arXiv subjects

S. Dietrich

Publications and source records attributed to S. Dietrich.

At least 37 records · Page 2Linked to original sources

arXiv2019

Cassie-Wenzel transition of a binary liquid mixture on a nano-sculptured surface

The Cassie-Wenzel transition of a symmetric binary liquid mixture in contact with a nano-corrugated wall is studied. The corrugation consists of a periodic array of nano-pits with square cross sections. The substrate potential is the sum over Lennard-Jones interactions, describing the pairwise interaction between the wall particles $C$ and the fluid particles. The liquid is composed of two species of particles, $A$ and $B$, which have the same size and equal $A - A$ and $B - B$ interactions. The liquid particles interact between each other also via $A - B$ Lennard-Jones potentials. We have employed classical density functional theory to determine the equilibrium structure of binary liquid mixtures in contact with the nano-corrugated surface. Liquid intrusion into the pits is studied as a function of various system parameters such as the composition of the liquid, the strengths of various inter-particle interactions, as well as the geometric parameters of the pits. The binary liquid mixture is taken to be at its mixed-liquid-vapor coexistence. For various sets of parameters the results obtained for the Cassie - Wenzel transition, as well as for the metastability of the two corresponding thermodynamic states, are compared with macroscopic predictions in order to check the range of validity of the macroscopic theories for systems exposed to nanoscopic confinements. Distinct from the macroscopic theory, it is found that the Cassie - Wenzel transition cannot be predicted based on the knowledge of a single parameter, such as the contact angle within the macroscopic theory.

physics.comp-ph↗

arXiv2019

Dynamics of the critical Casimir force for a conserved order parameter after a critical quench

Fluctuation-induced forces occur generically when long-ranged correlations (e.g., in fluids) are confined by external bodies. In classical systems, such correlations require specific conditions, e.g., a medium close to a critical point. On the other hand, long-ranged correlations appear more commonly in certain non-equilibrium systems with conservation laws. Consequently, a variety of non-equilibrium fluctuation phenomena, including fluctuation-induced forces, have been discovered and explored recently. Here, we address a long-standing problem of non-equilibrium critical Casimir forces emerging after a quench to the critical point in a confined fluid with order-parameter-conserving dynamics and non-symmetry-breaking boundary conditions. The interplay of inherent (critical) fluctuations and dynamical non-local effects (due to density conservation) gives rise to striking features, including correlation functions and forces exhibiting oscillatory time-dependences. Complex transient regimes arise, depending on initial conditions and the geometry of the confinement. Our findings pave the way for exploring a wealth of non-equilibrium processes in critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In certain regimes, our results are applicable to active matter.

cond-mat.stat-mech↗

arXiv2019

Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions

In a recent study [Phys. Rev. E \textbf{94}, 022103 (2016)] it has been shown that, for a fluid film subject to critical adsorption, the resulting critical Casimir force (CCF) may significantly depend on the thermodynamic ensemble. Here, we extend that study by considering fluid films within the so-called ordinary surface universality class. We focus on mean-field theory, within which the OP profile satisfies Dirichlet boundary conditions and produces a nontrivial CCF in the presence of external bulk fields or, respectively, a nonzero total order parameter within the film. Our analytical results are supported by Monte Carlo simulations of the three-dimensional Ising model. We show that, in the canonical ensemble, i.e., when fixing the so-called total mass within the film, the CCF is typically repulsive instead of attractive as in the grand canonical ensemble. Based on the Landau-Ginzburg free energy, we furthermore obtain analytic expressions for the order parameter profiles and analyze the relation between the total mass in the film and the external bulk field.

cond-mat.stat-mech↗

arXiv2019

Interface structures in ionic liquid crystals

Ionic liquid crystals (ILCs) are anisotropic mesogenic molecules which additionally carry charges. This combination gives rise to a complex interplay of the underlying (anisotropic) contributions to the pair interactions. It promises interesting and distinctive structural and orientational properties to arise in systems of ILCs, combining properties of liquid crystals and ionic liquids. While previous theoretical studies have focused on the phase behavior of ILCs and the structure of the respective bulk phases, in the present study we provide new results, obtained within density functional theory, concerning (planar) free interfaces between an isotropic liquid $L$ and two types of smectic-A phases ($S_A$ or $S_{AW}$). We discuss the structural and orientational properties of these interfaces in terms of the packing fraction profile $η(\vec{r})$ and the orientational order parameter profile $S_2(\vec{r})$ concerning the tilt angle $α$ between the (bulk) smectic layer normal and the interface normal. The asymptotic decay of $η(\vec{r})$ and of $S_2(\vec{r})$ towards their values in the isotropic bulk is discussed, too.

