A fluid droplet, in general, deforms if subject to active driving, such as a finite slip velocity... more A fluid droplet, in general, deforms if subject to active driving, such as a finite slip velocity or active tractions on its interface. Starting from Stokes equations, we show that these deformations and their dynamics can be computed analytically in a perturbation theory in the inverse of the surface tension γ, by using an approach based on vector spherical harmonics. We consider squirmer models and general active tractions, such as inhomogeneous surface tensions, which may result from the Marangoni effects. In the lowest order, the deformation is of order [Formula: see text], yet it affects the flow fields inside and outside of the droplet in order to [Formula: see text]. Hence, a correct description of the flow has to allow for shape fluctuations, —even in the limit of large surface tension. We compute stationary shapes and relaxation times and compare our results to an approach, which discards all effects of deformations on surface tensions. This approach leads to the same propu...
We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming ... more We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming micro-organisms or artificial micro-swimmers. In contrast to approaches that start from active velocity fields produced by the system, we consider active interface tractions, body force densities and active stresses as the origin of autonomous swimming. For negligible Reynolds number and given activity, we compute the external and internal flow fields as well as the centre of mass velocity and angular velocity of the droplet at fixed time. To construct trajectories from single time snapshots, the evolution of active forces or stresses must be determined in the laboratory frame. Here, we consider the case of active matter, which is carried by a continuously distributed rigid but sparse (cyto)-skeleton that is immersed in the droplet interior. We calculate examples of trajectories of a droplet and its skeleton from force densities or stresses, which may be explicitly time-dependent in a fr...
Long-time effects in a simulation model of sputter erosion. Alexander K. Hartmann * and Reiner Kr... more Long-time effects in a simulation model of sputter erosion. Alexander K. Hartmann * and Reiner Kree Institut für Theoretische Physik, University of Göttingen, Bunsenstr. 9, 37073 Göttingen, Germany. Ulrich Geyer and Matthias ...
We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spheric... more We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position $$\varvec{r}_s$$ r s . The squirmer is subject to an external force and torque in addition to the slip velocity on its surface. We have derived exact analytical expressions for the linear and rotational velocity of the squirmer as well as the linear velocity of the drop for general, non-axisymmetric configurations. The mobilities of both, squirmer and drop, are in general anisotropic, depending on the orientation of $$\varvec{r}_s$$ r s , relative to squirmer axis, external force or torque. We discuss their dependence on the size of the squirmer, its distance from the center of the drop and the viscosities. Our results provide a framework for the discussion of the trajectories of the composite system of drop and enclosed squirmer. Graphical Abstract
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected ... more We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation functions of the Gibbs states may be calculated exactly as a function of the box length and temperature. This allows for a detailed test of results obtained by the replica variational approximation scheme. We show that this scheme provides a reasonable estimate of the averaged free energy. Furthermore our results shed more light on the validity of the concept of approximate ultrametricity which is a central assumption of the replica variational method.
A fluid droplet, in general, deforms if subject to active driving, such as a finite slip velocity... more A fluid droplet, in general, deforms if subject to active driving, such as a finite slip velocity or active tractions on its interface. Starting from Stokes equations, we show that these deformations and their dynamics can be computed analytically in a perturbation theory in the inverse of the surface tension γ, by using an approach based on vector spherical harmonics. We consider squirmer models and general active tractions, such as inhomogeneous surface tensions, which may result from the Marangoni effects. In the lowest order, the deformation is of order [Formula: see text], yet it affects the flow fields inside and outside of the droplet in order to [Formula: see text]. Hence, a correct description of the flow has to allow for shape fluctuations, —even in the limit of large surface tension. We compute stationary shapes and relaxation times and compare our results to an approach, which discards all effects of deformations on surface tensions. This approach leads to the same propu...
We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming ... more We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming micro-organisms or artificial micro-swimmers. In contrast to approaches that start from active velocity fields produced by the system, we consider active interface tractions, body force densities and active stresses as the origin of autonomous swimming. For negligible Reynolds number and given activity, we compute the external and internal flow fields as well as the centre of mass velocity and angular velocity of the droplet at fixed time. To construct trajectories from single time snapshots, the evolution of active forces or stresses must be determined in the laboratory frame. Here, we consider the case of active matter, which is carried by a continuously distributed rigid but sparse (cyto)-skeleton that is immersed in the droplet interior. We calculate examples of trajectories of a droplet and its skeleton from force densities or stresses, which may be explicitly time-dependent in a fr...
Long-time effects in a simulation model of sputter erosion. Alexander K. Hartmann * and Reiner Kr... more Long-time effects in a simulation model of sputter erosion. Alexander K. Hartmann * and Reiner Kree Institut für Theoretische Physik, University of Göttingen, Bunsenstr. 9, 37073 Göttingen, Germany. Ulrich Geyer and Matthias ...
We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spheric... more We have analyzed the dynamics of a spherical, uniaxial squirmer which is located inside a spherical liquid drop at general position $$\varvec{r}_s$$ r s . The squirmer is subject to an external force and torque in addition to the slip velocity on its surface. We have derived exact analytical expressions for the linear and rotational velocity of the squirmer as well as the linear velocity of the drop for general, non-axisymmetric configurations. The mobilities of both, squirmer and drop, are in general anisotropic, depending on the orientation of $$\varvec{r}_s$$ r s , relative to squirmer axis, external force or torque. We discuss their dependence on the size of the squirmer, its distance from the center of the drop and the viscosities. Our results provide a framework for the discussion of the trajectories of the composite system of drop and enclosed squirmer. Graphical Abstract
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected ... more We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation functions of the Gibbs states may be calculated exactly as a function of the box length and temperature. This allows for a detailed test of results obtained by the replica variational approximation scheme. We show that this scheme provides a reasonable estimate of the averaged free energy. Furthermore our results shed more light on the validity of the concept of approximate ultrametricity which is a central assumption of the replica variational method.
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Papers by Reiner Kree