arXiv subjects

Steffen Hardt

Publications and source records attributed to Steffen Hardt.

At least 37 records · Page 2Linked to original sources

arXiv2020

Thermoelectricity in confined liquid electrolytes

The electric field in an extended phase of a liquid electrolyte exposed to a temperature gradient is attributed to different thermophoretic mobilities of the ion species. As shown herein, such Soret-type ion thermodiffusion is not required to induce thermoelectricity even in the simplest electrolyte if it is confined between charged walls. The space charge of the electric double layer leads to selective ion diffusion driven by a temperature-dependent electrophoretic ion mobility, which -- for narrow channels -- may cause thermo-voltages larger in magnitude than for the classical Soret equilibrium.

physics.flu-dyn↗

arXiv2020

The effective shear and dilatational viscosity of a particle-laden interface in the dilute limit

The effective dilatational and shear viscosities of a particle-laden fluid interface are computed in the dilute limit under the assumption of an asymptotically vanishing viscosity ratio between both fluids. Spherical particles with a given contact angle of the fluid interface at the particle surface are considered. A planar fluid interface and a small Reynolds number are assumed. The theoretical analysis is based on a domain perturbation expansion in the deviation of the contact angle from $90^\circ$ up to the second order. The resulting effective dilatational viscosity shows a stronger dependence on the contact angle than the effective shear viscosity, and its magnitude is larger for all contact angles. As an application of the theory, the stability of a liquid cylinder decorated with particles is considered. The limits of validity of the theory and possible applications in terms of numerical simulations of particle-laden interfaces are discussed.

physics.flu-dyn↗

arXiv2019

Wetting of an annular liquid in a capillary tube

In this paper, we systematically investigate the wetting behavior of a liquid ring in a cylindrical capillary tube. We obtain analytical solutions of the axisymmetric Young-Laplace equation for arbitrary contact angles. We find that, for specific values of the contact angle and the volume of the liquid ring, two solutions of the Young-Laplace equation exist, but only the one with the lower value of the total interfacial energy corresponds to a stable configuration. The transition to an unstable configuration is characterized by specific critical parameters such as the liquid volume, throat diameter etc. Beyond the stable regime, the liquid ring transforms into a plug. Based on numerical simulations, we also discuss the transition of an axisymmetric ring into non-axisymmetric configurations. Such a transition can be induced by the Rayleigh-Plateau instability of a slender liquid ring. The results are presented in terms of a map showing the different liquid morphologies as a function of the parameters governing the problem.

physics.flu-dyn↗

arXiv2019

Forced dynamic dewetting of structured surfaces: Influence of surfactants

We analyse the dewetting of printing plates for gravure printing with well-defined gravure cells. The printing plates were mounted on a rotating horizontal cylinder that is half immersed in an aqueous solution of the anionic surfactant sodium 1-decanesulfonate. The gravure plates and the presence of surfactants serve as one example of a real-world dewetting situation. When rotating the cylinder, a liquid meniscus was partially drawn out of the liquid forming a dynamic contact angle at the contact line. The dynamic contact angle is decreased on a structured surface as compared to a smooth one. This is due to contact line pinning at the borders of the gravure cells. Additionally, surfactants tend to decrease the dynamic receding contact angle. We consider the interplay between these two effects. We compare the height differences of the meniscus on the structured and unstructured area as function of dewetting speeds. The height difference increases with increasing dewetting speed. With increasing size of the gravure cells this height difference and the induced changes in the dynamic contact angle increased. By adding surfactant, the height difference and the changes in the contact angle for the same surface decreased. We further note that although the liquid dewets the printing plates some liquid is always left in the gravure cell. At high enough surfactant concentrations or high enough dewetting speed, the dynamic contact angles in the structured surface approach those in flat surfaces. We conclude that surfactant reduces the influence of surface structure on dynamic dewetting.

cond-mat.soft↗

arXiv2018

Thermophoresis of Janus particles at large Knudsen numbers

The force and torque on a Janus sphere moving in a rarefied gas with a thermal gradient are calculated. The regime of large Knudsen number is considered, with the momenta of impinging gas molecules either obtained from a Chapman-Enskog distribution or from a binary Maxwellian distribution between two opposing parallel plates at different temperature. The reflection properties at the surface of the Janus particle are characterized by accommodation coefficients having constant but dissimilar values on each hemisphere. It is shown that the Janus particle preferentially orients such that the hemisphere with a larger accommodation coefficient points towards the lower temperature. The thermophoretic velocity of the particle is computed, and the influence of the thermophoretic motion on the magnitude of the torque responsible for the particle orientation is studied. The analytical calculations are supported by Direct Simulation Monte Carlo results, extending the scope of the study towards smaller Knudsen numbers. The results shed light on the efficiency of oriented deposition of nanoparticles from the gas phase onto a cold surface.