cond-mat.soft↗

arXiv2019

Current-mediated synchronization of a pair of beating non-identical flagella

The basic phenomenology of experimentally observed synchronization (i.e., a stochastic phase locking) of identical, beating flagella of a biflagellate alga is known to be captured well by a minimal model describing the dynamics of coupled, limit-cycle, noisy oscillators (known as the noisy Kuramoto model). As demonstrated experimentally, the amplitudes of the noise terms therein, which stem from fluctuations of the rotary motors, depend on the flagella length. Here we address the conceptually important question which kind of synchrony occurs if the two flagella have different lengths such that the noises acting on each of them have different amplitudes. On the basis of a minimal model, too, we show that a different kind of synchrony emerges, and here it is mediated by a current carrying, steady-state; it manifests itself via correlated "drifts" of phases. We quantify such a synchronization mechanism in terms of appropriate order parameters $Q$ and $Q_{\cal S}$ - for an ensemble of trajectories and for a single realization of noises of duration ${\cal S}$, respectively. Via numerical simulations we show that both approaches become identical for long observation times ${\cal S}$. This reveals an ergodic behavior and implies that a single-realization order parameter $Q_{\cal S}$ is suitable for experimental analysis for which ensemble averaging is not always possible.

cond-mat.soft↗

arXiv2019

Correlations and forces in sheared fluids with or without quenching

Spatial correlations play an important role in characterizing material properties related to non-local effects. Inter alia, they can give rise to fluctuation-induced forces. Equilibrium correlations in fluids provide an extensively studied paradigmatic case, in which their range is typically bounded by the correlation length. Out of equilibrium, conservation laws have been found to extend correlations beyond this length, leading, instead, to algebraic decays. In this context, here we present a systematic study of the correlations and forces in fluids driven out of equilibrium simultaneously by quenching and shearing, both for non-conserved as well as for conserved Langevin-type dynamics. We identify which aspects of the correlations are due to shear, due to quenching, and due to simultaneously applying both, and how these properties depend on the correlation length of the system and its compressibility. Both shearing and quenching lead to long-ranged correlations, which, however, differ in their nature as well as in their prefactors, and which are mixed up by applying both perturbations. These correlations are employed to compute non-equilibrium fluctuation-induced forces in the presence of shear, with or without quenching, thereby generalizing the framework set out by Dean and Gopinathan. These forces can be stronger or weaker compared to their counterparts in unsheared systems. In general, they do not point along the axis connecting the centers of the small inclusions considered to be embedded in the fluctuating medium. Since quenches or shearing appear to be realizable in a variety of systems with conserved particle number, including active matter, we expect these findings to be relevant for experimental investigations.

cond-mat.stat-mech↗

arXiv2018

Probing interface localization-delocalization transitions by colloids

Interface localization-delocalization transitions (ILDT) occur in two-phase fluids confined in a slit with competing preferences of the walls for the two fluid phases. At low temperatures the interface between the two phases is localized at one of the walls. Upon increasing temperature it unbinds. Although intensively studied theoretically and computationally, such transitions have not yet been observed experimentally due to severe challenges in resolving fine details of the fluid structure. Here, using mean field theory and Monte Carlo simulations of the Ising model, we propose to detect these ILDT by using colloids. We show that the finite-size and fluctuation induced force acting on a colloid confined in such a system experiences a vivid change if, upon lowering the temperature, the interface localizes at one of the walls. This change can serve as a more easily accessible experimental indicator of the transition.

cond-mat.soft↗

arXiv2018

Electrostatic interaction of particles trapped at fluid interfaces: Effects of geometry and wetting properties

