Squeezing for Entangled States of Two Entangled Particles with Different Masses

Using the technique of integration within an ordered product of operators we present a convenient approach for introducing the squeezing operator for the entangled states of two entangled particles with different masses.We also introduce one-sided squeezing operators.

Characteristics of settling of dilute suspension of particles with different density at high Reynolds numbers

Dilute suspension of particles with same density and size develops clusters when settle at high Reynolds number(≥250).It is due to particles entrapment in the wakes produced by upstream particles.In this work,this phenomenon is studied for suspension having particles with different densities by numerical simulations.The particle-fluid interactions are modelled using immersed boundary method and inter-particle collisions are modelled using discrete element method.In simulations,settling Reynolds number is always kept above 250 and the suspension solid volume fraction is nearly 0.1 percent.Two particle density ratios(i.e.density of heavy particles to lighter particles)equal to 4:1 and 2:1 and particles with same density are studied.For each density ratio,the percentage volume fraction of each particle density is nearly varied from 0.8 to 0.2.Settling characteristics such as microstructures of settling particle,average settling velocity and velocity fluctuations of settling particles are studied.Simulations show that for different density particles settling characteristics of suspension is largely dominated by heavy particles.At the end of paper,the underlying physics is explained for the anomalies observed in simulation.

The Effect of Particle Shape on the Structure and Rheological Properties of Carbon-based Particle Suspensions

The structure and rheological properties of carbon-based particle suspensions, i.e., carbon black（CB）, multi-wall carbon nanotube（MWNT）, graphene and hollow carbon sphere（HCS） suspended in polydimethylsiloxane（PDMS）, are investigated. In order to study the effect of particle shape on the structure and rheological properties of suspensions, the content of surface oxygen-containing functional groups of carbon-based particles is controlled to be similar. Original spherical-like CB（fractal filler）, rod-like MWNT and sheet-like graphene form large agglomerates in PDMS, while spherical HCS particles disperse relatively well in PDMS. The dispersion state of carbon-based particles affects the critical concentration of forming a rheological percolation network. Under weak shear, negative normal stress differences（ΔN） are observed in CB, MWNT and graphene suspensions, while ΔN is nearly zero for HCS suspensions. It is concluded that the vorticity alignment of CB, MWNT and graphene agglomerates under shear results in the negative ΔN. However, no obvious structural change is observed in HCS suspension under weak shear, and accordingly, the ΔN is almost zero.

DC dielectrophoresis separation of marine algae and particles in a microfluidic chip

This paper reports a microfluidic method of continuous separation of marine algae and particles by DC dielectrophoresis. The locally non-uniform electric field is generated by an insulating PDMS triangle hurdle fabricated within a PDMS microchannel. Both the particles and algae are subject to negative DEP forces at the hurdle where the gradient of local electric-field strength is the strongest. The DEP force acting on the particle or the algae depends on particles' or algae's volume, shape and dielectric properties. Thus the moving particles and algae will be repelled to different streamlines when passing the hurdle. In this way, combined with the electroosmotic flow, continuous separation of algae of two different sizes, and continuous separation of polystyrene particles and algae with similar volume but different shape were achieved. This first demonstration of DC DEP separation of polystyrene particles and algae with similar sizes illustrates the great influence of dielectric properties on particle separation and potentials for sample pretreatment.