ISSN 1063-7710, Acoustical Physics, 2015, Vol. 61, No. 2, pp. 173–177. © Pleiades Publishing, Ltd., 2015. Original Russian Text © P.V. Lebedev-Stepanov, O.V. Rudenko, 2015, published in Akusticheskii Zhurnal, 2015, Vol. 61, No. 2, pp. 191–195. 173 INTRODUCTION The work studies slow vortex flows in a thin cylindri- cal layer of a viscous fluid. Flows are generated by cap- illary waves on the free surface of the layer; these waves in turn are initiated by indentor oscillations or vibra- tions of the substrate. The effect is similar to acoustic flows occurring in an ultrasound wave field [1]. This phenomenon has been well studied and has found application in a number of technologies. In particular, review [2] is devoted to biomedical applications of acoustic flows. Flows within thin layers and fluid drops are used in nanotechnologies to form ordered nanoparticle struc- tures [3, 4]. In connection with these applications, the authors of [5] calculated a flow in a layer excited by sur- face waves traveling along the solid–liquid interface. The authors also analyzed the generation of flows by capillary waves in a thin plane layer [6]. The formula- tion of the problem and the scheme for its solution in [6] are analogous to those described in this paper; however, the cylindrical geometry of the problem adopted here significantly complicates calculations in comparison to those in [6]. In addition, the cylindrical shape of the drop makes it possible during its drying to create ring particle structures, which can be used as zonal plates to focus waves and create Bessel wave beams. CAPILLARY WAVES AND RADIATION FORCES Let us consider a fluid layer in the form of a round cylinder of radius R and height forming H. The fluid occupies area ; a horizontal plate is located on its upper surface (this is the plane ). The polar coordinates are introduced as shown in Fig. 1. Both types of motion—a wave and slow flow—can be described by a system of viscous incompressible fluid dynamics equations: (1) Here, u is the velocity, p is pressure, ρ is density, and ν is the kinematic viscosity of the fluid. In Eqs. 1, we 0 , r R < < 0 H z - < < z H =- ( ) , div 0. p t ∇ ∂ + ∇ =- + νΔ = ∂ ρ u u u u u NONLINEAR ACOUSTICS Acoustic Microfluidics: Capillary Waves and Vortex Flows in the Cylindrical Volume of a Fluid Drop P. V. Lebedev-Stepanov a, g and O. V. Rudenko b, c, d, e, f a Center for Photochemistry, Russian Academy of Sciences, Moscow, Russia b Physics Falculty, Moscow State University, Moscow, 119991 Russia c Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia d Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia e School of Engineering, Blekinge Institute of Technology, 37179 Karlskrona, Sweden f Nizhni Novgorod State University, Nizhni Novgorod, Russia g National Research Nuclear University Moscow Engineering Physics Institute (MEPhI), Moscow Russia e-mail: petrls@mail.ru; rudenko@acs366.phys.msu.ru Received September 30, 2014 Abstract—We calculate the field of radiation forces in a cylindrical fluid layer on a solid substrate formed as a result of the action on a fluid of a capillary wave propagating from the axis along a free surface. We study the structure of acoustic flows excited by the radiation forces. We discuss the action of flows on small-sized par- ticles and the possibilities of these particles to form ordered structures. Keywords: acoustic microfluidics, capillary waves, radiation forces, nonlinearity, acoustic flows, fluid drop, evaporation, nanoparticle structures DOI: 10.1134/S1063771015020098 z R r –H Fig. 1. Layer of fluid on substrate and polar coordinate sys- tem pertaining to it. Capillary waves on free surface are shown by dashed lines.