Swimming of a sphere in a viscous incompressible fluid with inertia

The swimming of a sphere immersed in a viscous incompressible fluid with inertia is studied for surface modulations of small amplitude on the basis of the Navier-Stokes equations. The mean swimming velocity and the mean rate of dissipation are expressed as quadratic forms in term of the surface displacements. With a choice of a basis set of modes the quadratic forms correspond to two hermitian matrices. Optimization of the mean swimming velocity for given rate of dissipation requires the solution of a generalized eigenvalue problem involving the two matrices. It is found for surface modulations of low multipole order that the optimal swimming efficiency depends in intricate fashion on a dimensionless scale number involving the radius of the sphere, the period of the cycle, and the kinematic viscosity of the fluid.Comment: 19 pages, 4 figure

Optimal translational swimming of a sphere at low Reynolds number

Swimming velocity and rate of dissipation of a sphere with surface distortions are discussed on the basis of the Stokes equations of low Reynolds number hydrodynamics. At first the surface distortions are assumed to cause an irrotational axisymmetric flow pattern. The efficiency of swimming is optimized within this class of flows. Subsequently more general axisymmetric polar flows with vorticity are considered. This leads to a considerably higher maximum efficiency. An additional measure of swimming performance is proposed based on the energy consumption for given amplitude of stroke.Comment: 34 pages, 12 figure

Dielectrophoretic levitation of droplets and bubbles

Uncharged droplets and bubbles can be levitated dielectrophoretically in liquids using strong, nonuniform electric fields. The general equations of motion for a droplet or bubble in an axisymmetric, divergence-free electrostatic field allow determination of the conditions necessary and sufficient for stable levitation. The design of dielectrophoretic (DEP) levitation electrode structures is simplified by a Taylor-series expansion of cusped axisymmetric electrostatic fields. Extensive experimental measurements on bubbles in insulating liquids verify the simple dielectrophoretic model. Other have extended dielectrophoretic levitation to very small particles in aqueous media. Applications of DEP levitation to the study of gas bubbles, liquid droplets, and solid particles are discussed. Some of these applications are of special interest in the reduced gravitational field of a spacecraft

Human comfort in relation to sinusoidal vibration

An investigation was made to assess the overall subjective comfort levels to sinusoidal excitations over the range 1 to 19 Hz using a two axis electrohydraulic vibration simulator. Exposure durations of 16 minutes, 25 minutes, 1 hour, and 2.5 hours have been considered. Subjects were not exposed over such durations, but were instructed to estimate the overall comfort levels preferred had they been constantly subjected to vibration over such durations

End-point of the rp process and periodic gravitational wave emission

The general end-point of the rp process in rapidly accreting neutron stars is believed to be a surface distribution of matter whose nuclear composition may depend on position. Its evolution during compression beyond the neutron-drip threshold density is determined by the presence of nuclear formation enthalpy minima at the proton closed shells. At threshold, a sequence of weak interactions with capture or emission of neutron pairs rapidly transform nuclei to the most accessible proton closed shell. Therefore, angular asymmetries in nuclear composition present in accreted matter at neutron drip are preserved during further compression to higher densities provided transition rates between closed shells are negligible. Although it has been confirmed that this condition is satisfied for predicted internal temperatures and for the formation enthalpy distribution used in this work, it would not be so if the true enthalpy differences between maxima and minima in the distribution were a factor of two smaller. For this reason, it does not appear possible to assert with any confidence that position-dependent surface composition can lead to significant angle-dependence of the equation of state and to potentially observable gravitational radiation. The effect of non-radial internal temperature gradients on angle-dependency of the equation of state is also not quantifiable.Comment: This version corrects a major error in estimating the effect of composition asymmetry on the equation of state. Its conclusions are less definite than those of the previous version. 9 pages RevTex; 1 figure. To be published in Phys. Rev.