physics.flu-dyn↗

arXiv2017

Stability of a horizontal viscous fluid layer in a vertical time periodic electric field

The stability of a horizontal interface between two viscous fluids, one of which is conducting and the other is dielectric, acted upon by a vertical time-periodic electric field is considered. The two fluids are bounded by electrodes separated by a finite distance. By means of Floquet theory, the marginal stability curves are obtained, thereby elucidating the dependency of the critical voltage and wavenumber upon the fluid viscosities. The limit of vanishing viscosities is shown to be in excellent agreement with the marginal stability curves predicted by means of a Mathieu equation. The methodology to obtain the marginal stability curves developed here is applicable to any arbitrary but time periodic-signal, as demonstrated for the case of a signal with two different frequencies. As a special case, the marginal stability curves for an applied ac voltage biased by a dc voltage are depicted. It is shown that the mode coupling caused by the normal stress at the interface due to the electric field leads to appearance of harmonic modes and subharmonic modes. This is in contrast to the application of a voltage with a single frequency which always leads to a harmonic mode. Whether a harmonic or subharmonic mode is the most unstable one depends on details of the excitation signal. It is also shown that the electrode spacing has a distinct effect on the stability bahavior of the system.

physics.flu-dyn↗

arXiv2017

Knudsen pump inspired by Crookes radiometer with a specular wall

A rarefied gas is considered in a channel consisting of two infinite parallel plates between which an evenly spaced array of smaller plates is arranged normal to the channel direction. Each of these smaller plates is assumed to possess one ideally specularly reflective and one ideally diffusively reflective side. When the temperature of the small plates differs from the temperature of the sidewalls of the channel, these boundary conditions result in a temperature profile around the edges of each small plate which breaks the reflection symmetry along the channel direction. This in turn results in a force on each plate and a net gas flow along the channel. The situation is analysed numerically using the direct simulation Monte Carlo (DSMC) method and compared with analytical results where available. The influence of the ideally specularly reflective wall is assessed by comparing with simulations using a finite accommodation coefficient at the corresponding wall. The configuration bears some similarity with a Crookes radiometer, where a non-symmetric temperature profile at the radiometer vanes is generated by different temperatures on each side of the vane, resulting in a motion of the rotor. The described principle may find applications in pumping gas on small scales driven by temperature gradients.

physics.flu-dyn↗

arXiv2016

Conjugated liquid layers driven by the short-wavelength Bénard-Marangoni instability: experiment and numerical simulation

The coupled dynamics of two conjugated liquid layers of disparate thicknesses, which coat a solid substrate and are subjected to a transverse temperature gradient, is investigated. The upper liquid layer evolves under the short-wavelength (SW) Bénard-Marangoni (BM) instability, whereas the lower, much thinner film undergoes a shear-driven long-wavelength deformation. Although the lubricating film should reduce the viscous stresses acting on the up to one hundred times thicker upper layer by only 10%, it is found that the critical Marangoni number of marginal stability may be as low as if a stress-free boundary condition were applied at the bottom of the upper layer, i.e. much lower than the classical value of 79.6 known for a single film. Furthermore, it is experimentally verified that the deformation of the liquid-liquid interface, albeit small, has a non-negligible effect on the temperature distribution along the liquid-gas interface of the upper layer. This stabilizes the hexagonal pattern symmetry towards external disturbances and indicates a two-way coupling of the different layers. The experiments also demonstrate how convection patterns formed in a liquid film can be used to pattern a second conjugated film. The experimental findings are verified by a numerical model of the coupled layers.

physics.flu-dyn↗

arXiv2016

Interfacial instability of liquid films coating the walls of a parallel-plate channel and sheared by a gas flow

