0.45 m/s for stationary trials. The results indicate that continuous rotation is optimal for fish survival at approach velocities between 0.30 and 0.45 m/s. However, intermittent operation at average approach velocities of 0.30 m/s or less may be acceptable for fishes with equal or greater swimming ability than those tested in this study.

Mind your step: predicting maximum ankle inversion during cutting movements in soccer

ABSTRACT The objective of this investigation was to identify parameters at initial contact that would predict the subsequent maximum ankle inversion angle during cutting movements. We conducted a secondary data analysis and calculated kinematics of 1,400 cuttings performed by 46 male soccer athletes. The movement task consisted of an approach run, followed by a pre-planned cutting movement. A linear mixed regression model was applied to predict the maximum ankle inversion angle during the first 100 ms of ground contact. The prediction was made based on six predictors that describe change-of-direction intensity and foot placement as found to be relevant in the literature. The model explained 62% of the variance of maximum ankle inversion angles. A change of the main predictors (foot rotation, cutting angle and initial ankle inversion) by 1 SD caused a reduction of the subsequent maximum ankle inversion angle by 2.6–4.4°. Regarding the intensity of a change-of-direction movement, cutting angle seems to have a higher influence on maximum ankle inversion angle than approach velocity. With respect to the individual foot positioning, the maximum ankle inversion angle can be reduced by increasing exorotation and eversion of the foot while shifting towards forefoot landing.

Dynamics of a particle-laden bubble colliding with an air-liquid interface

The collision, bouncing and potential bursting of air bubbles with air-liquid interfaces are key processes involved in the initial stage of foam formation. While fundamental studies of these processes, especially for gas-liquid-solid froth systems, are very valuable for a better understanding of various chemical engineering separation systems, these are scarce. This paper investigates the dynamics of rising bubbles, without particles attached and with various particle coverages, as they collide with an air-liquid interface. For uncoated bubbles, an increase in distance from the bubble releasing point to the air-liquid interface resulted in higher bubble approach velocities, although with minor changes in the velocity fluctuation frequency. This increase in approach velocity was not observed for bubbles with relatively high particle coverage. For particle-laden bubbles, the collision with the interface is associated with movement of the particles over the surface of the decelerating bubble. This particle motion on the bubble surface, combined with bubble shape pulsation, contributes to the kinetic energy dissipation of the approaching bubble. A damped oscillation model was derived to represent the velocity of the bubble interacting with the interface, which shows that the amplitude of the velocity decreases gradually with the increase in particle coverage. The damping coefficient in the model, introduced to quantify the influence of attached particles, is shown to increase with particle coverage, confirming the key role that particles play in bubble collision dynamics at an air-liquid interface and allowing, for the first time, the prediction of their behavior.

Correlating the weld-bead's ‘macro-, micro-features’ with the weld-pool's ‘fluid flow’ for electron beam welded SS 201 plates

The phenomenological modeling, a CFD-based simulation tool, was implemented to study the nature and magnitude of fluid flow within the weld zone (WZ) at varying heat input conditions, and further, analyzed its effect on the macroscopic (bead geometry and spiking) and the microscopic (hardness and ferrite arm spacing) features of the WZ during electron beam welding of SS201 plates. Upon calculation of the fluid flow parameters, the mean flow velocity ‘Vm’, Reynolds number, Peclet number, and Grashof number of the molten fluid in the weld-pool were observed to increase by around 3 times with the increase in heat input. The fluid convection was found to be a dominant factor in determining the mode of heat transfer. The weld-bead geometrical features, namely depth and width, were determined by the fluid flow velocities ‘(Vf)depth or width’ along the respective axes. The micro-hardness (MH) and secondary ferrite arm spacing (SFAS) were observed to have an inverse relationship. The increment in SFAS by approximately 1.3 times, due to the (a) decrease in the weld zone cooling rate by around 2.5 times and (b) increase in the coarsening coefficient by approximately 2 times because of Cr diffusion at the higher mean flow velocity ‘Vm’, was observed. Upon microstructural investigation, it was found that the slower cooling rate through the transformation temperature zones favored the formation of vermicular δ-ferrite in the austenite ‘γ’ phase matrix in the WZ, and thus, MH of base metal was observed to be more than that of the weld zone. The spiking amplitude was observed to be influenced by the gap generated between the capillary tip and the weld-pool bottom, and the velocity of approach ‘Va’ of the molten fluid, and the same was found to increase by around 2.5 times with the increase in the melting efficiency by approximately 1.4 times.

