Stokes flow near the contact line of an evaporating drop

The evaporation of sessile drops in quiescent air is usually governed by vapour diffusion. For contact angles below $90^\circ$, the evaporative flux from the droplet tends to diverge in the vicinity of the contact line. Therefore, the description of the flow inside an evaporating drop has remained a challenge. Here, we focus on the asymptotic behaviour near the pinned contact line, by analytically solving the Stokes equations in a wedge geometry of arbitrary contact angle. The flow field is described by similarity solutions, with exponents that match the singular boundary condition due to evaporation. We demonstrate that there are three contributions to the flow in a wedge: the evaporative flux, the downward motion of the liquid-air interface and the eigenmode solution which fulfils the homogeneous boundary conditions. Below a critical contact angle of $133.4^\circ$, the evaporative flux solution will dominate, while above this angle the eigenmode solution dominates. We demonstrate that for small contact angles, the velocity field is very accurately described by the lubrication approximation. For larger contact angles, the flow separates into regions where the flow is reversing towards the drop centre.Comment: Journal of Fluid Mechanics 709 (2012

Laser-to-droplet alignment sensitivity relevant for laser-produced plasma sources of extreme ultraviolet light

We present and experimentally validate a model describing the sensitivity of the tilt angle, expansion and propulsion velocity of a tin micro-droplet irradiated by a 1 {\mu}m Nd:YAG laser pulse to its relative alignment. This sensitivity is particularly relevant in industrial plasma sources of extreme ultraviolet light for nanolithographic applications. Our model has but a single parameter: the dimensionless ratio of the laser spot size to the effective size of the droplet, which is related to the position of the plasma critical density surface. Our model enables the development of straightforward scaling arguments in turn enabling precise control the alignment sensitivity.Comment: 7 pages, 5 figure

The Formative Years of the Modern Corporation: The Dutch East India Company VOC, 1602-1623

With their legal personhood, permanent capital with transferable shares, separation of ownership and management, and limited liability for both shareholders and managers, the Dutch East India Company (VOC) and subsequently the English East India Company (EIC) are generally considered a major institutional breakthrough. Our analysis of the business operations and notably the financial policy of the VOC during the company’s first two decades in existence shows that its c

An Admiralty for Asia: Isaac le Maire and conflicting conceptions about the corporate governance of the VOC

The Dutch East India Company or VOC in 1602 showed many characteristics of modern corporations, including limited liability, freely transferable shares, and well-defined managerial functions. However, we challenge the notion of the VOC as the precursor of modern corporations to argue that the company was a hybrid, combining elements from traditional partnerships with a governance structure modeled on existing public-private partnerships. The company’s charter r

Mass Partitioning in Fragmenting Tin Sheets

We experimentally study the mass partitioning of a fragmenting liquid sheet formed after the impact of a ns-laser pulse on a tin microdroplet, and its dependence on laser pulse energy and droplet size. We present the temporal evolution of individual liquid fractions: the sheet and its bounding rim, ligaments protruding from the rim, and droplets shed by the ligaments, applying machine learning to analyze subresolution fragments. Our results show that the temporal evolution of the mass partitioning between the sheet, rim, ligaments, and fragments is independent of the deformation Weber number - following Wang and Bourouiba [J. Fluid Mech. 935, A29 (2022)] for the analogous droplet-pillar impact case, extending the work to larger Weber numbers and to a system where the timescale of deformation is fully decoupled from impact. The full mass partitioning is accounted for by quantifying the further contributions unique to the laser-droplet impact case: that of a centrally located mass remnant, and the mass ablated by the laser pulse. These findings can be employed to optimize the mass utilization of the liquid tin that is used as target material in the production of extreme ultraviolet light for nanolithography.</p

Speed of fragments ejected by an expanding liquid tin sheet

We experimentally investigate the speed of fragments produced by ligament breakup in the laser-induced deformation of tin microdroplets into axisymmetric sheets. The experiments were carried out covering a wide range of droplet diameters and laser-pulse energies. In addition to fragments produced by end-pinching, we also observe fragments shed via Rayleigh-Plateau breakup of long ligaments at late times. A double-frame backlit camera was used to obtain the speeds of the fragments u(f) and the time of their detachment t(d). We show that by normalizing u(f) to the initial expansion speed of the sheet R-0, all data collapse onto a single, universal curve that is a function of the dimensionless time t(d)/tau(c) only, where tau(c) is the capillary time. This universal curve is explicitly independent of the droplet's Weber number. The collapse of u(f) is supported by energy conservation arguments. Our findings enable the prediction of the instantaneous speed and position of the fragments shed from liquid tin targets used in state-of-the-art extreme ultraviolet nanolithography, facilitating the design of effective mitigation strategies against microparticulate debris

Drop fragmentation by laser-pulse impact

We study the fragmentation of a liquid drop that is hit by a laser pulse. The drop expands into a thin sheet that breaks by the radial expulsion of ligaments from its rim and the nucleation and growth of holes on the sheet. By combining experimental data from two liquid systems with vastly different time- and length scales we show how the early-time laser-matter interaction affects the late-time fragmentation. We identify two Rayleigh--Taylor instabilities of different origins as the prime cause of the fragmentation and derive scaling laws for the characteristic breakup time and wavenumber. The final web of ligaments results from a subtle interplay between these instabilities and deterministic modulations of the local sheet thickness, which originate from the drop deformation dynamics and spatial variations in the laser-beam profile.Comment: about to be submitted to JF

Expansion Dynamics After Laser-Induced Cavitation in Liquid Tin Microdroplets

The cavitation-driven expansion dynamics of liquid tin microdroplets is investigated, set in motion by the ablative impact of a 15-ps laser pulse. We combine high-resolution stroboscopic shadowgraphy with an intuitive fluid dynamic model that includes the onset of fragmentation, and find good agreement between model and experimental data for two different droplet sizes over a wide range of laser pulse energies. The dependence of the initial expansion velocity on these experimental parameters is heuristically captured in a single power law. Further, the obtained late-time mass distributions are shown to be governed by a single parameter. These studies are performed under conditions relevant for plasma light sources for extreme-ultraviolet nanolithography.Comment: 7 pages, 6 figure

TThe ENCCA-WP7/EuroSarc/EEC/PROVABES/EURAMOS 3rd European Bone Sarcoma Networking Meeting/Joint Workshop of EU Bone Sarcoma Translational Research Networks; Vienna, Austria, September 24–25, 2015. Workshop Report

This report summarizes the results of the 3rd Joint ENCCA-WP7, EuroSarc, EEC, PROVABES, and EURAMOS European Bone Sarcoma Network Meeting, which was held at the Children's Cancer Research Institute in Vienna, Austria on September 24-25, 2015. The joint bone sarcoma network meetings bring together European bone sarcoma researchers to present and discuss current knowledge on bone sarcoma biology, genetics, immunology, as well as results from preclinical investigations and clinical trials, to generate novel hypotheses for collaborative biological and clinical investigations. The ultimate goal is to further improve therapy and outcome in patients with bone sarcomas

The economics of debt clearing mechanisms

We examine the evolution of decentralized clearinghouse mechanisms from the 13th to the 18th century; in particular, we explore the clearing of non- or limitedtradable debts like bills of exchange. We construct a theoretical model of these clearinghouse mechanisms, similar to the models in the theoretical matching literature, and show that specific decentralized multilateral clearing algorithms known as rescontre, skontrieren or virement des parties used by merchants were efficient in specific historical contexts. We can explain both the evolutionary self-organizing emergence of late medieval and early modern fairs, and its robustness during the 17th and 18th century