The stability of liquid films coating the walls of a parallel-plate channel and sheared by a pressure-driven gas flow along the channel centre is studied. The films are susceptible to a long-wavelength instability, whose dynamic behaviour is found - for sufficiently low Reynolds numbers and thick gas layers - to be described by two coupled non-linear partial differential equations. To the best of our knowledge, such coupled fully non-linear equations for the film thicknesses have not been derived previously. A linear stability analysis conducted under the condition that the material properties and the initial undisturbed liquid film thicknesses are equal can be utilized to determine whether the interfaces are predominantly destabilized by the variations of the shear stress or by the pressure gradient acting upon them. The analysis of the weakly non-linear equations performed for this case shows that instabilities corresponding to a vanishing Reynolds number are absent from the system. Moreover, for this configuration, the patterns emerging along the two interfaces are found to be identical in the long-time limit, implying that the films are fully synchronized. A different setup, where the liquid films have identical material properties but their undisturbed thicknesses differ, is studied numerically. The results show that even for this configuration the interfacial waves remain phase-synchronized and closely correlated for a broad range of parameters. These findings are particularly relevant for multiphase flow in narrow ducts, for example in the respiratory system or in microfluidic channels.

physics.flu-dyn↗

arXiv2015

Brownian dynamics of rigid particles in an incompressible fluctuating fluid by a meshfree method

A meshfree Lagrangian method for the fluctuating hydrodynamic equations (FHEs) with fluid-structure interactions is presented. Brownian motion of the particle is investigated by direct numerical simulation of the fluctuating hydrodynamic equations. In this framework a bidirectional coupling has been introduced between the fluctuating fluid and the solid object. The force governing the motion of the solid object is solely due to the surrounding fluid particles. Since a meshfree formulation is used, the method can be extended to many real applications involving complex fluid flows. A three-dimensional implementation is presented. In particular, we observe the short and long-time behaviour of the velocity autocorrelation function (VACF) of Brownian particles and compare it with the analytical expression. Moreover, the Stokes-Einstein relation is reproduced to ensure the correct long-time behaviour of Brownian dynamics.

math.DS↗

arXiv2015

Driven particles at fluid interfaces acting as capillary dipoles

The dynamics of spherical particles driven along an interface between two immiscible fluids is investigated asymptotically. Under the assumptions of a pinned three-phase contact line and very different viscosities of the two fluids, a particle assumes a tilted orientation. As it moves, it causes a deformation of the fluid interface which is also computed. The case of two interacting driven particles is studied via the Linear Superposition Approximation. It is shown that the capillary interaction force resulting from the particle motion is dipolar in terms of the azimuthal angle and decays with the fifth power of the inter-particle separation, similar to a capillary quadrupole originating from undulations of the three-phase contact line. The dipolar interaction is demonstrated to exceed the quadrupolar interaction at moderate particle velocities.

cond-mat.soft↗

arXiv2015

Drag and diffusion coefficients of a spherical particle attached to a fluid interface

Explicit analytical expressions for the drag and diffusion coefficients of a spherical particle attached to the interface between two immiscible fluids are constructed for the case of a small viscosity ratio between the fluid phases. The model is designed to explicitly account for the dependence on the contact angle between the two fluids and the solid surface. The Lorentz reciprocal theorem is applied in the context of a geometric perturbation approach, which is based on the deviation of the contact angle from a 90°-value. By testing the model against experimental and numerical data from the literature, good agreement is found within the entire range of contact angles below 90°. As an advantage of the method reported, the drag and diffusion coefficients can be calculated up to second order in the perturbation parameter, while it is sufficient to know the velocity and pressure fields only up to first order. Extensions to other particle shapes with known velocity and pressure fields are straightforward.

cond-mat.soft↗

arXiv2014

Line tension and reduction of apparent contact angle associated with electric double layers

The line tension of an electrolyte wetting a non-polar substrate is computed analytically and numerically. The results show that, depending on the value of the apparent contact angle, positive or negative line tension values may be obtained. Furthermore, a significant difference between Young's contact angle and the apparent contact angle measured several Debye lengths remote from the three-phase contact line occurs. When applying the results to water wetting highly charged surfaces, line tension values of the same order of magnitude as found in recent experiments can be achieved. Therefore, the theory presented may contribute to the understanding of line tension measurements and points to the importance of the electrostatic line tension. Being strongly dependent on the interfacial charge density, electrostatic line tension is found to be tunable via the pH value of the involved electrolyte. As a practical consequence, the stability of nanoparticles adsorbed at fluid-fluid interfaces is predicted to be dependent on the pH value. The theory is suited for future incorporation of effects due to surfactants where even larger line tension values can be expected.

