Peter Ehrhard | Dortmund University of Technology - Technische Universität Dortmund (original) (raw)
Papers by Peter Ehrhard
Springer eBooks, 2001
Using lubrication theory, a model to investigate spreading of solidifying melts is presented. We ... more Using lubrication theory, a model to investigate spreading of solidifying melts is presented. We concentrate on crust-formation at the free interface between melt and ambient gas. Crust-formation leads to a noslip condition between liquid melt and solid crust, whereas the problem without crusts has a free-slip condition at the free interface. This leads to a change in the kinematic boundary conditions and can have a significant influence on the spreading flow. Results show that crust-formation can increase or decrease the front velocity from what is expected in the case without crusts.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
This article deals with a liquid displacing a gas in a thin heterogeneous porous material, which ... more This article deals with a liquid displacing a gas in a thin heterogeneous porous material, which occurs e.g. during the filling process of a lithium-ion battery with an electrolyte. The investigation is based upon the local volume-averaged Navier-Stokes equations, using a Volume-of-Fluid method to treat the interface. For the flow the wall effect and capillary forces have to be considered. Capillary rise experiments are used to determine the permeability. Since the layers are thin and the characteristic size of the particles is comparatively large, friction with the electrode is taken into account with respect to the mobility of the contact line. The implemented models are validated against analytical results, showing a good agreement.
Chemie Ingenieur Technik, Dec 23, 2011
Für die Ausbreitung eines dünnen rotierenden Tropfens wird, unter Ausnutzung der Schmierfilmappro... more Für die Ausbreitung eines dünnen rotierenden Tropfens wird, unter Ausnutzung der Schmierfilmapproximation, eine Entwicklungsgleichung zur Beschreibung der Position der freien Grenzfläche abgeleitet. Die dynamische Benetzung wird mit dem empirischen Tanner'schen Gesetz beschrieben und die Modellierung mit Experimenten aus der Literatur verglichen. Eine lineare Störungsanalyse liefert die instabilen Moden und das Einsetzen von Fingerbildung während der Ausbreitung. Betrachtet wird auch Konvektion aufgrund der temperaturabhängigen Oberflächenspannung und Dichte sowie deren Stabilität.
Proceedings in applied mathematics & mechanics, Dec 1, 2008
Disperse gas bubbles play an important role in many industrial applications. Knowing the rising v... more Disperse gas bubbles play an important role in many industrial applications. Knowing the rising velocity, the interfacial area, or the critical size for break-up or coalescence in different systems can be crucial for the process design. Hence, knowing the fundamental behaviour of a single bubble appears mandatory for the examination of bubble swarms and for the Euler-Lagrange or Euler-Euler modelling of disperse systems. In the present work a level-set-based volume-tracking method is implemented into the CFD-code OpenFOAM to follow the free interface of a single bubble. The volume-tracking method is coupled with a transport model for surfactants on the interface, including adsorption and desorption processes. The dependency of surface tension on the local surfactant concentration on the interface is modelled by a non-linear (Langmuir) equation of state. Marangoni forces, resulting from surface tension gradients, are included. The rise of a single air bubble (i) in pure water and (ii) in the presence of surfactants of different strengths is simulated. The results show good agreement with available correlations from literature.
We investigate the influence of internal electrodes onto the flow field, governed by electroosmos... more We investigate the influence of internal electrodes onto the flow field, governed by electroosmosis and electrophoresis in a modular rectangular microchannel. As internal electrodes can be positioned at lower distances, they can be operated at lower voltages and still ensure strong electrical field strength. Even at lower voltages, electrode reactions influence the species concentration fields, and the crucial question arises, whether at the electrodes all species can be kept in dissolution or whether some species are released in gaseous form. The position and charge of multiple internal electrodes is a further focus of our investigations: wall-tangential electrical field components are responsible for pumping, wall-normal electrical field components are responsible for mixing. Hence, an optimized position and charge of all electrodes will lead to an optimized electrical field, designed to fulfill the desired tasks of the modular microchannel. The mathematical model for the numerical treatment relies on a first-principle description of the EDL and the electrical forces caused by the electrical field between the internal electrodes. Hence, the so-called Debye-Hu¨ckel approximation is avoided. The governing system of equations consists of a Poisson equation for the electrical potential, the continuity and Navier-Stokes equations for the flow field, species transport equations, based on the Nernst-Planck equation, and a charge transport equation. Further, a model for the electrode reactions, based on the Butler-Volmer equation, is in place. The simulations are time-dependent and two-dimensional in nature and employ a FVM.