The electrostatic interaction between pairs of spherical or macroscopically long, parallel cylindrical colloids trapped at fluid interfaces is studied theoretically for the case of small inter-particle separations. Starting from the effective interaction between two planar walls and by using the Derjaguin approximation, we address the issue of how the electrostatic interaction between such particles is influenced by their curvatures and by the wetting contact angle at their surfaces. Regarding the influence of curvature, our findings suggest that the discrepancies between linear and nonlinear Poisson-Boltzmann theory, which have been noticed before for planar walls, also occur for spheres and macroscopically long, parallel cylinders, though their magnitude depends on the wetting contact angle. Concerning the influence of the wetting contact angle $θ$ simple relations are obtained for equally sized particles which indicate that the inter-particle force varies significantly with $θ$ only within an interval around $90^\circ$. This interval depends on the Debye length of the fluids and on the size of the particles but not on their shape. For unequally sized particles, a more complicated relation is obtained for the variation of the inter-particle force with the wetting contact angle.

cond-mat.soft↗

arXiv2018

Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry

Using analytic and numerical approaches, we study the spatio-temporal evolution of a conserved order parameter of a fluid in film geometry, following an instantaneous quench to the critical temperature $T_c$ as well as to supercritical temperatures. The order parameter dynamics is chosen to be governed by model B within mean field theory and is subject to no-flux boundary conditions as well as to symmetric surface fields at the confining walls. The latter give rise to critical adsorption of the order parameter at both walls and provide the driving force for the non-trivial time evolution of the order parameter. During the dynamics, the order parameter is locally and globally conserved; thus, at thermal equilibrium, the system represents the canonical ensemble. We furthermore consider the dynamics of the nonequilibrium critical Casimir force, which we obtain based on the generalized force exerted by the order parameter field on the confining walls. We identify various asymptotic regimes concerning the time evolution of the order parameter and the critical Casimir force and we provide, within our approach, exact expressions of the corresponding dynamic scaling functions.

cond-mat.stat-mech↗

arXiv2018

Science with e-ASTROGAM (A space mission for MeV-GeV gamma-ray astrophysics)

e-ASTROGAM (enhanced ASTROGAM) is a breakthrough Observatory space mission, with a detector composed by a Silicon tracker, a calorimeter, and an anticoincidence system, dedicated to the study of the non-thermal Universe in the photon energy range from 0.3 MeV to 3 GeV - the lower energy limit can be pushed to energies as low as 150 keV for the tracker, and to 30 keV for calorimetric detection. The mission is based on an advanced space-proven detector technology, with unprecedented sensitivity, angular and energy resolution, combined with polarimetric capability. Thanks to its performance in the MeV-GeV domain, substantially improving its predecessors, e-ASTROGAM will open a new window on the non-thermal Universe, making pioneering observations of the most powerful Galactic and extragalactic sources, elucidating the nature of their relativistic outflows and their effects on the surroundings. With a line sensitivity in the MeV energy range one to two orders of magnitude better than previous generation instruments, e-ASTROGAM will determine the origin of key isotopes fundamental for the understanding of supernova explosion and the chemical evolution of our Galaxy. The mission will provide unique data of significant interest to a broad astronomical community, complementary to powerful observatories such as LIGO-Virgo-GEO600-KAGRA, SKA, ALMA, E-ELT, TMT, LSST, JWST, Athena, CTA, IceCube, KM3NeT, and LISA.

astro-ph.HE↗

arXiv2018

Effective squirmer models for self-phoretic chemically active spherical colloids

Various aspects of self-motility of chemically active colloids in Newtonian fluids can be captured by simple models for their chemical activity plus a phoretic slip hydrodynamic boundary condition on their surface. For particles of simple shapes (e.g., spheres) -- as employed in many experimental studies -- which move at very low Reynolds numbers in an unbounded fluid, such models of chemically active particles effectively map onto the well studied so-called hydrodynamic squirmers [S. Michelin and E. Lauga, J. Fluid Mech. \textbf{747}, 572 (2014)]. Accordingly, intuitively appealing analogies of "pusher/puller/neutral" squirmers arise naturally. Within the framework of self-diffusiophoresis we illustrate the above mentioned mapping and the corresponding flows in an unbounded fluid for a number of choices of the activity function (i.e., the spatial distribution and the type of chemical reactions across the surface of the particle). We use the central collision of two active particles as a simple, paradigmatic case for demonstrating that in the presence of other particles or boundaries the behavior of chemically active colloids may be \textit{qualitatively} different, even in the far field, from the one exhibited by the corresponding "effective squirmer", obtained from the mapping in an unbounded fluid. This emphasizes that understanding the collective behavior and the dynamics under geometrical confinement of chemically active particles necessarily requires to explicitly account for the dependence of the hydrodynamic interactions on the distribution of chemical species resulting from the activity of the particles.