physics.chem-ph↗

arXiv2014

Droplet Formation via Solvent Shifting in a Microfluidic Device

Solvent shifting is a process in which a non-solvent is added to a solvent/solute mixture and extracts the solvent. The solvent and the non-solvent are miscible. Because of solution supersaturation a portion of the solute transforms to droplets. In this paper, based on this process, we present an investigation on droplet formation and their radial motion in a microfluidic device in which a jet is injected in a co-flowing liquid stream. Thanks to the laminar flow, the microfluidic setup enables studying diffusion mass transfer in radial direction and obtaining well-defined concentration distributions. Such profiles together with Ternary Phase Diagram (TPD) give detailed information about the conditions for droplet formation condition as well as their radial migration in the channel. The ternary system is composed of ethanol (solvent), de-ionized water (non-solvent) and divinyle benzene (solute). We employ analytical/numerical solutions of the diffusion equation to obtain concentration profiles of the components. We show that in the system under study droplets are formed in a region of the phase diagram between the binodal and the spinodal, i.e. via a thermally activated process. The droplets are driven to the channel centerline by the solutal Marangoni effect but are not able to significantly penetrate into the single-phase region, where they get rapidly dissolved. Therefore, the radial motion of the binodal surface carries the droplets to the centerline where they get collected.

physics.flu-dyn↗

arXiv2014

Coupled self-organization: Thermal interaction between two liquid films undergoing long-wavelength instabilities

The effects of thermal coupling between two thin liquid layers, separated by a gas layer, are discussed. The liquid layers undergo long-wavelength instabilities driven by gravitational and thermocapillary stresses. To study the dynamics, both a linear stability analysis and a full numerical solution of the thin-film equations are performed. The results demonstrate that the stability properties of the combined system differ substantially from the case where both layers evolve independently from each other. Most prominently, oscillatory instabilities, not present in single-liquid layer configurations, may occur.

nlin.PS↗

arXiv2014

Numerical simulation of moving rigid body in rarefied gases

In this paper we present a numerical scheme to simulate a moving rigid body with arbitrary shape suspended in a rarefied gas. The rarefied gas is simulated by solving the Boltzmann equation using a DSMC particle method. The motion of the rigid body is governed by the Newton-Euler equations, where the force and the torque on the rigid body is computed from the momentum transfer of the gas molecules colliding with the body. On the other hand, the motion of the rigid body influences the gas flow in its surroundings. We validate the numerical results by testing the Einstein relation for Brownian motion of the suspended particle. The translational as well as the rotational degrees of freedom are taken into account. It is shown that the numerically computed translational and rotational diffusion coefficients converge to the theoretical values.

physics.comp-ph↗

arXiv2014

Numerical simulation of wetting phenomena by a meshfree particle method

Simulations of wetting phenomena by a meshfree particle method are presented. The incompressible Navier-Stokes equations are used to model the two-phase flow. The continuous surface force model is used to incorporate the surface tension force. Chorin's projection method is applied to discretize the Navier-Stokes equations. The different fluid phases are identified by assigning different colors and different material properties (density, viscosity) to the particles that remain unchanged throughout a simulation. Two-phase flow is captured by a one-fluid model via using weighted averages of the density and viscosity in a region around the fluid-fluid interface. The differential operators at each particle are computed from the surrounding cloud of particles with the help of the least-squares method. The numerical results are compared with specific analytical solutions, but also with previously considered test cases involving wetting of a container and sessile drops. A good overall agreement is found.

math.NA↗

arXiv2014

Energy harvesting through gas dynamics in the free molecular flow regime between structured surfaces at different temperatures

For a gas confined between surfaces held at different temperatures the velocity distribution shows a significant deviation from the Maxwell distribution when the mean free path of the molecules is comparable to or larger than the channel dimensions. If one of the surfaces is suitably structured, this non-equilibrium distribution can be exploited for momentum transfer in tangential direction between the two surfaces. This opens up the possibility to extract work from the system which operates as a heat engine. Since both surfaces are held at constant temperatures, the mode of momentum transfer is different from thermal creep flow that has gained more attention so far. This situation is studied in the limit of free-molecular flow for the case that an unstructured surface is allowed to move tangentially with respect to a structured surface. Parameter studies are conducted, and configurations with maximum thermodynamic efficiency are identified. Overall, it is shown that significant efficiencies can be obtained by tangential momentum transfer between structured surfaces.

physics.flu-dyn↗