Proceedings in applied mathematics & mechanics, Dec 1, 2012
We investigate the electrokinetic flow in microchannels with internal electrodes. Experiments and... more We investigate the electrokinetic flow in microchannels with internal electrodes. Experiments and numerical simulations are performed. The micro–particle–image velocimetry method is used to measure two–dimesional, two–component velocity fields over the complete height of the microchannel. Based on this measurements, the third velocity component, which cannot be measured directly, is calculated by an integration of the continuity equation. Due to the fact that microparticles, used for the μPIV are electrically non‐neutral leads to the problem that these particles experience electrophoretic forces. That means that the particle movement appears to be a superposition of electroosmotic and electrophorectic effects. To verify the influence of electrophoretic effects on the microparticles, additional numerical calculations are made. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
In general, the modeling of electroosmotic flows can be approached in two fundamentally–different... more In general, the modeling of electroosmotic flows can be approached in two fundamentally–different ways. (i) The thickness of electrical double layer (EDL) is ignored and the effect of the electrical forces within the EDL is imaged into a modified kinematic boundary condition, the so-called Helmholtz–Smoluchowski slip condition. This approach is numerically simple and inexpensive, but implies several restrictions. (ii) The EDL is fully resolved, using a first–principle approach based on differential conservation equations for mass, momentum, and charge. This approach is enormously elaborate and numerically expensive, but appears to be applicable for a much wider range of problems. As an example, the treatment of internal electrodes, adjacent to insulating walls at defined zeta potential, appears difficult with the simple approach (i), since any non–continuous potential distribution at the wall leads to a singularity of the electrical field strength. To avoid these difficulties, we develop a hybrid model which, on the one hand, electrically resolves the EDL to reveal a perfectly-continuous potential distribution in the complete microchannel. On the other hand, the flow equations are solved in the fluid bulk only, not comprising the EDL. Hence, the effect of the EDL is still incorporated by means of modified kinematic boundary conditions. The advantage of this hybrid model is, firstly, to avoid artificial singularities of the electrical field strength, where regions of different surface charge meet. These singularities are clearly artificial, since they result from neglecting the extend of the EDL. Secondly, the hybrid model, at each time step, needs to solve only once for the potential distribution, which makes it numerically inexpensive and simple. Hence, systematic parameter studies are within reach. We apply the hybrid model to investigate the influence of internal electrodes onto the flow field, driven by electroosmosis in a modular rectangular microchannel. As internal electrodes can be positioned at lower distances (if compared to external electrodes), they can be operated at lower voltages and still ensure strong electrical field strength. Systematic studies on the effect of different electrode positions and voltages are presented, leading to optimized settings for specific tasks as pumping or mixing. Further, a comparison to first-principle simulations using the approach (ii) is presented for selected cases. This demonstrates that the hybrid model perfectly captures the dominant physics.Copyright © 2010 by ASME
We investigate the electrokinetic flow and mass transport in a microchannel junction, serving as ... more We investigate the electrokinetic flow and mass transport in a microchannel junction, serving as an injector of a microelectrophoresis device. In order to consider all essential features of this complex system, the electrical situation, the fluid dynamics, and the (physical) chemistry is ...