cond-mat.soft↗

arXiv2018

Electrolyte solutions at heterogeneously charged substrates

The influence of a chemically or electrically heterogeneous distribution of interaction sites at a planar substrate on the number density of an adjacent fluid is studied by means of classical density functional theory (DFT). In the case of electrolyte solutions the effect of this heterogeneity is particularly long ranged, because the corresponding relevant length scale is set by the Debye length which is large compared to molecular sizes. The DFT used here takes the solvent particles explicitly into account and thus captures phenomena, inter alia, due to ion-solvent coupling. The present approach provides closed analytic expressions describing the influence of chemically and electrically nonuniform walls. The analysis of isolated δ-like interactions, isolated interaction patches, and hexagonal periodic distributions of interaction sites reveals a sensitive dependence of the fluid density profiles on the type of the interaction, as well as on the size and the lateral distribution of the interaction sites.

cond-mat.soft↗

arXiv2018

Self-diffusiophoresis induced by fluid interfaces

The influence of a fluid-fluid interface on self-phoresis of chemically active, axially symmetric, spherical colloids is analyzed. Distinct from the studies of self-phoresis for colloids trapped at fluid interfaces or in the vicinity of hard walls, here we focus on the issue of self-phoresis close to a fluid-fluid interface. In order to provide physically intuitive results highlighting the role played by the interface, the analysis is carried out for the case that the symmetry axis of the colloid is normal to the interface; moreover, thermal fluctuations are not taken into account. Similarly to what has been observed near hard walls, we find that such colloids can be set into motion even if their whole surface is homogeneously active. This is due to the anisotropy along the direction normal to the interface owing to the partitioning by diffusion, among the coexisting fluid phases, of the product of the chemical reaction taking place at the colloid surface. Different from results corresponding to hard walls, in the case of a fluid interface the direction of motion, i.e., towards the interface or away from it, can be controlled by tuning the physical properties of one of the two fluid phases. This effect is analyzed qualitatively and quantitatively, both by resorting to a far-field approximation and via an exact, analytical calculation which provides the means for a critical assessment of the approximate analysis.

cond-mat.soft↗

arXiv2017

Solvent coarsening around colloids driven by temperature gradients

Using mesoscopic numerical simulations and analytical theory we investigate the coarsening of the solvent structure around a colloidal particle emerging after a temperature quench of the colloid surface. Qualitative differences in the coarsening mechanisms are found, depending on the composition of the binary liquid mixture forming the solvent and on the adsorption preferences of the colloid. For an adsorptionwise neutral colloid, as function of time the phase being next to its surface alternates. This behavior sets in on the scale of the relaxation time of the solvent and is absent for colloids with strong adsorption preferences. A Janus colloid, with a small temperature difference between its two hemispheres, reveals an asymmetric structure formation and surface enrichment around it, even if the solvent is within its one-phase region and if the temperature of the colloid is above the critical demixing temperature $T_c$ of the solvent. Our phenomenological model turns out to capture recent experimental findings according to which, upon laser illumination of a Janus colloid and due to the ensuing temperature gradient between its two hemispheres, the surrounding binary liquid mixture develops a concentration gradient.

cond-mat.soft↗

arXiv2017

Shape-dependent guidance of active Janus particles by chemically patterned surfaces