Coalescence of fluid particles with deformable interfaces in non-Newtonian media

The drainage of the non-Newtonian film between two approaching fluid particles are studied. The non-Newtonian continuous phase is a generalized Newtonian fluid that obeys the power-law model, and the deformable particle interfaces are allowed to have any degree of tangential mobility. The interaction is a gentle collision with a constant relative approach velocity. The film equations are simplified by using the lubrication theory in the thin film limit and combined with the boundary integral method. The effect of the non-Newtonian behavior on the film drainage and on the coalescence time is investigated through the power index. It is found that the non-Newtonian behavior significantly affects the number and type of the rims emerging at the interfaces. At a given approach velocity, when there are no rims or when the interfaces are fully mobile, the coalescence times for Newtonian and non-Newtonian fluids appear to be the same. Otherwise, the coalescence time increases with the power index, i.e., it is faster for shear-thinning fluids and slower for shear-thickening ones. This effect of the non-Newtonian behavior is found to amplify with the tangential mobility of the interfaces and the relative approach velocity.

Particle pair statistics of inertial particles at small separation using stereoscopic particle tracking

Particle pair statistics of inertial particles having average Stokes numbers of 2.1 and 14 are measured in isotropic turbulence at a Reynolds number of Reλ = 240. The radial distribution function (RDF) and mean relative approach velocity are obtained at small separation distances using 2-frame stereoscopic particle tracking velocimetry (stereo-PTV). At small separation distance, the RDF varies by an order of magnitude in the range of Stokes numbers investigated. However, the mean relative approach velocity is found to have a weak dependence on Stokes number. The results are shown to have high accuracy when compared to analogous mono-PTV datasets, and can be used to provide a more reliable estimate of the inter-particle collision rate. The main limitation of the measurement is observed at separation distances less than the laser sheet thickness, where the technique tended to underestimate the mean relative approach velocity.

Flocking of Multi-agent Systems with Unknown Nonlinear Dynamics and Heterogeneous Virtual Leader

This paper investigates the flocking control of multi-agent systems with unknown nonlinear dynamics while the virtual leader information is heterogeneous. The uncertain nonlinearity in the virtual leader information is considered, and the weaker constraint on the velocity information measurements is assumed. In addition, a bounded assumption on the unknown nonlinear dynamics is also considered. It is weaker than the Lipschitz condition adopted in the most flocking control methods. To avoid fragmentation, we construct a new potential function based on the penalty idea when the initial network is disconnected. A dynamical control law including a adjust parameter is designed to achieve the stable flocking. It is proven that the velocities of all agents approach to consensus and no collision happens between the mobile agents. Finally, several simulations verify the effectiveness of the new design, and indicate that the proposed method has high convergence and the broader applicability in practical applications with more stringent restrictions.

Collision risk analysis on ferry ships in Jiangsu Section of the Yangtze River based on AIS data

To assess the collision risk of ferries in the Yangtze River during crossing, the collision risk modeling is conducted based on AIS data. Risk Influencing Factors (RIFs) including Distance to Closest Point of Approach (DCPA), Time to Closest Point of Approach (TCPA), distance and relative velocity are involved. First, the historical multi-ship encounter scenarios involved ferry during crossing are identified from AIS data. Then, the value of RIFs is calculated according to their cumulative distribution, and their corresponding weights are determined using entropy theory. Next, the Collision Risk Index of Ferry (CRIF) is proposed considering the behavior of ferry and multiple target ships, which makes it possible to assess real-time collision risk during crossing and to integrate collision risk of each voyage based on historical encounter scenarios. The performance of the proposed model is evaluated according to the analysis on several encounter scenarios with different collision risk. Furthermore, the areas with higher collision risk are identified. The results bring some new insights to enhancing navigation safety of ferries.

Influence of Side Uncertainty on Knee Kinematics of Female Handball Athletes During Sidestep Cutting Maneuvers.

Noncontact anterior cruciate ligament ruptures generally occur during unanticipated sidestep cutting maneuvers when athletes have their visual attention focused on the opponent. The authors investigated the influence of uncertainty related to the side to perform the sidestep cutting maneuver on knee kinematics of female handball athletes. A total of 31 female handball athletes performed the sidestep cutting maneuver during anticipated and uncertain conditions. During the uncertain condition, visual cues indicated the direction of the reactive sidestep cutting maneuver. Between-condition differences were compared using the Student t test for paired samples calculated with statistical parametric mapping. Lower knee flexion angle was detected during the uncertain condition compared with the anticipated condition for the nondominant limb (0%-8% of the sidestep cycle). Knee abduction was larger during the uncertain condition for both the dominant (15%-41% of the sidestep cycle) and nondominant (0%-18% of the sidestep cycle) limbs compared with the anticipated condition. The nondominant leg showed higher knee abduction (36%-68% of the sidestep cycle) during the uncertain condition compared with the anticipated condition. The athletes' approach velocity was slower during the uncertain condition. The uncertain condition impacted knee kinematics and potentially positioned the joint at greater risk of injury by decreasing the flexion angle in the nondominant leg and increasing the joint valgus bilaterally.

