Mixing presents a notoriously difficult problem in small amounts of fluids. Herein, surface acoustic waves provide a convenient technique to generate time-dependent flow patterns. These flow patterns can be optimized in such a way that advected particles are mixed most efficiently in the fluid within a short time compared to the time pure diffusion would take. Investigations are presented for the mixing efficiency of a flat cylinder that is driven by two surface acoustic waves. The experimental results favorably agree with model calculations of the flow patterns and the advective transport.

Abstract-This work presents an approach for determining the streaming patterns that are generated by Rayleigh surface acoustic waves in arbitrary 3-D geometries by finite element method (FEM) simulations. An efficient raytracing algorithm is applied on the acoustic subproblem to avoid the unbearable memory demands and computational time of a conventional FEM acoustics simulation in 3-D. The acoustic streaming interaction is modeled by a body force term in the Stokes equation. In comparisons between experiments and simulated flow patterns, we demonstrate the quality of the proposed technique.

A model of childhood epidemics focusing on the impact of the school-year is presented. At the onset of the epidemic season, a new cohort of susceptible students enter the school, all other age-classes advance one year, while the oldest age-group leaves the mixing pool. If the susceptible pool is sufficiently large at the onset of the season, an epidemic will arise and run to its conclusion prior to the end of the school-year. The system is expressed in terms of a discrete dynamical system giving the changes in the age-dependent immunity structure on a year-to-year basis. If disease transmission is independent of age, the system settles at epidemics of constant size in each season. If disease transmission is age-dependent, more complicated dynamics may occur, including multiple stable states and chaos. Introduction. Disease transmission in schools played a central role in main-taining the regularly recurring epidemics of childhood diseases during the prevaccination era. In particular the summer break with low transmission, the annual infusion of a new cohort of (susceptible) first-year students, and the progression of students through the school system contributed substantially to the external forcing and the well-known two-year cycle in measles epidemics [42,18,38,3]. The aim of this paper is to include this pulsed forcing in a mathematically tractable, age-structured epidemic model.From an analytical viewpoint, the discontinuous nature of student admission and class-progression makes it rather awkward to incorporate the phenomenon into an epidemic model describing disease transmission dynamics in terms of the flow of hosts from the susceptible through the infected to the recovered class (SIR-model). Consequently the previous models of childhood epidemics with annual updates of the host structure have not been amenable to analytic methods. However, these "realistic age-structured" models (RAS-models) reflect quite accurately the prevaccination measles epidemics in England [42,10,23,28], although recent results suggest that a detailed description of the seasonal variation in contact rates-rather than age-structure-is essential for matching the observed pattern of childhood diseases in England [16,8,18,29,41]. To simplify the analysis most mathematical studies of seasonally driven childhood epidemics have assumed that transmission strength varies sinusoidally with a period of one year, neglecting the details of the school-year [13,31,7,33,37]. Recently Billings and Schwartz [9] have provided a detailed description of the Poincaré return map associated with a forced SIR-model and showed how noise may lead to stochastic chaotic dynamics in such models.

A challenging topic o f the lab-on-a-chip research is to implement sorting mechanisms on low cost disposable chips. In many applications, surface acoustic waves (SAW) have recently proven to be a versatile and efficient technique for microfluidic actuation. A SAW is excited by applying a high frequency signal to a piezoelectric substrate. When the wave hits the solid/liquid interface it transmits its acoustic energy into the liquid and a local pressure gradient emerges, leading to surface acoustic streaming. Experiments can be performed directly on the piezoelectric substrate or on a separate glass slide positioned on top of the SAW source. We developed a technique for the accumulation o f solid and soft objects in SAW generated microvortices in microfluidic channels. For this purpose, the comer of a rectangular microchannel is irradiated by a wide SAW beam. There, the SAW excites sound waves in the fluid producing a typical acoustic streaming flow pattern which typically exhibits two vortices. Particles injected into the flow are accumulated and dynamically trapped in one of these vortices. After the flow is stopped, the collected particles stay in the position of the vortex. In our experiments, we use open microfluidic channels with functionalized hydrophilic-hydrophobic surfaces on glass substrates as well as closed channels build with the elastomer PDMS via soft lithography. We find that the accumulation efficiency for particles is strongly size dependent. Below a critical radius of 500 nm, particles tend to flow through the vortex and are not captured in the comer. Generally, larger particles can be collected at more moderate SAW power levels compared to smaller particles. Therefore, by adjusting the SAW power level, one is able to collect particles above a designated size. This concept is not limited to solid particles but can also be applied to soft objects like cells.

Surface acoustic waves are used to induce acoustic streaming in small amounts of liquid on a chip surface. Both mixing as well as actuation of the fluid can be achieved in an efficient and controllable manner. This way, highly complex chip based assay laboratories can be created. Combined with elastomer microfluidic devices and droplet based microreactors, high speed and very selective cell sorters have been recently demonstrated.