Self-phoretic Janus particles move by inducing -- via non-equilibrium chemical reactions occurring on their surfaces -- changes in the chemical composition of the solution in which they are immersed. This process leads to gradients in chemical composition along the surface of the particle, as well as along any nearby boundaries, including solid walls. Chemical gradients along a wall can give rise to chemi-osmosis, i.e., the gradients drive surface flows which, in turn, drive flow in the volume of the solution. This bulk flow couples back to the particle, and thus contributes to its self-motility. Since chemi-osmosis strongly depends on the molecular interactions between the diffusing molecular species and the wall, the response flow induced and experienced by a particle encodes information about any chemical patterning of the wall. Here, we extend previous studies on self-phoresis of a sphere near a chemically patterned wall to the case of particles with elongated shape. We focus our analysis on the new phenomenology potentially emerging from the coupling -- which is inoperative for a spherical shape -- of the elongated particle to the strain rate tensor of the chemi-osmotic flow. Via numerical calculations, we show that the dynamics of a rod-like particle exhibits a novel "edge-following" steady state: the particle translates along the edge of a chemical step at a steady distance from the step and with a steady orientation. Within a certain range of system parameters, the edge-following state co-exists with a "docking" state (the particle stops at the step, oriented perpendicular to the step edge), i.e., a bistable dynamics occurs. These findings are rationalized as a consequence of the competition between fluid vorticity and the rate of strain by using analytical theory based on the point-particle approximation which captures quasi-quantitatively the dynamics of the system.

cond-mat.soft↗

arXiv2017

Statistical field theory with constraints: application to critical Casimir forces in the canonical ensemble

The effect of imposing a constraint on a fluctuating scalar order parameter field in a system of finite volume is studied within statistical field theory. The canonical ensemble, corresponding to a fixed total integrated order parameter, is obtained as a special case of the theory. A perturbative expansion is developed which allows one to systematically determine the constraint-induced finite-volume corrections to the free energy and to correlation functions. In particular, we focus on the Landau-Ginzburg model in a film geometry (i.e., a rectangular parallelepiped with a small aspect ratio) with periodic, Dirichlet, or Neumann boundary conditions in the transverse direction and periodic boundary conditions in the remaining, lateral directions. Within the expansion in terms of $ε=4-d$, where $d$ is the spatial dimension of the bulk, the finite-size contribution to the free energy and the associated critical Casimir force are calculated to leading order in $ε$ and are compared to the corresponding expressions for an unconstrained (grand canonical) system. The constraint restricts the fluctuations within the system and it accordingly modifies the residual finite-size free energy. The resulting Casimir force is shown to depend on whether it is defined by assuming a fixed transverse area or a fixed total volume. In the former case, the constraint is typically found to significantly enhance the attractive character of the force as compared to the grand canonical case. In contrast to the grand canonical Casimir force, which, for supercritical temperatures, vanishes in the limit of thick films, the canonical Casimir force defined for fixed transverse area attains for thick films a negative value for all boundary conditions studied here. Typically, the dependence of the Casimir force both on the temperature- and on the field-like scaling variables is different in the two ensembles.

cond-mat.stat-mech↗

arXiv2017

Liquid bridging of cylindrical colloids in near-critical solvents

Within mean field theory, we investigate the bridging transition between a pair of parallel cylindrical colloids immersed in a binary liquid mixture as a solvent which is close to its critical consolute point $T_c$. We determine the universal scaling functions of the effective potential and of the force between the colloids. For a solvent which is at the critical concentration and close to $T_c$, we find that the critical Casimir force is the dominant interaction at close separations. This agrees very well with the corresponding Derjaguin approximation for the effective interaction between the two cylinders, while capillary forces originating from the extension of the liquid bridge turn out to be more important at large separations. In addition, we are able to infer from the wetting characteristics of the individual colloids the first-order transition of the liquid bridge connecting two colloidal particles to the ruptured state. While specific to cylindrical colloids, the results presented here provide also an outline for identifying critical Casimir forces acting on bridged colloidal particles as such, and for analyzing the bridging transition between them.

cond-mat.soft↗

arXiv2017

Electrolyte solutions at curved electrodes. I. Mesoscopic approach

Within the Poisson-Boltzmann (PB) approach electrolytes in contact with planar, spherical, and cylindrical electrodes are analyzed systematically. The dependences of their capacitance $C$ on the surface charge density $σ$ and the ionic strength $I$ are examined as function of the wall curvature. The surface charge density has a strong effect on the capacitance for small curvatures whereas for large curvatures the behavior becomes independent of $σ$. An expansion for small curvatures gives rise to capacitance coefficients which depend only on a single parameter, allowing for a convenient analysis. The universal behavior at large curvatures can be captured by an analytic expression.

cond-mat.soft↗