Proceedings in applied mathematics & mechanics, Dec 1, 2012
Thin droplets spreading on a solid substrate are investigated, with a special focus on temperatur... more Thin droplets spreading on a solid substrate are investigated, with a special focus on temperature effects. The aim is to manipulate the fingering instability which may occur in the spreading in a spin coating process. The analysis bases on lubrication approximation, valid for flat thin droplets, which usually is the case. The dynamic of the wetting is implemented by using a generalized law of Tanner, coupling the contact angle (CA) of the droplet at the (apparent) contact line (CL) with its speed. A one‐way coupling is used to investigate, whether viscous heating has to be taken into account. It can be derived that its role is negligible in the spreading process of a thin droplet, even for a relatively large viscous influence (large capillary number). Analyzing the results of a linear stability analysis of the fingering instability and taking Marangoni‐stresses (MS) into account reveals, that the instability may be suppressed by cooling the ambient gas or heating the substrate during the spreading. Unfortunately an comparison with experiments for spreading droplets in a heated gas shows deviations for larger spreading radii. The influence of temperature on density is investigated and on the way a criteria, from which it may be obtained whether a simple Boussinesq‐approximation (BA) is appropriate or not. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Proceedings in applied mathematics & mechanics, Dec 1, 2011
Thin-film flows are involved in many coating processes, where it is desirable to achieve thin and... more Thin-film flows are involved in many coating processes, where it is desirable to achieve thin and homogeneous fluid layers. In the present investigations, we treat droplets, spreading on rotating solid substrates. Micro-scale effects appear, firstly, at the wetting front, where the film height tends to zero. Secondly, micro-scale effects may appear at other locations, where the free liquid/gas-interface approaches the solid substrate, as e.g. at film rupture. For such situations, molecular effects need to be considered, e.g. in form of the disjoining pressure (DJP), to get physically-correct solutions. Otherwise, the spreading can be modeled within the frame of continuum mechanics, augmented by the (empirical) law of Tanner to capture the contact-line dynamics. We present, on the one hand, an overview of several interesting issues, as (i) spreading with and without considering the DJP, (ii) spreading after central rupture, including hysteresis effects, and (iii) non-isothermal spreading, including temperaturedependent surface tension (Marangoni effect) and temperature-dependent density (Rayleigh-Bénard effect). On the other hand, we present results for the instability of the contact line, for which the contact line gets corrugated (under isothermal conditions). This instability goes along with a transition from (rotationally-symmetric) two-dimensional to three-dimensional behavior.
Bulletin of the American Physical Society, Nov 22, 2005
Submitted for the DFD05 Meeting of The American Physical Society Countering capillary pressure wi... more Submitted for the DFD05 Meeting of The American Physical Society Countering capillary pressure with electroosmotic pressure at small scales PAUL STEEN, MICHAEL VOGEL, Cornell University, PETER EHRHARD, IKET, FzK Germany-Electroosmosis, originating in the doublelayer of a small liquid-filled pore (size R) and driven by a voltage V , is shown to be effective in pumping liquid against the capillary pressure of a larger liquid droplet (size B) provided the dimensionless parameter R 2 σ/ε|ζ|V B is small enough. Here σ is surface tension of the droplet liquid/gas interface, ε the liquid dielectric constant, and ζ the zeta potential of the solid/liquid pair. As droplet size diminishes, the voltage required to pump eletroosmotically scales as V ∼ R 2 /B. Accordingly, the voltage needed to pump against smaller higher-pressure droplets can actually decrease provided the pump pore-size scales down with droplet size appropriately. In this talk, we shall focus on the electroosmotic droplet-switch, two droplets coupled by an electroosmotic pump. For millimeter-size droplets and micron-size pores, 5 volts yields switching times under 5 seconds in experiment. The down-scaling of this voltage and switching-time are of interest.
Proceedings in applied mathematics & mechanics, Dec 1, 2014
Proceedings in applied mathematics & mechanics, Dec 1, 2014
Particles that are placed in a laminar pipe flow rotate and migrate transversally to a radial equ... more Particles that are placed in a laminar pipe flow rotate and migrate transversally to a radial equilibrium position. This so called Segré-Silberberg effect is used in a new method for size separation of particles. The particles to be separated are placed in a pipe flow and subsequently enter an expansion chamber, where the flow is split and the particles are divided into two fractions. This paper reports the results of two-dimensional Euler-Lagrange simulations of the motion of neutrally-buoyant particles inside the expansion chamber. The simulation results agree well with experimental data on the separation and show that the Saffman force has a significant impact onto the particle trajectories.
Proceedings in applied mathematics & mechanics, 2021
We investigate how the walls of cylindrical capillaries affect the velocity of rising gas bubbles... more We investigate how the walls of cylindrical capillaries affect the velocity of rising gas bubbles of various diameters. Of course, as the capillary diameter increases, the velocity of the rising bubble will approach the case of free rising. Such systematic experiments on bubble rise in capillaries, in which the ratio of bubble diameter and capillary diameter is varied from one towards smaller values, can hardly be found in literature. First orienting experiments within the system water/air have been conducted and will be discussed in this paper.
