Simulations of a weakly conducting droplet under the influence of an alternating electric field

We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based finite volume flow solver. The mean amplitude of shape oscillations of a droplet subjected to an alternating electric field for leaky dielectric fluids is the same as the steady-state deformation under an equivalent root mean squared direct electric field for all possible electrical conductivity ratio $(K_r)$ and permittivity ratio $(S)$ of the droplet to the surrounding fluid. In contrast, our simulations for weakly conducting media show that this equivalence between alternating and direct electric fields does not hold for $K_r \ne S$. Moreover, for a range of parameters, the deformation obtained using the alternating and direct electric fields is qualitatively different, i.e. for low $K_r$ and high $S$, the droplet becomes prolate under alternating electric field but deforms to an oblate shape in the case of the equivalent direct electric field. A parametric study is conducted by varying the time period of the applied alternating electric field, the permittivity and the electrical conductivity ratios. It is observed that while increasing $K_r$ has a negligible effect on the deformation dynamics of the droplet for $K_r<S$, it enhances the deformation of the droplet when $K_r>S$ for both alternating and direct electric fields. We believe that our results may be of immense consequence in explaining the morphological evolution of droplets in a plethora of scenarios ranging from nature to biology.Comment: 10 pages, 8 figure

Tuning the Mechanical Properties in Model Nanocomposites: Influence of the Polymer-Filler Interfacial Interactions

This paper presents a study of the polymer-filler interfacial effects on filler dispersion and mechanical reinforcement in Polystyrene (PS) / silica nanocomposites by direct comparison of two model systems: un-grafted and PS-grafted silica dispersed in PS matrix. The structure of nanoparticles has been investigated by combining Small Angle Neutron Scattering (SANS) measurements and Transmission Electronic Microscopic (TEM) images. The mechanical properties were studied over a wide range of deformation by plate/plate rheology and uni-axial stretching. At low silica volume fraction, the particles arrange, for both systems, in small finite size non-connected aggregates and the materials exhibit a solid-like behavior independent of the local polymer/fillers interactions suggesting that reinforcement is dominated by additional long range effects. At high silica volume fraction, a continuous connected network is created leading to a fast increase of reinforcement whose amplitude is then directly dependent on the strength of the local particle/particle interactions and lower with grafting likely due to deformation of grafted polymer.Comment: Journal Polymer Science (2011

Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki

These notes survey the main ideas, concepts and objects of the work by Shinichi Mochizuki on interuniversal Teichmüller theory [31], which might also be called arithmetic deformation theory, and its application to diophantine geometry. They provide an external perspective which complements the review texts [32] and [33]. Some important developments which preceded [31] are presented in the first section. Several important aspects of arithmetic deformation theory are discussed in the second section. Its main theorem gives an inequality–bound on the size of volume deformation associated to a certain log-theta-lattice. The application to several fundamental conjectures in number theory follows from a further direct computation of the right hand side of the inequality. The third section considers additional related topics, including practical hints on how to study the theory

Deformation of a liquid film by an impinging gas jet: Modelling and experiments

© 2019, Avestia Publishing. We consider liquid in a cylindrical beaker and study the deformation of its surface under the influence of an impinging gas jet. Analyzing such a system not only is of fundamental theoretical interest, but also of industrial importance, e.g., in metallurgical applications. The solution of the full set of governing equations is computationally expensive. Therefore, to obtain initial insight into relevant regimes and timescales of the system, we first derive a reduced-order model (a thin-film equation) based on the long-wave assumption and on appropriate decoupling the gas problem from that for the liquid and taking into account a disjoining pressure. We also perform direct numerical simulations (DNS) of the full governing equations using two different approaches, the Computational Fluid Dynamics (CFD) package in COMSOL and the volume-of-fluid Gerris package. The DNS are used to validate the results for the thinfilm equation and also to investigate the regimes that are beyond the range of validity of this equation. We additionally compare the computational results with experiments and find good agreement

Lectures on Knot Homology and Quantum Curves

Besides offering a friendly introduction to knot homologies and quantum curves, the goal of these lectures is to review some of the concrete predictions that follow from the physical interpretation of knot homologies. In particular, this interpretation allows one to pose questions that would not have been asked otherwise, such as, "Is there a direct relation between Khovanov homology and the A-polynomial of a knot?" We will explain that the answer to this question is "yes," and introduce a certain deformation of the planar algebraic curve defined by the zero locus of the A-polynomial. This novel deformation leads to a categorified version of the Generalized Volume Conjecture that completely describes the "color behavior" of the colored sl(2) knot homology, and eventually to a similar version for the colored HOMFLY homology. Furthermore, this deformation is strong enough to distinguish mutants, and its most interesting properties include relations to knot contact homology and knot Floer homology

"Wet-to-Dry" Conformational Transition of Polymer Layers Grafted to Nanoparticles in Nanocomposite

The present communication reports the first direct measurement of the conformation of a polymer corona grafted around silica nano-particles dispersed inside a nanocomposite, a matrix of the same polymer. This measurement constitutes an experimental breakthrough based on a refined combination of chemical synthesis, which permits to match the contribution of the neutron silica signal inside the composite, and the use of complementary scattering methods SANS and SAXS to extract the grafted polymer layer form factor from the inter-particles silica structure factor. The modelization of the signal of the grafted polymer on nanoparticles inside the matrix and the direct comparison with the form factor of the same particles in solution show a clear-cut change of the polymer conformation from bulk to the nanocomposite: a transition from a stretched and swollen form in solution to a Gaussian conformation in the matrix followed with a compression of a factor two of the grafted corona. In the probed range, increasing the interactions between the grafted particles (by increasing the particle volume fraction) or between the grafted and the free matrix chains (decreasing the grafted-free chain length ratio) does not influence the amplitude of the grafted brush compression. This is the first direct observation of the wet-to-dry conformational transition theoretically expected to minimize the free energy of swelling of grafted chains in interaction with free matrix chains, illustrating the competition between the mixing entropy of grafted and free chains, and the elastic deformation of the grafted chains. In addition to the experimental validation of the theoretical prediction, this result constitutes a new insight for the nderstanding of the general problem of dispersion of nanoparticles inside a polymer matrix for the design of new nanocomposites materials

Visualizing the strain evolution during the indentation of colloidal glasses

We use an analogue of nanoindentation on a colloidal glass to elucidate the incipient plastic deformation of glasses. By tracking the motion of the individual particles in three dimensions, we visualize the strain field and glass structure during the emerging deformation. At the onset of flow, we observe a power-law distribution of strain indicating strongly correlated deformation, and reflecting a critical state of the glass. At later stages, the strain acquires a Gaussian distribution, indicating that plastic events become uncorrelated. Investigation of the glass structure using both static and dynamic measures shows a weak correlation between the structure and the emerging strain distribution. These results indicate that the onset of plasticity is governed by strong power-law correlations of strain, weakly biased by the heterogeneous glass structure.Comment: 13 pages, 8 figure