-Recently, an active microswimmer was constructed where a micron-sized droplet of bromine water was placed into a surfactant-laden oil phase. Due to a bromination reaction of the surfactant at the interface, the surface tension locally increases and becomes non-uniform. This drives a Marangoni flow which propels the squirming droplet forward. We develop a diffusionadvection-reaction equation for the order parameter of the surfactant mixture at the droplet interface using a mixing free energy. Numerical solutions reveal a stable swimming regime above a critical Marangoni number M but also stopping and oscillating states when M is increased further. The swimming droplet is identified as a pusher whereas in the oscillating state it oscillates between being a puller and a pusher.
The Marangoni effect refers to fluid flow induced by a gradient in surface tension at a fluid-fluid interface. We determine the full three-dimensional Marangoni flow generated by a non-uniform surface tension profile at the interface of a self-propelled spherical emulsion droplet. For all flow fields inside, outside, and at the interface of the droplet, we give analytical formulas. We also calculate the droplet velocity vector v D , which describes the swimming kinematics of the droplet, and generalize the squirmer parameter β, which distinguishes between different swimmer types called neutral, pusher, or puller. In the second part of this paper, we present two illustrative examples, where the Marangoni effect is used in active emulsion droplets. First, we demonstrate how micelle adsorption can spontaneously break the isotropic symmetry of an initially surfactant-free emulsion droplet, which then performs directed motion. Second, we think about light-switchable surfactants and laser light to create a patch with a different surfactant type at the droplet interface. Depending on the setup such as the wavelength of the laser light and the surfactant type in the outer bulk fluid, one can either push droplets along unstable trajectories or pull them along straight or oscillatory trajectories regulated by specific parameters. We explore these cases for strongly absorbing and for transparent droplets.
Lattice models in biological physics PACS 87.16.Ka -Filaments in subcellular structure and processes PACS 87.16.Qp -FlagellaAbstract -The growth of bacterial flagellar filaments is a self-assembly process where flagellin molecules are transported through the narrow core of the flagellum and are added at the distal end. To model this situation, we generalize a growth process based on the TASEP model by allowing particles to move both forward and backward on the lattice. The bias in the forward and backward jump rates determines the lattice tip speed, which we analyze and also compare to simulations. For positive bias, the system is in a non-equilibrium steady state and exhibits boundary-induced phase transitions. The tip speed is constant. In the no-bias case we find that the length of the lattice grows as N (t) ∝ √ t, whereas for negative drift N (t) ∝ ln t. The latter result agrees with experimental data of bacterial flagellar growth.
A micron-sized droplet of bromine water immersed in a surfactant-laden oil phase can swim (S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13 073021 (2011). The bromine reacts with the surfactant at the droplet interface and generates a surfactant mixture. It can spontaneously phase-separate due to solutocapillary Marangoni flow, which propels the droplet. We model the system by a diffusion-advection-reaction equation for the mixture order parameter at the interface including thermal noise and couple it to fluid flow. Going beyond previous work, we illustrate the coarsening dynamics of the surfactant mixture towards phase separation in the axisymmetric swimming state. Coarsening proceeds in two steps: an initially slow growth of domain size followed by a nearly ballistic regime. On larger time scales thermal fluctuations in the local surfactant composition initiates random changes in the swimming direction and the droplet performs a persistent random walk, as observed in experiments. Numerical solutions show that the rotational correlation time scales with the square of the inverse noise strength. We confirm this scaling by a perturbation theory for the fluctuations in the mixture order parameter and thereby identify the active emulsion droplet as an active Brownian particle.
Water hardness is determined by titration with EDTÁ using a mixed indicator containing Arsenazo I and a buffer containing THAM. The end point is sharp and quick; iron, copper, aluminum, and common anions do not interfere in the amounts present in most water samples. A rapid and accurate spectrophotometric titration procedure is also reported. Formation constants for the calcium(ll) and magnesium(ll) complexes with Arsenazo I at pH 10 have also been determined.Few analytical methods compare in importance with the EDTA titration of total hardness in water. Despite this, the existing procedures for water hardness (1-5) have several unfortunate drawbacks. Eriochrome Black T, Calmagite, and other indicators (which are all of similar general structure) change color slowly at the end point and thus require that the end point be approached slowly and carefully. Further, traces of iron, copper, and certain other metal ions dissolved in the water block these indicators and either prevent an end point or seriously reduce its sharpness. Cyanide and other masking agents may be employed, but cyanide is a potential safety hazard.
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