# Use of dynamic schlieren interferometry to study fluctuations during free diffusion.

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TL;DR: This work presents a novel experimental approach that combines optical microscopy, holography, and light scattering for studying inhomogeneous and dynamic media and can be regarded as the spatial equivalent of Fourier transform infrared spectroscopy.

Abstract: Fourier transform light scattering (FTLS) is a novel experimental approach that combines optical microscopy, holography, and light scattering for studying inhomogeneous and dynamic media. In FTLS the optical phase and amplitude of a coherent image field are quantified and propagated numerically to the scattering plane. Because it detects all the scattered angles (spatial frequencies) simultaneously in each point of the image, FTLS can be regarded as the spatial equivalent of Fourier transform infrared spectroscopy, where all the temporal frequencies are detected at each moment in time.

146 citations

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25 Jun 2015

TL;DR: In this article, the authors consider the interaction between a Particle of Immobile Surface Interacting with a Solid Wall 5.5.2 and Fluid Particles and Films of Tangentially Mobile Surfaces.

Abstract: 5.5 HYDRODYNAMIC INTERACTIONS IN DISPERSIONS 106 5.5.1 Basic Equations. Lubrication Approximation 5.5.2 Interaction Between Particles of Tangentially Immobile Surfaces 5.5.2.1 Taylor and Reynolds Equations, and Influence of the Particle Shape 5.5.2.2 Interactions Among Non-Deformable Particles at Large Distances 5.5.2.3 Stages of Thinning of a Liquid Film 5.5.2.4 Dependence of Emulsion Stability on the Droplet Size 5.5.3 Effect of Surface Mobility 5.5.3.1 Diffusive and Convective Fluxes at an Interface; Marangoni Effect 5.5.3.2 Fluid Particles and Films of Tangentially Mobile Surfaces 5.5.3.3 Bancroft Rule for Emulsions 5.5.3.4 Demulsification and Defoaming 5.5.4 Interactions in Non-Preequilibrated Emulsions 5.5.4.1 Surfactant Transfer from Continuous to Disperse Phase (Cyclic Dimpling) 5.5.4.2 Surfactant Transfer form Disperse to Continuous Phase (Osmotic Swelling) 5.5.4.3 Equilibration of Two Droplets Across a Thin Film 5.5.5 Hydrodynamic Interaction of a Particle with an Interface 5.5.5.1 Particle of Immobile Surface Interacting with a Solid Wall 5.5.5.2 Fluid Particles of Mobile Surfaces 5.5.6 Bulk Rheology of Dispersions

134 citations

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University of Edinburgh

^{1}, University of Glasgow^{2}, Paris Diderot University^{3}, Harvard University^{4}TL;DR: A fast, high-throughput method for characterizing the motility of microorganisms in three dimensions based on standard imaging microscopy by analyzing the spatiotemporal fluctuations of the intensity in the sample from time-lapse images and obtaining the intermediate scattering function of the system.

Abstract: We present a fast, high-throughput method for characterizing the motility of microorganisms in three dimensions based on standard imaging microscopy. Instead of tracking individual cells, we analyze the spatiotemporal fluctuations of the intensity in the sample from time-lapse images and obtain the intermediate scattering function of the system. We demonstrate our method on two different types of microorganisms: the bacterium Escherichia coli (both smooth swimming and wild type) and the biflagellate alga Chlamydomonas reinhardtii. We validate the methodology using computer simulations and particle tracking. From the intermediate scattering function, we are able to extract the swimming speed distribution, fraction of motile cells, and diffusivity for E. coli, and the swimming speed distribution, and amplitude and frequency of the oscillatory dynamics for C. reinhardtii. In both cases, the motility parameters were averaged over ∼10(4) cells and obtained in a few minutes.

115 citations

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TL;DR: A theoretical model for microscope imaging is derived that accounts for the three-dimensional nature of the sample, the arbitrary coherence properties of the light source, and the effect of the finite numerical aperture of the microscope objective and extends to the class of microscopy techniques that can be described by a linear space-invariant imaging of the density of the scattering centers, which includes, for example, dynamic fluorescence microscopy.

