Dynamics of an electrostatically charged elastic rod in fluid

2010 ◽  
Vol 467 (2126) ◽  
pp. 569-590 ◽  
Author(s):  
Sookkyung Lim ◽  
Yongsam Kim ◽  
David Swigon
Keyword(s):  
Immersed Boundary Method ◽  
Stable Equilibrium ◽  
Equations Of Motion ◽  
Initial Perturbation ◽  
Hard Core ◽  
Unstable Equilibrium ◽  
Immersed Boundary ◽  
Governing Equations ◽  
Elastic Rod ◽  
Equilibrium Configurations

We investigate the effects of electrostatic and steric repulsion on the dynamics of a pre-twisted charged elastic rod immersed in a viscous incompressible fluid. Equations of motion of the rod include the fluid–structure interaction, rod elasticity and a combination of two interactions that prevent self-contact, namely the electrostatic interaction and hard-core repulsion. The governing equations are solved using the generalized immersed-boundary method. We find that after perturbation, a pre-twisted minicircle collapses into a compact supercoiled configuration. The collapse proceeds along a complex trajectory that may pass near several unstable equilibrium configurations, before it settles in a locally stable equilibrium. The dwell time near an unstable equilibrium can be up to several microseconds. Both the final configuration and the transition path are sensitive to the initial excess link, ionic strength of the solvent and the initial perturbation.

SIMULATION OF INCOMPRESSIBLE VISCOUS FLOWS BY BOUNDARY CONDITION-IMPLEMENTED IMMERSED BOUNDARY METHOD

2009 ◽  
Vol 23 (03) ◽  
pp. 345-348
Author(s):  
Q. LI ◽  
C. SHU ◽  
H. Q. CHEN
Keyword(s):  
Immersed Boundary Method ◽  
Incompressible Flows ◽  
Viscous Flows ◽  
Numerical Approach ◽  
Present Approach ◽  
Immersed Boundary ◽  
Solid Boundary ◽  
Local Domain ◽  
Governing Equations ◽  
Boundary Method

A new numerical approach is presented in this work to simulate incompressible flows. The present approach combines the ideas of the conventional immersed boundary method (IBM) for decoupling the solution of governing equations with the solid boundary and the local domain-free discretization (DFD) method for implementation of boundary conditions. Numerical results for simulation of flows around a circular cylinder showed that the present approach can provide accurate solutions effectively.

Free Rotation of an Elastic Rod With an End Mass

1986 ◽  
Vol 53 (4) ◽  
pp. 864-868 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Angular Momentum ◽  
Large Deformations ◽  
Free Rotation ◽  
Centrifugal Forces ◽  
Governing Equations ◽  
Elastic Rod ◽  
Critical Rotation ◽  
Minimum Total Energy ◽  
Equilibrium Configurations ◽  
Flexible Antenna

This paper models a rotating space satellite with a long flexible antenna. Large deformations of the elastic rod are caused by the centrifugal forces. Bifurcation analysis shows the effect of end mass on the critical rotation speeds above which sinuous equilibrium configurations occur. The nonlinear governing equations are then integrated numerically. We find a class of solutions with a looped configuration whose existence requires a certain minimum total energy and minimum angular momentum. Catastrophic changes are possible.

Mass Conservation in the Immersed Boundary Method

2005 ◽  
Author(s):  
Frank Muldoon ◽  
Sumanta Acharya
Keyword(s):  
Boundary Conditions ◽  
Immersed Boundary Method ◽  
Incompressible Flows ◽  
Mass Conservation ◽  
Steady State Solution ◽  
Immersed Boundary ◽  
Governing Equations ◽  
Time Step ◽  
Backward Euler ◽  
Divergence Free

The immersed boundary approach for the modeling of complex geometries in incompressible flows is examined critically from the perspective of satisfying boundary conditions and mass conservation. The system of discretized equations for mass and momentum can be inconsistent if the real velocities are used in defining the forcing terms used to satisfy the boundary conditions. As a result, the velocity is generally not divergence free and the pressure at locations in the vicinity of the immersed boundary is not physical. However, the use of the pseudo velocities in defining the forcing (as frequently done when the governing equations are solved using a fractional step or projection method) combined with the use of the specified velocity on the immersed boundary is shown to result in a consistent set of equations which allows a divergence free velocity but, depending on the time step used to obtain a steady state solution, is shown to have an undesirable effect of allowing significant permeability of the immersed boundary. An improvement is shown if the pressure gradient is integrated in time using the Crank-Nicholson scheme instead of the backward Euler scheme. However, even with this improvement a significant reduction in the time step and hence increase in computational expense is still required for sufficient satisfaction of the boundary conditions.

scholarly journals On the experimental identification of unstable static equilibria

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160172 ◽  
Author(s):  
R. Wiebe ◽  
L. N. Virgin
Keyword(s):  
Energy Surface ◽  
Stable Equilibrium ◽  
Continuous System ◽  
Experimental System ◽  
Initial Energy ◽  
Unstable Equilibrium ◽  
Shallow Arch ◽  
Single Degree Of Freedom ◽  
Equilibrium Configurations ◽  
Unstable Configuration

This paper shows how the presence of unstable equilibrium configurations of elastic continua is reflected in the behaviour of transients induced by large perturbations. A beam that is axially loaded beyond its critical state typically exhibits two buckled stable equilibrium configurations, separated by one or more unstable equilibria. If the beam is then loaded laterally (effectively like a shallow arch) it may snap-through between these states, including the case in which the loading is applied dynamically and of short duration, i.e. an impact. Such impacts, if applied at random locations and of random strength, will generate an ensemble of transient trajectories that explore the phase space. Given sufficient variety, some of these trajectories will possess initial energy that is close to (just less than or just greater than) the energy required to cause snap-through and will have a tendency to slowdown as they pass close to an unstable configuration: a saddle point in a potential energy surface, for example. Although this close-encounter is relatively straightforward in a system characterized by a single degree of freedom, it is more challenging to identify in a higher order or continuous system, especially in a (necessarily) noisy experimental system. This paper will show how the identification of unstable equilibrium configurations can be achieved using transient dynamics.

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