Proceedings in applied mathematics & mechanics, Nov 1, 2019
The beads in a packed bed are usually distributed randomly. Therefore, on a macroscopic scale, a ... more The beads in a packed bed are usually distributed randomly. Therefore, on a macroscopic scale, a fluid flows uniformly through such a porous medium. For thin porous media, deviations are known near the regions of confinement. This so-called wall effect is extensively investigated in literature for circular confinements. In this work, the wall effect and the flow through porous media in a rectangular domain is studied. This has great importance during the initial filling process of lithium-ion batteries with the liquid electrolyte. Such batteries consist of collector foils, on which the porous electrodes are attached. Their thickness is only 5-10 times a particle diameter dP and may be modeled as a monodisperse bed of spheres. The filling flow is extremely slow and may be in the pre-Darcy flow region, wherefore the validity of Darcy's law is experimentally checked. Then, the local porosity function depending on the distance to the wall is experimentally determined. For very thin porous media, the wall effect of each wall may overlap each other, which is taken into account by using an overlapping model from the literature. The widely used model of Carman-Kozeny [1] relates the permeability with the porosity. Its validity in the near-wall region is checked by comparing experimentally-obtained mean pore diameters to those related to the model of Carman-Kozeny. The flow through a porous media is computed and compared to experimental results from literature for circular confinement and preliminary optically-matched PIV measurements.
Proceedings in applied mathematics & mechanics, Dec 1, 2009
We investigate the influence of flow field and electrode reactions onto an electrical double laye... more We investigate the influence of flow field and electrode reactions onto an electrical double layer (EDL), which is located in the immediate vicinity of the walls of a rectangular microchannel. The precise knowledge of the EDL appears to be important for many technical applications in microchannels of small width, since the electrokinetic effects, as electroosmosis or electrophoresis, in such cases depend on the detailed charge distribution. Furthermore, the influence of internal electrodes onto the flow field is of interest. The mathematical model for the numerical treatment relies on a first-principle description of the EDL and the electrical forces, caused by the electrical field between internal electrodes. Hence, the so-called Debye-Hueckel approximation is avoided. The simulations are time-dependent and two-dimensional (plane) in nature and employ a finite-volume method.
Proceedings in applied mathematics & mechanics, Dec 1, 2006
The rapid mixing of small quantities, with the goal of reducing analysis and reaction times, is o... more The rapid mixing of small quantities, with the goal of reducing analysis and reaction times, is one of the key steps within innovative miniaturized total analysis systems (µTAS). To achieve wellmixed liquids with homogenous properties within an acceptable process time, the ...
Springer eBooks, 2001
Using lubrication theory, a model to investigate spreading of solidifying melts is presented. We ... more Using lubrication theory, a model to investigate spreading of solidifying melts is presented. We concentrate on crust-formation at the free interface between melt and ambient gas. Crust-formation leads to a noslip condition between liquid melt and solid crust, whereas the problem without crusts has a free-slip condition at the free interface. This leads to a change in the kinematic boundary conditions and can have a significant influence on the spreading flow. Results show that crust-formation can increase or decrease the front velocity from what is expected in the case without crusts.
Proceedings in applied mathematics & mechanics, Oct 1, 2015
This article deals with a liquid displacing a gas in a thin heterogeneous porous material, which ... more This article deals with a liquid displacing a gas in a thin heterogeneous porous material, which occurs e.g. during the filling process of a lithium-ion battery with an electrolyte. The investigation is based upon the local volume-averaged Navier-Stokes equations, using a Volume-of-Fluid method to treat the interface. For the flow the wall effect and capillary forces have to be considered. Capillary rise experiments are used to determine the permeability. Since the layers are thin and the characteristic size of the particles is comparatively large, friction with the electrode is taken into account with respect to the mobility of the contact line. The implemented models are validated against analytical results, showing a good agreement.
Chemie Ingenieur Technik, Dec 23, 2011
Für die Ausbreitung eines dünnen rotierenden Tropfens wird, unter Ausnutzung der Schmierfilmappro... more Für die Ausbreitung eines dünnen rotierenden Tropfens wird, unter Ausnutzung der Schmierfilmapproximation, eine Entwicklungsgleichung zur Beschreibung der Position der freien Grenzfläche abgeleitet. Die dynamische Benetzung wird mit dem empirischen Tanner'schen Gesetz beschrieben und die Modellierung mit Experimenten aus der Literatur verglichen. Eine lineare Störungsanalyse liefert die instabilen Moden und das Einsetzen von Fingerbildung während der Ausbreitung. Betrachtet wird auch Konvektion aufgrund der temperaturabhängigen Oberflächenspannung und Dichte sowie deren Stabilität.