Abstract: We describe the use of a bright-field microscope for dynamic light scattering experiments on weakly scattering samples. The method is based on collecting a time sequence of microscope images and analyzing them in the Fourier space to extract the characteristic time constants as a function of the scattering wave vector. We derive a theoretical model for microscope imaging that accounts for (a) the three-dimensional nature of the sample, (b) the arbitrary coherence properties of the light source, and (c) the effect of the finite numerical aperture of the microscope objective. The model is tested successfully against experiments performed on a colloidal dispersion of small spheres in water, by means of the recently introduced differential dynamic microscopy technique [R. Cerbino and V. Trappe, Phys. Rev. Lett. 100, 188102 (2008)]. Finally, we extend our model to the class of microscopy techniques that can be described by a linear space-invariant imaging of the density of the scattering centers, which includes, for example, dynamic fluorescence microscopy.

107 citations

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TL;DR: Digital Fourier microscopy (DFM) as discussed by the authors has been proposed to study the correlation properties of the sample in the reciprocal space via spatial Fourier analysis of images collected in the real space.

Abstract: Soft matter is studied with a large portfolio of methods. Light scattering and video microscopy are the most employed at optical wavelengths. Light scattering provides ensemble-averaged information on soft matter in the reciprocal space. The wave-vectors probed correspond to length scales ranging from a few nanometers to fractions of millimetre. Microscopy probes the sample directly in the real space, by offering a unique access to the local properties. However, optical resolution issues limit the access to length scales smaller than approximately 200 nm. We describe recent work that bridges the gap between scattering and microscopy. Several apparently unrelated techniques are found to share a simple basic idea: the correlation properties of the sample can be characterized in the reciprocal space via spatial Fourier analysis of images collected in the real space. We describe the main features of such digital Fourier microscopy (DFM), by providing examples of several possible experimental implementations of it, some of which not yet realized in practice. We also provide an overview of experimental results obtained with DFM for the study of the dynamics of soft materials. Finally, we outline possible future developments of DFM that would ease its adoption as a standard laboratory method.

78 citations

##### References

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TL;DR: CRC handbook of chemistry and physics, CRC Handbook of Chemistry and Physics, CRC handbook as discussed by the authors, CRC Handbook for Chemistry and Physiology, CRC Handbook for Physics,

Abstract: CRC handbook of chemistry and physics , CRC handbook of chemistry and physics , کتابخانه مرکزی دانشگاه علوم پزشکی تهران

51,056 citations

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05 Feb 1976

TL;DR: In this paper, a comprehensive introduction to principles underlying laser light scattering focuses on time dependence of fluctuations in fluid systems and provides an introduction to theory of time correlation functions, with chapters on projection operator techniques in statistical mechanics.

Abstract: This comprehensive introduction to principles underlying laser light scattering focuses on time dependence of fluctuations in fluid systems It also serves as introduction to theory of time correlation functions, with chapters on projection operator techniques in statistical mechanics Over 60 text figures 1976 edition

2,435 citations

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TL;DR: The correlation length of the pattern decreased rapidly with increasing control parameter so that the size of a correlated area became much smaller than the area of the cell, suggesting that the chaotic behavior is intrinsic to large aspect ratio geometries.

Abstract: We report experiments on convection patterns in a cylindrical cell with a large aspect ratio. The fluid had a Prandtl number [sigma][approx]1. We observed a chaotic pattern consisting of many rotating spirals and other defects in the parameter range where theory predicts that steady straight rolls should be stable. The correlation length of the pattern decreased rapidly with increasing control parameter so that the size of a correlated area became much smaller than the area of the cell. This suggests that the chaotic behavior is intrinsic to large aspect ratio geometries.

215 citations

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TL;DR: In this article, a multi-tau software correlator was used to measure dynamic light scattering at many angles simultaneously, from 0.07° to 5.1°, in order to cover the wide spectrum of decay times associated with the large range of accessible angles, where the correlator channel spacing is quasilogarithmic rather than linear.

Abstract: We use a charge coupled device (CCD) camera and a multi-tau software correlator to measure dynamic light scattering (DLS) at many angles simultaneously, from 0.07° to 5.1°. Real-time autocorrelation functions are calculated by averaging both over time and over CCD pixels, each corresponding to a different coherence area. In order to cover the wide spectrum of decay times associated with the large range of accessible angles, we adopt the multitau scheme, where the correlator channel spacing is quasilogarithmic rather than linear. A detailed analysis is presented of the effects of dark noise, stray light, and finite pixel area, and methods to correct the data for these effects are developed, making a CCD camera a viable alternative for a DLS detector. We test the apparatus on a dilute suspension of colloidal particles. Very good agreement is found between the particle radius derived from the CCD data, and that obtained with a conventional DLS setup.

181 citations

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