The dynamics of bouncing, partially coalescing, liquid metal droplets in a viscous medium

Planar partial coalescence is a phenomenon in which a droplet at a free surface or interface between two fluids coalesces into the plane surface producing a smaller droplet rather than coalescing completely. This smaller, ‘daughter’ droplet will be driven towards the interface by gravity and capillary forces resulting in a cascade effect of progressively small daughter droplets until the Ohnesorge Number approaches $\sim$ 1 and the cascade terminates with a full coalescence event. This paper utilizes a room temperature liquid metal alloy composed of gallium, indium and tin to study partial coalescence in a viscous quiescent medium and observed bouncing of the coalescing droplets on the interface. We observed the event using high speed videography measuring effects such as the droplet to daughter droplet ratio, droplet velocities, droplet bounce heights and coefficients of restitution for the bouncing event. An existing model (Honey & Kavehpour, Phys. Rev. E, vol. 73, 2006) from our group was used, validated and expanded upon to include buoyancy effects to estimate the initial velocity of the droplet and we developed two new models for the droplet travel and maximum bounce height. The first utilizes the Stokes model for drag to moderate success while the second utilizes a model from Beard & Pruppacher (J. Atmos. Sci., vol. 26, 1969, pp. 1066–1072) and a fourth-order Runge–Kutta numerical integration scheme to predict the droplet velocity and position as functions of time. Additionally the coefficient of restitution was determined from the model using a shooting method technique in tandem with measured data to find a coefficient of restitution value of $A = 0.27 \pm 0.06$ . This ‘bouncing drop’ phenomenon continues in a quiescent viscous fluid to the sub-micron scale and was facilitated by the material properties of the liquid metal including the high density, moderate viscosity and particularly high interfacial tension.

The Effect of Wood Type on the Reflection of a Table Tennis Ball

The table tennis game table can be made of any material with certain bounce height requirements according to ITTF regulations. Wood as the main material for the table is found in Indonesia. Various types of wood have the potential to be a dining table material. This study was conducted to determine the effect of the type of wood on the bounce of a table tennis ball. Experiments were carried out on 9 types of wood, namely hardwoods (teak, sono, coconut), medium hardwoods (meranti, plywood and jackfruit) and soft woods (waru, randu and sengon). The height of the falling ball is determined to be 30 cm for the ball's bounce recorded by the camera. The ball used is a ball with a weight of 24 grams and 30 grams. Camera recording data is processed with Kinovea 08.15 to get the reflection height. The bounce height is used as a reference for ITTF standard compliance. The initial height and reflection height were then used to calculate the coefficient of restitution (COR). Data collection was carried out 5 times and the average value was calculated. The level of wood hardness is influenced by its specific gravity. Hard wood has a relatively high specific gravity. Teak wood which is relatively hard has a specific gravity value of 0.59 – 0.82 gr/cm3

Dynamics of a bouncing table tennis ball from the acoustic signature using an optical fibre sensor

We describe an optical fibre-based method to estimate impact force and collision duration using time measurements recorded from acoustic signals of a table tennis ball bouncing on a table. The technique combines measurements obtained from a polarisation dependent optical fibre sensor with graphical analysis and kinetics through numerical calculations. The presented coefficient of restitution, collision time, impact force, and elastic deformation during each bounce of the table tennis ball were obtained using corresponding time series measurements and numerical analysis. A peak impact force of 38.4N was estimated for a ball of mass 2.83g and 39.7mm diameter dropped from a height of 31.5cm. The impact duration for the associated bounce was 0.68ms with a centre of gravity shift of 0.40mm and coefficient of restitution of 0.88. While the observed results are unique to the ball and table surface, the approach is an attempt to fully quantify collision parameters from basic measurement and instrumentation applicable to undergraduate students. The sensor developed in this paper finds application in sports performance monitoring, infrastructural health early warning systems and pressure sensitive manufacturing processes.

Detachment Detection in Cam Follower System Due to Nonlinear Dynamics Phenomenon

The detachment between the cam and the follower was investigated for different cam speeds (N) and different internal distance of the follower guide from inside (I.D.). The detachment between the cam and the follower were detected using largest Lyapunov exponent parameter, power density function of Fast Fourier Transform (FFT), and Poincare’ maps due to the nonlinear dynamics phenomenon of the follower. The follower displacement and the contact force between the cam and the follower were used in the detection of the detachment heights. Multi-degrees of freedom (spring-damper-mass) systems at the very end of the follower were used to improve the dynamic performance and to reduce the detachment between the cam and the follower. Nonlinear response of the follower displacement was calculated at different cam speeds, different coefficient of restitution, different contact conditions, and different internal distance of the follower guide from inside. SolidWorks program was used in the numerical solution while high speed camera at the foreground of the OPTOTRAK 30/20 equipment was used to catch the follower position. The friction and impact were considered between the cam and the follower and between the follower and its guide. The peak of nonlinear response of the follower displacement was reduced to (15%, 32%, 45%, and 62%) after using multiple degrees of freedom systems.

Interval of restitution coefficient for chattering in impact damper

Based on the impact damper, a dynamic model of a non-fixed constrained collision system was established. The coefficient of restitution is used as the main control parameter to analyze the system’s periodic movement and its bifurcation region. The chattering movement characteristics of the system were revealed. The interval of restitution coefficient for the chattering of collision system under various mass ratio and frequency ratio was obtained. The results show that the chattering phenomenon occurs in the collision system when the coefficient of restitution is greater than 0.5; as the mass ratio decreases, the interval of restitution coefficient for chattering continues to expand; as the frequency increases, the interval of restitution coefficient for chattering narrows.

CO2-ice Collisions: A New Experimental Approach

The coagulation of micrometer-sized particles marks the beginning of planet formation. For silicates a comprehensive picture already exists, which describes under which conditions growth can take place and which barriers must be overcome. With increasing distance to the central star volatiles freeze out and the collision dynamics is governed by the properties of the frozen volatiles. We present a novel experiment facility to analyze collisions of CO2 agglomerates consisting of micrometer-sized particles with agglomerate sizes up to 100 μm. Experiments are conducted at temperatures around 100 K with collision velocities up to 3.4 m s−1. Below impact velocities of around 0.1 m s−1 sticking is observed and at collision velocities of 1 m s−1 fragmentation also starts to occur. The experiments show that agglomerates of CO2 ice behave like silicate agglomerates with a comparable grain size distribution. Models developed to describe the collision dynamics of silicate dust can be applied to CO2 ice. This holds for the coefficient of restitution as well as for the threshold conditions for the transitions between sticking, bouncing, or fragmentation.

Simultaneous Collision of the Rigid Body at Two Points

We present a new approach based on the notion of inertance for the simultaneous collisions without friction of a rigid solid. The calculations are performed using the screw (plückerian) coordinates, while the results are obtained in matrix form, and they may be easily implemented for different practical situations. One calculates the velocities after collision, the energy of lost velocities, and the loss of the kinetic energy. The general algorithm of calculation is described in the paper. The main assumption is that the normal velocities at the contact points vanish simultaneously. The coefficients of restitution at the contact points may be equal or not. Some completely solved applications are also presented, and the numerical results are discussed. The numerical values depend on which coefficient of restitution is used.