Proceedings in applied mathematics & mechanics, Dec 1, 2008
Disperse gas bubbles play an important role in many industrial applications. Knowing the rising v... more Disperse gas bubbles play an important role in many industrial applications. Knowing the rising velocity, the interfacial area, or the critical size for break-up or coalescence in different systems can be crucial for the process design. Hence, knowing the fundamental behaviour of a single bubble appears mandatory for the examination of bubble swarms and for the Euler-Lagrange or Euler-Euler modelling of disperse systems. In the present work a level-set-based volume-tracking method is implemented into the CFD-code OpenFOAM to follow the free interface of a single bubble. The volume-tracking method is coupled with a transport model for surfactants on the interface, including adsorption and desorption processes. The dependency of surface tension on the local surfactant concentration on the interface is modelled by a non-linear (Langmuir) equation of state. Marangoni forces, resulting from surface tension gradients, are included. The rise of a single air bubble (i) in pure water and (ii) in the presence of surfactants of different strengths is simulated. The results show good agreement with available correlations from literature.
We investigate the influence of internal electrodes onto the flow field, governed by electroosmos... more We investigate the influence of internal electrodes onto the flow field, governed by electroosmosis and electrophoresis in a modular rectangular microchannel. As internal electrodes can be positioned at lower distances, they can be operated at lower voltages and still ensure strong electrical field strength. Even at lower voltages, electrode reactions influence the species concentration fields, and the crucial question arises, whether at the electrodes all species can be kept in dissolution or whether some species are released in gaseous form. The position and charge of multiple internal electrodes is a further focus of our investigations: wall-tangential electrical field components are responsible for pumping, wall-normal electrical field components are responsible for mixing. Hence, an optimized position and charge of all electrodes will lead to an optimized electrical field, designed to fulfill the desired tasks of the modular microchannel. The mathematical model for the numerical treatment relies on a first-principle description of the EDL and the electrical forces caused by the electrical field between the internal electrodes. Hence, the so-called Debye-Hu¨ckel approximation is avoided. The governing system of equations consists of a Poisson equation for the electrical potential, the continuity and Navier-Stokes equations for the flow field, species transport equations, based on the Nernst-Planck equation, and a charge transport equation. Further, a model for the electrode reactions, based on the Butler-Volmer equation, is in place. The simulations are time-dependent and two-dimensional in nature and employ a FVM.
Proceedings in applied mathematics & mechanics, Dec 1, 2012
We investigate the electrokinetic flow in microchannels with internal electrodes. Experiments and... more We investigate the electrokinetic flow in microchannels with internal electrodes. Experiments and numerical simulations are performed. The micro–particle–image velocimetry method is used to measure two–dimesional, two–component velocity fields over the complete height of the microchannel. Based on this measurements, the third velocity component, which cannot be measured directly, is calculated by an integration of the continuity equation. Due to the fact that microparticles, used for the μPIV are electrically non‐neutral leads to the problem that these particles experience electrophoretic forces. That means that the particle movement appears to be a superposition of electroosmotic and electrophorectic effects. To verify the influence of electrophoretic effects on the microparticles, additional numerical calculations are made. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
In general, the modeling of electroosmotic flows can be approached in two fundamentally–different... more In general, the modeling of electroosmotic flows can be approached in two fundamentally–different ways. (i) The thickness of electrical double layer (EDL) is ignored and the effect of the electrical forces within the EDL is imaged into a modified kinematic boundary condition, the so-called Helmholtz–Smoluchowski slip condition. This approach is numerically simple and inexpensive, but implies several restrictions. (ii) The EDL is fully resolved, using a first–principle approach based on differential conservation equations for mass, momentum, and charge. This approach is enormously elaborate and numerically expensive, but appears to be applicable for a much wider range of problems. As an example, the treatment of internal electrodes, adjacent to insulating walls at defined zeta potential, appears difficult with the simple approach (i), since any non–continuous potential distribution at the wall leads to a singularity of the electrical field strength. To avoid these difficulties, we develop a hybrid model which, on the one hand, electrically resolves the EDL to reveal a perfectly-continuous potential distribution in the complete microchannel. On the other hand, the flow equations are solved in the fluid bulk only, not comprising the EDL. Hence, the effect of the EDL is still incorporated by means of modified kinematic boundary conditions. The advantage of this hybrid model is, firstly, to avoid artificial singularities of the electrical field strength, where regions of different surface charge meet. These singularities are clearly artificial, since they result from neglecting the extend of the EDL. Secondly, the hybrid model, at each time step, needs to solve only once for the potential distribution, which makes it numerically inexpensive and simple. Hence, systematic parameter studies are within reach. We apply the hybrid model to investigate the influence of internal electrodes onto the flow field, driven by electroosmosis in a modular rectangular microchannel. As internal electrodes can be positioned at lower distances (if compared to external electrodes), they can be operated at lower voltages and still ensure strong electrical field strength. Systematic studies on the effect of different electrode positions and voltages are presented, leading to optimized settings for specific tasks as pumping or mixing. Further, a comparison to first-principle simulations using the approach (ii) is presented for selected cases. This demonstrates that the hybrid model perfectly captures the dominant physics.Copyright © 2010 by ASME
We investigate the electrokinetic flow and mass transport in a microchannel junction, serving as ... more We investigate the electrokinetic flow and mass transport in a microchannel junction, serving as an injector of a microelectrophoresis device. In order to consider all essential features of this complex system, the electrical situation, the fluid dynamics, and the (physical) chemistry is ...
