Arjan van der Bos

Controlled impact of a disk on a water surface : cavity dynamics

In this paper we study the transient surface cavity which is created by the controlled impact of a disk of radius h 0 on a water surface at Froude numbers below 200. The dynamics of the transient free surface is recorded by high-speed imaging and compared to boundary integral simulations giving excellent agreement. The flow surrounding the cavity is measured with high-speed particle image velocimetry and is found to also agree perfectly with the flow field obtained from the simulations. We present a simple model for the radial dynamics of the cavity based on the collapse of an infinite cylinder. This model accounts for the observed asymmetry of the radial dynamics between the expansion and the contraction phases of the cavity. It reproduces the scaling of the closure depth and total depth of the cavity which are both found to scale roughly as ∝ Fr 1/2 with a weakly Froude-number-dependent prefactor. In addition, the model accurately captures the dynamics of the minimal radius of the cavity and the scaling of the volume V bubble of air entrained by the process, namely, V bubble / h 0 3 ∝(1 + 0.26 Fr 1/2 ) Fr 1/2 .

Noncontinuous Froude Number Scaling for the Closure Depth of a Cylindrical Cavity

A long, smooth cylinder is dragged through a water surface to create a cavity with an initially cylindrical shape. This surface void then collapses due to the hydrostatic pressure, leading to a rapid and axisymmetric pinch-off in a single point. Surprisingly, the depth at which this pinch-off takes place does not follow the expected Froude(1/3) power law. Instead, it displays two distinct scaling regimes separated by discrete jumps, both in experiment and in numerical simulations (employing a boundary integral code). We quantitatively explain the above behavior as a capillary wave effect. These waves are created when the top of the cylinder passes the water surface. Our work thus gives further evidence for the nonuniversality of the void collapse.

Acoustic measurement of bubble size in an inkjet printhead.

The volume of a bubble in a piezoinkjet printhead is measured acoustically. The method is based on a numerical model of the investigated system. The piezo not only drives the system but it is also used as a sensor by measuring the current it generates. The numerical model is used to predict this current for a given bubble volume. The inverse problem is to infer the bubble volume from an experimentally obtained piezocurrent. By solving this inverse problem, the size and position of the bubble can thus be measured acoustically. The method is experimentally validated with an inkjet printhead that is augmented with a glass connection channel, through which the bubble was observed optically, while at the same time the piezocurrent was measured. The results from the acoustical measurement method correspond closely to the results from the optical measurement.

Infrared imaging and acoustic sizing of a bubble inside a micro-electro-mechanical system piezo ink channel

Piezo drop-on-demand inkjet printers are used in an increasing number of applications because of their reliable deposition of droplets onto a substrate. Droplets of a few picoliters are ejected from an inkjet nozzle at frequencies of up to 100 kHz. However, the entrapment of an air microbubble in the ink channel can severely impede the productivity and reliability of the printing system. The air bubble disturbs the channel acoustics, resulting in disrupted drop formation or failure of the jetting process. Here we study a micro-electro-mechanical systems-based printhead. By using the actuating piezo transducer in receive mode, the acoustical field inside the channel was monitored, clearly identifying the presence of an air microbubble inside the channel during failure of the jetting process. The infrared visualization technique allowed for the accurate sizing of the bubble, including its dynamics, inside the intact printhead. A model was developed to calculate the mutual interaction between the channel acoustics and the bubble dynamics. The model was validated by simultaneous acoustical and infrared detection of the bubble. The model can predict the presence and size of entrapped air bubbles inside an operating ink channel purely from the acoustic response.