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Floaters on faraday waves: Clustering and heterogeneous flow

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  1. Tez No: 402225
  2. Yazar: CEYDA SANLI
  3. Danışmanlar: PROF. DR. DETLEF LOHSE, DR. DEVARAJ VAN DER MEER
  4. Tez Türü: Doktora
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2012
  8. Dil: İngilizce
  9. Üniversite: University of Twente
  10. Enstitü: Yurtdışı Enstitü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 161

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Özet (Çeviri)

Floating bubbles on our drinks, a collection of sea plants floating on a wavy sea surface, or as was studied in this Thesis, floating spherical particles on a surface wave all exhibit a variety of phenomena which look particularly simple, but require detailed study upon closer inspection. When we pour our favorite drink in a glass cup, lots of bubbles are generated at the surface. Most of them immediately move towards the wall of the glass cup, and accumulate there. When we try this with a plastic cup, the bubbles stay in the middle of the surface. A collection of sea plants agglomerate and move with respect to the surface wave elevation. Floating spherical particles on a Faraday wave agglomerate, drift, and as a result, demonstrate pattern formation. In Chapter 2, following the literature we showed that a macroscopic sphere can float on a static liquid-air interface in four different situations depending on its hydrophobicity and density relative to the carrier liquid. These four possibilities are nicely summarized in a single equation, which describes the shape of the meniscus generated around the floater, and determines the direction of surface tension force. Furthermore, we showed that a single small sphere with a finite wetting angle has to drift towards either the amplitude maximum (antinode) or minimum (node). Contrary to what has been stated in the literature, we found that if the meniscus around the sphere is convex (i.e., when surface tension acts upwards) the sphere drifts towards the antinode, whereas if it is concave (and surface tension acts downwards) the sphere drifts towards the node. Next to the drift, there is an attractive interaction among the floaters induced by gravity and surface tension. We present analysis of both the drift force of a single macroscopic sphere on a standing wave and the attractive capillary force of floating two identical macroscopic spheres on a static liquid-air interface. In Chapter 3, we found that the same floaters that cluster at the antinodes of the standing water wave at low ϕ , cluster at the nodal lines of the wave at high ϕ . We systematically studied the transition from low to high ϕ . Using high-speed video imaging, we observed that, when the pattern is inverted from antinode to node clus-ters, not only the position of the floater clusters, but also their dynamics is changed. The antinode clusters breath, i.e., the floaters periodically move towards and away from the antinodes and, as a consequence, also from each other, whereas the node clusters do not breath. By considering drift energy, attractive capillary energy, and the breathing effect, we developed an energy calculation from which we were able to explain the antinode to node cluster transition. Here, including the breathing effect is essential: Without breathing, no transition occurs. Pattern formation, emergence of order, and self-organization have been observed in many systems from geophysics to biophysics. There, usually a variation in a control parameter enforces the system to form or change a certain pattern. In our system, however, the driving parameters, i.e., the wavelength and amplitude of the wave, are kept constant. Patterns form, change and even invert solely by increasing the number of floating particles per unit of surface area. This sets our system apart from most others that show pattern formation. In Chapter 4, we characterized the observed floater patterns on a standing Faraday wave from low ϕ to high ϕ , applying both global and local analysis. In a global picture, we employed the Minkowski functionals point pattern approach. We showed that it is a very useful tool to study a variety of properties, such as cluster size, aspect ratio, and connectivity, of the complex floater patterns. In a local context, we studied the local bond orientational order parameter | Ψ6 |, which measures the deviation from a hexagonal packing, and the pair correlation function g(r). We found that even though | Ψ6 | is not a robust tool to characterize our patterns, which often are far from hexagonal order, the method provides a nice illustration of them. g(r) constitutes a better representation of the increasing local order with increasing ϕ . In summary, the concentration dependent floater patterns were characterized as follows: The circular irregularly packed antinode clusters at low ϕ are replaced by loosely packed filamentary structures at intermediate ϕ , and then followed by densely packed grid-shaped node clusters at high ϕ . In Chapter 5, we turned to a different regime and drove a densely packed monolayer of the same floaters using nonlinear chaotic Faraday waves with a wavelength of the order of the size of a single floater. In this regime, we observed that the flow is composed of floater domains. At low ϕ , small floater groups initially moving together, break up some time later. This process repeats itself continuously. During the break-up process, the initial floater group morphologically deforms such that the initially selected compact, circular subgroups evolve into a stretched, filamentary floater clusters. At intermediate and high ϕ however, the break-up process is less likely to occur and the motion of the floater clusters is dominated by the morphological deformation due to the stretching. To characterize the resultant heterogenous dynamics of the floater clusters, we developed a morphological method, inspired by the Minkowski point pattern approach of Chapter 4. We also evaluated the dynamical heterogeneities generated by our densely packed cohesive floaters using the fourpoint dynamic susceptibility known from the literature. When comparing the time scale from the morphological approach with that from the dynamic susceptibility we find good qualitative agreement. This suggests that the morphological approach constitutes a valuable alternative representation of the dynamical heterogeneities. It may even be a stronger tool since it not only provides the time scale and amount of the heterogeneities, as can also be deduced from the dynamic susceptibility, but in addition abundant information on the dynamics of the system, such as providing a visualization of the flow (see the back side of the Thesis cover), morphological deformations in time, and the correlation of the simultaneous motion of many floaters in space. To obtain those from the dynamic susceptibility is hardly (if at all) feasible.

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