Proceedings in applied mathematics & mechanics, Dec 1, 2012
Thin droplets spreading on a solid substrate are investigated, with a special focus on temperatur... more Thin droplets spreading on a solid substrate are investigated, with a special focus on temperature effects. The aim is to manipulate the fingering instability which may occur in the spreading in a spin coating process. The analysis bases on lubrication approximation, valid for flat thin droplets, which usually is the case. The dynamic of the wetting is implemented by using a generalized law of Tanner, coupling the contact angle (CA) of the droplet at the (apparent) contact line (CL) with its speed. A one‐way coupling is used to investigate, whether viscous heating has to be taken into account. It can be derived that its role is negligible in the spreading process of a thin droplet, even for a relatively large viscous influence (large capillary number). Analyzing the results of a linear stability analysis of the fingering instability and taking Marangoni‐stresses (MS) into account reveals, that the instability may be suppressed by cooling the ambient gas or heating the substrate during the spreading. Unfortunately an comparison with experiments for spreading droplets in a heated gas shows deviations for larger spreading radii. The influence of temperature on density is investigated and on the way a criteria, from which it may be obtained whether a simple Boussinesq‐approximation (BA) is appropriate or not. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Proceedings in applied mathematics & mechanics, Dec 1, 2011
Thin-film flows are involved in many coating processes, where it is desirable to achieve thin and... more Thin-film flows are involved in many coating processes, where it is desirable to achieve thin and homogeneous fluid layers. In the present investigations, we treat droplets, spreading on rotating solid substrates. Micro-scale effects appear, firstly, at the wetting front, where the film height tends to zero. Secondly, micro-scale effects may appear at other locations, where the free liquid/gas-interface approaches the solid substrate, as e.g. at film rupture. For such situations, molecular effects need to be considered, e.g. in form of the disjoining pressure (DJP), to get physically-correct solutions. Otherwise, the spreading can be modeled within the frame of continuum mechanics, augmented by the (empirical) law of Tanner to capture the contact-line dynamics. We present, on the one hand, an overview of several interesting issues, as (i) spreading with and without considering the DJP, (ii) spreading after central rupture, including hysteresis effects, and (iii) non-isothermal spreading, including temperaturedependent surface tension (Marangoni effect) and temperature-dependent density (Rayleigh-Bénard effect). On the other hand, we present results for the instability of the contact line, for which the contact line gets corrugated (under isothermal conditions). This instability goes along with a transition from (rotationally-symmetric) two-dimensional to three-dimensional behavior.
Bulletin of the American Physical Society, Nov 22, 2005
Submitted for the DFD05 Meeting of The American Physical Society Countering capillary pressure wi... more Submitted for the DFD05 Meeting of The American Physical Society Countering capillary pressure with electroosmotic pressure at small scales PAUL STEEN, MICHAEL VOGEL, Cornell University, PETER EHRHARD, IKET, FzK Germany-Electroosmosis, originating in the doublelayer of a small liquid-filled pore (size R) and driven by a voltage V , is shown to be effective in pumping liquid against the capillary pressure of a larger liquid droplet (size B) provided the dimensionless parameter R 2 σ/ε|ζ|V B is small enough. Here σ is surface tension of the droplet liquid/gas interface, ε the liquid dielectric constant, and ζ the zeta potential of the solid/liquid pair. As droplet size diminishes, the voltage required to pump eletroosmotically scales as V ∼ R 2 /B. Accordingly, the voltage needed to pump against smaller higher-pressure droplets can actually decrease provided the pump pore-size scales down with droplet size appropriately. In this talk, we shall focus on the electroosmotic droplet-switch, two droplets coupled by an electroosmotic pump. For millimeter-size droplets and micron-size pores, 5 volts yields switching times under 5 seconds in experiment. The down-scaling of this voltage and switching-time are of interest.