The effect of approach velocity on pelvis and kick leg angular momentum conversion strategies during football instep kicking

ABSTRACT During football instep kicking, whole-body deceleration during the final stride has been associated with greater kick leg angular momentum and enhanced foot and ball velocities, but the influence of approach velocity on these mechanisms is unknown. This study assessed how approach velocity affects momentum conversion strategies of experienced players performing fast and accurate kicks. Eleven semi-professional footballers performed instep kicks from self-selected (3.34 ± 0.43 m/s), fast (3.71 ± 0.33 m/s) and slow (2.77 ± 0.32 m/s) approaches. Kicking motions and ground reaction forces under the support leg were captured using 3D motion analysis (1000 Hz). The players responded to perturbations in approach velocity by using the support leg to regulate whole-body deceleration and create ideal conditions for co-ordinated pelvic and kick leg momentums during the downswing. Further, the pelvis was key for generating transverse momentum at the kick leg, but the participants displayed distinctly different pelvis transverse rotation strategies. Identification of these inter-individual strategies may provide a basis for technical and strength training practices to be tailored for individual players. Future research might investigate if training practices that expose footballers to varying approach velocities of between 2.5 and 4.0 m/s promotes development of movement strategies that are robust to perturbations in approach conditions.

The Biomechanical Characterization of the Turning Phase during a 180° Change of Direction.

The aim of this study was to characterize the turning phase during a modified 505 test. Forty collegiate basketball students, divided into faster and slower performers and high-playing-level and low-playing-level groups, were evaluated for the force-time characteristics (braking and/or propulsive phase) of the penultimate foot contact (PFC), final foot contact (FFC), and first accelerating foot contact (AFC), and for completion time and approach velocity. Based on the composition of the AFC, trials were classified as braking/propulsive or only propulsive. Regression analysis for the prediction of completion time was performed. The AFC contributed to reacceleration through shorter contact times and step length, and lower braking force production (p < 0.05). Faster performers and the high-playing-level group demonstrated (p < 0.05): lower completion times, higher approach velocities, longer steps length in the PFC and FFC, greater braking forces and impulses in the PFC; greater braking and propulsive forces, braking impulses, lower contact times in the FFC; greater braking and propulsive horizontal forces, horizontal impulses, lower contact times and vertical impulses in the AFC. Kinetic variables from only the FFC and AFC and approach velocity predicted 75% (braking/propulsive trials) and 76.2% (only-propulsive trials) of completion times. The characterization of the turning phase demonstrated the specific contribution of each foot contact and the possible implications for training prescription.

A model of feedforward, global, and lateral inhibition in the locust visual system predicts responses to looming stimuli.

Detection of looming obstacles is a vital task for both natural and artificial systems. Locusts possess a visual nervous system with an extensively studied obstacle detection pathway, culminating in the lobula giant movement detector (LGMD) neuron. While numerous models of this system exist, none to date have incorporated recent data on the anatomy and function of feedforward and global inhibitory systems in the input network of the LGMD. Moreover, the possibility that global and lateral inhibition shape the feedforward inhibitory signals to the LGMD has not been investigated. To address these points, a novel model of feedforward inhibitory neurons in the locust optic lobe was developed based on the recent literature. This model also incorporated global and lateral inhibition into the afferent network of these neurons, based on their observed behaviour in existing data and the posited role of these mechanisms in the inputs to the LGMD. Tests with the model showed that it accurately replicates the behaviour of feedforward inhibitory neurons in locusts; the model accurately coded for stimulus angular size in an overall linear fashion, with decreasing response saturation and increasing linearity as stimulus size increased or approach velocity decreased. The model also exhibited only phasic responses to the appearance of a grating, along with sustained movement by it at constant speed. By observing the effects of altering inhibition schemes on these responses, it was determined that global inhibition serves primarily to normalize growing excitation as collision approaches, and keeps coding for subtense angle linear. Lateral inhibition was determined to suppress tonic responses to wide-field stimuli translating at constant speed. Based on these features being shared with characterizations of the LGMD input network, it was hypothesized that the feedforward inhibitory neurons and the LGMD share the same excitatory afferents; this necessitates further investigation.

