Three-dimensional phenomena in microbubble acoustic streaming

Ultrasound-driven oscillating micro-bubbles have been used as active actuators in microfluidic devices to perform manifold tasks such as mixing, sorting and manipulation of microparticles. A common configuration consists on side-bubbles, created by trapping air pockets in blind channels perpendicular to the main channel direction. This configuration consists of acoustically excited bubbles with a semi-cylindrical shape that generate significant streaming flow. Due to the geometry of the channels, such flows have been generally considered as quasi two-dimensional. Similar assumptions are often made in many other microfluidic systems based on \emph{flat} micro-channels. However, in this paper we show that microparticle trajectories actually present a much richer behavior, with particularly strong out-of-plane dynamics in regions close to the microbubble interface. Using Astigmatism Particle Tracking Velocimetry, we reveal that the apparent planar streamlines are actually projections of a \emph{streamsurface} with a pseudo-toroidal shape. We therefore show that acoustic streaming cannot generally be assumed as a two-dimensional phenomenon in confined systems. The results have crucial consequences for most of the applications involving acoustic streaming as particle trapping, sorting and mixing.Comment: 5 pages, 4 high quality figures. Accepted for Publication in Phys. Rev. Applied, March 201

Global Operator Calculus on Spin Groups

Acknowledgements The work of P. Cerejeiras, M. Ferreira, and U. Kähler was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT– “Fundação para a Ciência e a Tecnologia”, within project UIDB/04106/2020 and UIDP/04106/2020. The present paper was supported by the project “Global operator calculi on compact and non-compact Lie groups”, Ações Integradas Luso-Alemãs – Acção No. A-42/16. Funding Open access funding provided by FCT|FCCN (b-on).n this paper, we use the representation theory of the group Spin(m) to develop aspects of the global symbolic calculus of pseudo-differential operators on Spin(3) and Spin(4) in the sense of Ruzhansky–Turunen–Wirth. A detailed study of Spin(3) and Spin(4)-representations is made including recurrence relations and natural differential operators acting on matrix coefficients. We establish the calculus of left-invariant differential operators and of difference operators on the group Spin(4) and apply this to give criteria for the subellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of first and second order globally hypoelliptic differential operators are given, including some that are locally neither invertible nor hypoelliptic. The paper presents a particular case study for higher dimensional spin groups.info:eu-repo/semantics/publishedVersio

Random lattice superstrings

We propose some new simplifying ingredients for Feynman diagrams that seem necessary for random lattice formulations of superstrings. In particular, half the fermionic variables appear only in particle loops (similarly to loop momenta), reducing the supersymmetry of the constituents of the Type IIB superstring to N=1, as expected from their interpretation in the 1/N expansion as super Yang-Mills.Comment: Section 5 which describes contributions of the string measure adde

Scaling of droplet breakup in high-pressure homogenizer orifices. Part I: Comparison of velocity profiles in scaled coaxial orifices

Properties of emulsions such as stability, viscosity or color can be influenced by the droplet size distribution. High-pressure homogenization (HPH) is the method of choice for emulsions with a low to medium viscosity with a target mean droplet diameter of less than 1 µm. During HPH, the droplets of the emulsion are exposed to shear and extensional stresses, which cause them to break up. Ongoing work is focused on better understanding the mechanisms of droplet breakup and relevant parameters. Since the gap dimensions of the disruption unit (e.g., flat valve or orifice) are small (usually below 500 µm) and the droplet breakup also takes place on small spatial and time scales, the resolution limit of current measuring systems is reached. In addition, the high velocities impede time resolved measurements. Therefore, a five-fold and fifty-fold magnified optically accessible coaxial orifice were used in this study while maintaining the dimensionless numbers characteristic for the droplet breakup (Reynolds and Weber number, viscosity and density ratio). Three matching material systems are presented. In order to verify their similarity, the local velocity profiles of the emerging free jet were measured using both a microparticle image velocimetry (µ-PIV) and a particle image velocimetry (PIV) system. Furthermore, the influence of the outlet geometry on the velocity profiles is investigated. Similar relationships were found on all investigated scales. The areas with the highest velocity fluctuations were identified where droplets are exposed to the highest turbulent forces. The Reynolds number had no influence on the normalized velocity fluctuation field. The confinement of the jet started to influence the velocity field if the outlet channel diameter is smaller than 10 times the diameter of the orifice. In conclusion, the scaling approach offers advantages to study very fast processes on very small spatial scales in detail. The presented scaling approach also offers chances in the optimization of the geometry of the disruption unit. However, the results also show challenges of each size scale, which can come from the respective production, measurement technology or experimental design. Depending on the problem to be investigated, we recommend conducting experimental studies at different scales

Generalized Gauge Theories and Weinberg-Salam Model with Dirac-K\"ahler Fermions

We extend previously proposed generalized gauge theory formulation of Chern-Simons type and topological Yang-Mills type actions into Yang-Mills type actions. We formulate gauge fields and Dirac-K\"ahler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one form gauge fields accommodated with the graded Lie algebra of $SU(2|1)$ supergroup leads Weinberg-Salam model. Thus the Weinberg-Salam model formulated by noncommutative geometry is a particular example of the present formulation.Comment: 33 pages, LaTe

Scaling of Droplet Breakup in High-Pressure Homogenizer Orifices. Part II: Visualization of the Turbulent Droplet Breakup

Emulsion formation is of great interest in the chemical and food industry and droplet breakup is the key process. Droplet breakup in a quiet or laminar flow is well understood, however, actual in-dustrial processes are always in the turbulent flow regime, leading to more complex droplet breakup phenomena. Since high resolution optical measurements on microscopic scales are extremely dif-ficult to perform, many aspects of the turbulent droplet breakup are physically unclear. To over-come this problem, scaled experimental setups (with scaling factors of 5 and 50) are used in con-junction with an original scale setup for reference. In addition to the geometric scaling, other non-dimensional numbers such as the Reynolds number, the viscosity ratio and the density ratio were kept constant. The scaling allows observation of the phenomena on macroscopic scales, whereby the objective is to show that the scaling approach makes it possible to directly transfer the findings from the macro- to the micro-/original scale. In this paper, which follows Part I where the flow fields were compared and found to be similar, it is shown by breakup visualizations that the turbulent droplet breakup process is similar on all scales. This makes it possible to transfer the results of detailed parameter variations investigated on the macro scale to the micro scale. The evaluation and analysis of the results imply that the droplet breakup is triggered and strongly influenced by the intensity and scales of the turbulent flow motion