Proceedings in applied mathematics & mechanics, Dec 1, 2014
Proceedings in applied mathematics & mechanics, Dec 1, 2014
Particles that are placed in a laminar pipe flow rotate and migrate transversally to a radial equ... more Particles that are placed in a laminar pipe flow rotate and migrate transversally to a radial equilibrium position. This so called Segré-Silberberg effect is used in a new method for size separation of particles. The particles to be separated are placed in a pipe flow and subsequently enter an expansion chamber, where the flow is split and the particles are divided into two fractions. This paper reports the results of two-dimensional Euler-Lagrange simulations of the motion of neutrally-buoyant particles inside the expansion chamber. The simulation results agree well with experimental data on the separation and show that the Saffman force has a significant impact onto the particle trajectories.
Proceedings in applied mathematics & mechanics, 2021
We investigate how the walls of cylindrical capillaries affect the velocity of rising gas bubbles... more We investigate how the walls of cylindrical capillaries affect the velocity of rising gas bubbles of various diameters. Of course, as the capillary diameter increases, the velocity of the rising bubble will approach the case of free rising. Such systematic experiments on bubble rise in capillaries, in which the ratio of bubble diameter and capillary diameter is varied from one towards smaller values, can hardly be found in literature. First orienting experiments within the system water/air have been conducted and will be discussed in this paper.
Proceedings in applied mathematics & mechanics, Nov 1, 2019
The beads in a packed bed are usually distributed randomly. Therefore, on a macroscopic scale, a ... more The beads in a packed bed are usually distributed randomly. Therefore, on a macroscopic scale, a fluid flows uniformly through such a porous medium. For thin porous media, deviations are known near the regions of confinement. This so-called wall effect is extensively investigated in literature for circular confinements. In this work, the wall effect and the flow through porous media in a rectangular domain is studied. This has great importance during the initial filling process of lithium-ion batteries with the liquid electrolyte. Such batteries consist of collector foils, on which the porous electrodes are attached. Their thickness is only 5-10 times a particle diameter dP and may be modeled as a monodisperse bed of spheres. The filling flow is extremely slow and may be in the pre-Darcy flow region, wherefore the validity of Darcy's law is experimentally checked. Then, the local porosity function depending on the distance to the wall is experimentally determined. For very thin porous media, the wall effect of each wall may overlap each other, which is taken into account by using an overlapping model from the literature. The widely used model of Carman-Kozeny [1] relates the permeability with the porosity. Its validity in the near-wall region is checked by comparing experimentally-obtained mean pore diameters to those related to the model of Carman-Kozeny. The flow through a porous media is computed and compared to experimental results from literature for circular confinement and preliminary optically-matched PIV measurements.
Proceedings in applied mathematics & mechanics, Dec 1, 2009
We investigate the influence of flow field and electrode reactions onto an electrical double laye... more We investigate the influence of flow field and electrode reactions onto an electrical double layer (EDL), which is located in the immediate vicinity of the walls of a rectangular microchannel. The precise knowledge of the EDL appears to be important for many technical applications in microchannels of small width, since the electrokinetic effects, as electroosmosis or electrophoresis, in such cases depend on the detailed charge distribution. Furthermore, the influence of internal electrodes onto the flow field is of interest. The mathematical model for the numerical treatment relies on a first-principle description of the EDL and the electrical forces, caused by the electrical field between internal electrodes. Hence, the so-called Debye-Hueckel approximation is avoided. The simulations are time-dependent and two-dimensional (plane) in nature and employ a finite-volume method.
Proceedings in applied mathematics & mechanics, Dec 1, 2006
The rapid mixing of small quantities, with the goal of reducing analysis and reaction times, is o... more The rapid mixing of small quantities, with the goal of reducing analysis and reaction times, is one of the key steps within innovative miniaturized total analysis systems (µTAS). To achieve wellmixed liquids with homogenous properties within an acceptable process time, the ...