Decrease in adhesion force at silica-mica interface with short contact time due to dynamic formation process of liquid bridge revealed on an AFM

ABSTRACT The influence of instrumental parameters of an atomic force microscope (AFM) on adhesion forces demands clarification. Adhesion forces between a tipless cantilever and mica were measured in a humid environment to investigate the influence of instrumental parameters. The adhesion force measured repeatedly at a location is relatively stable with excellent reproducibility. The force abnormally decreases by ~10% with dwell time (0 ~ 0.4 s), then remains almost stable (0.4 ~ 10 s). The reason was the dynamic formation process of a liquid bridge. Due to a large driving pressure, the volume of the liquid bridge can increase intensely to the maximum one, which is larger than that in saturation. This leads to the reduction in the bridge by liquid flow, eventually resulting in the decrease. The force increases by a small magnitude with approach velocity and then remains stable. However, it increases logarithmically with retraction velocity and increases with piezo velocity with a concave downward shape in the logarithmic coordinate. The velocity dependence was ascribed to the dynamic enhancement of viscous force and the contact time dependence. The outcomes may help to understand the influence of instrumental parameters, and deepen the understanding of the formation mechanism of a liquid bridge.

Mother-Infant Interaction Kinect Analysis (MIIKA): An automatic kinematic-based methodology for the investigation of interpersonal distance during early exchanges

Interpersonal distance is a core aspect of mother-child interaction. While conventional measures based on human coders do not fully capture the dynamics of this feature, computational methods provide automatic measures which can detect even small changes and more accurate estimates both spatially and temporally. Using RGB-D sensors (Microsoft Kinect V2), the present study describes a setup to automatically examine interpersonal distance during mother-child interactions, termed Mother-Infant Interaction Kinect Analysis (MIIKA). First, the laboratory setting and the data extraction method are described. By using an ad-hoc algorithm for kinematic data extraction, MIIKA returns three metrics: barycenter position (distance and velocity of approach and separation), movements (number of small, medium and large approaches and separations) and contributions (proportional contributions of mother and child to approaches and separations). Secondly, preliminary MIIKA metrics are described for a non-clinical mother-child dyad as an exemplification of the protocol. As interpersonal distance can be affected by contingent situations, we detected mother-infant full skeleton during three interactional contexts characterized by different kinds of dyadic exchanges: a free play session, a task-oriented activity and an emotionally arousing condition. Results highlighted similarities and differences between the three interactional contexts. MIIKA appears to be a promising setup to automatically examine interpersonal distance in early mother-child interactions.

Continuous measurement of attachment behavior: A multimodal view of the strange situation procedure

Infant attachment is a critical indicator of healthy infant social-emotional functioning, which is typically measured using the gold-standard Strange Situation Procedure (SSP). However, expert-based attachment classifications from the SSP are time-intensive (with respect both to expert training and rating), and do not provide an objective, continuous record of infant behavior. To continuously quantify predictors of key attachment behaviors and dimensions, multimodal movement and audio data were collected during the SSP. Forty-nine 1-year-olds and their mothers participated in the SSP and were tracked in three-dimensional space using five synchronized Kinect sensors; LENA recordings were used to quantify crying duration. Theoretically-informed multimodal measures of attachment-related behavior (e.g., dyadic contact duration, infant velocity of approach toward the mother, and infant crying) were used to predict expert rating scales and dimensional summaries of attachment outcomes. Stepwise regressions identified sets of multimodal objective measures that were significant predictors of eight of nine of the expert ratings of infant attachment behaviors in the SSP’s two reunions. These multimodal measures predicted approximately half of the variance in the summary approach/avoidance and resistance/disorganization attachment dimensions. Incorporating all objective measures as predictors regardless of significance levels, predicted individual ratings within an average of one point on the original Likert scales. The results indicate that relatively inexpensive Kinect and LENA sensors can be harnessed to quantify attachment behavior in a key assessment protocol, suggesting the promise of objective measurement to understanding infant-parent interaction.

Dynamics of shallow wakes on gravel-bed floodplains: dataset from field experiments

Abstract. Natural dynamics of river floodplains are driven by the interaction of flow and patchy riparian vegetation, which has implications for channel morphology and diversity of riparian habitats. Fundamental mechanisms affecting the dynamics of flow in such systems are still not fully understood due to a lack of experimental data collected in natural environments that are free of the unavoidable scaling effects in laboratory studies. Here we present a detailed dataset on the hydrodynamics of shallow wake flows that develop behind solid and porous obstructions. The dataset was collected during a field experimental campaign carried out in a side branch of the gravel-bed Tagliamento River in northeast Italy. The dataset consists of 30 experimental runs in which we varied the diameter of the surface-mounted obstruction, its solid volume fraction, its porosity at the leading edge, the object's submergence and the approach velocity. Each run included: (1) measurements of mean velocity and turbulence in the longitudinal transect through the centreline of the flow with up to 25–30 sampling locations and from 8 to 10 lateral profiles measured at 14 locations, (2) detailed surveys of the free surface topography and (3) flow visualizations and video recordings of the wake patterns using a drone. The field scale of the experimental setup, precise control of the approach velocity, configuration of models and natural gravel-bed context for this experiment makes this dataset unique. Besides enabling the examination of scaling effects, these data also allow the verification of numerical models and provide insight into the effects of driftwood accumulations on the dynamics of wakes. Data are available with open access via the Zenodo portal (Shumilova et al., 2020) with DOI https://doi.org/10.5281/zenodo.3968748.

Inward Flow of Intervening Liquid Films Driven by the Marangoni Effect during Bubble-Solid Collisions in Ethyl Alcohol-NaCl Aqueous Solutions.

The drainage dynamics of confined thin liquid films between an air bubble and a freshly cleaved mica surface were investigated in ethyl alcohol aqueous solutions. Focus was given to the holding stage, in which an unexpected increase in the thickness of a few hundred nanometers at the center of the film was captured by interferometry in ethyl alcohol-500 mM NaCl aqueous solutions. Such an increase in film thickness occurred when the ethyl alcohol concentration exceeded the critical value at a bubble approach velocity of 100 μm/s. For a given ethyl alcohol concentration, the increase in thickness at the center of the film did not happen when the bubble approach velocity was decreased to 10 μm/s. Compared to the cases in ethyl alcohol-500 mM NaCl solutions, no increase in thickness at the center of the film was observed in ethyl alcohol-water solutions under the same ethyl alcohol concentration and bubble approach velocity. The phenomenon of the increasing thickness at the center of the film was attributed to the net inward flow in the film, resulting from competition between the inward Marangoni flow and the outward drainage flow that was hindered by the narrow channel at the barrier rim of the film under a high electrolyte concentration. The inward Marangoni flow was achieved by a concentration gradient of ethyl alcohol between the film and the bulk solution resulting from the mobile air-liquid interface in the initial approaching period.

Differentiation reveals latent features of aging and an energy barrier in murine myogenesis.

Skeletal muscle experiences a decline in lean mass and regenerative potential with age, in part due to intrinsic changes in progenitor cells. However, it remains unclear how age-related changes in progenitors manifest across a differentiation trajectory. Here, we perform single-cell RNA sequencing (RNA-seq) on muscle mononuclear cells from young and aged mice and profile muscle stem cells (MuSCs) and fibro-adipose progenitors (FAPs) after differentiation. Differentiation increases the magnitude of age-related change in MuSCs and FAPs, but it also masks a subset of age-related changes present in progenitors. Using a dynamical systems approach and RNA velocity, we find that aged MuSCs follow the same differentiation trajectory as young cells but stall in differentiation near a commitment decision. Our results suggest that differentiation reveals latent features of aging and that fate commitment decisions are delayed in aged myogenic cells invitro.

Electrohydrodynamic-induced interactions between droplets

Dispersion of droplets in an emulsion is commonly seen in several chemical, pharmaceutical and petroleum industries. Electric field has been shown to affect the stability of these dispersions. We study the dynamics of a pair of leaky dielectric droplets in a leaky dielectric liquid in the presence of an externally applied electric field. A pair of droplets may coalesce or repel each other in the presence of an electric field. Interactions between a pair of drops have been shown to be governed by the ratio $\varepsilon _r/\sigma _r$ , where $\varepsilon _r$ and $\sigma _r$ are the ratios of drop to ambient fluid electric permittivities and conductivities, respectively. When inertia is neglected, the droplets approach each other if $\varepsilon _r/\sigma _r &gt; 1$ , whereas droplets repel when $\varepsilon _r/\sigma _r &lt; 1$ . However, inclusion of inertia permits interesting transient behaviour, where the droplets may attract due to the electrostatic dipole–dipole attraction even for $\varepsilon _r/\sigma _r &lt; 1$ . The approach velocity then is governed by the electrostatic forces and varies as $1/h^4$ , where $h$ is the separation distance between the droplets, in contrast to being hydrodynamically driven as predicted in the Stokes flow limit by Baygents et al. (J. Fluid Mech., vol. 368, 1998, pp. 359–375). For compound droplets, interactions between droplets are essentially governed by the electrical properties of the outer droplet and the ambient fluid. However, transient dynamics may also result in the breakup of a compound droplet and lead to formation of single droplets.