Stokes Force Research Articles

On the motion of inertial particles by sound waves

This paper describes the numerical simulation of the motion of a heavy spherical particle in an acoustic wave using the equation of motion for a point particle. Our results agree well with the recent experimental data of Gonzàlez, Hoffmann, and Gallego [“Precise measurements of particle entrainment in a standing-wave acoustic field between 20 and 3500 Hz,” J. Aerosol Sci. 31, 1461–1468 (2000)]. Our simulations cover a range of particle relaxation number, τ* = ωτ, where τ is the particle relaxation time and ω is the angular acoustic frequency from 0.06 to 10, particle to fluid density ratios, ρp/ρf, from 2500 to 2, and moderate acoustic velocity amplitudes. The results show that the Stokes force controls particle motion for τ* < 1 and ρp/ρf > 25. Within this regime it is appropriate to consider the Basset, pressure gradient, and virtual mass forces as “higher order” corrections to the Stokes force. The magnitude of the Basset force exceeds that of the Stokes force for ρp/ρf ⩾ 25 and τ* ⩾ 4. All the forces in the particle equation of motion should be accounted for when simulating particle motion in an acoustic wave for ρp/ρf < 25.

Simulation the sedimentation of a finely dispersed medium under the impact of pressure waves

A mathematical model for a disperse system of gas-solid particles when passing pressure waves is decribed. The following assumptions are made: dispersed particles are capable of coagulation with increasing concentration; the dispersed particles are acted upon by the Stokes forces on the side of the dispersion medium and by gravity. The results of numerical simulation of the processes of sedimentation of a dispersed medium are presented. It is shown that one of the mechanisms of precipitation of fine disperced medium can be coagulation of particles during the passage of pressure waves.

A Review on Aerosol-Based Direct-Write and Its Applications for Microelectronics

Aerosol-based direct-write refers to the additive process of printing CAD/CAM features from an apparatus which creates a liquid or solid aerosol beam. Direct-write technologies are poised to become useful tools in the microelectronics industry for rapid prototyping of components such as interconnects, sensors, and thin film transistors (TFTs), with new applications for aerosol direct-write being rapidly conceived. This paper aims to review direct-write technologies, with an emphasis on aerosol-based systems. The different currently available state-of-the-art systems such as Aerosol Jet CAB-DW, MCS, and aerodynamic lenses are described. A review and analysis of the physics behind the fluid-particle interactions including Stokes and Saffman force, experimental observations, and how a full understanding of theory and experiments can lead to new technology are presented. Finally, the applications of aerosol direct-write for microelectronics are discussed.

Electrical properties of water drops inside the dropwise cluster

The Letter shows that inside a dropwise cluster formed over the heated water surface, water drops are electrically charged. The charge of a separate drop reaches 103 units of an elementary charge. The drops are positioned from each other at the distance of double Debye radius length. It is fixed up that drops levitate over the water surface in consequence of the Stokes force acting from the side of gas–vapor flow rising from water surface. The Stokes force thousand times exceeds the Coulomb drop repulsion force from the water surface.

Improvement of the Size-Selective Separation of Microbeads in a Curved Microchannel Using Particle Focusing

The size-selective microfluidic separation of glass beads in a curved rectangular microchannel was fabricated in our previous work. In this study, we improve its separation performance and attempt an experimental visualization to examine the separation resolution. In the previous work, we found by visualization that the trajectory of 20 µm glass beads was influenced by their travelling path along a straight inlet channel. Using a forced sheath flow, a consistent bead trajectory along the middle of the straight inlet channel was obtained, and the sheath angle to minimize the focusing width of the flowing distributed beads was determined to be 45°. The physical explanation for the dynamic behavior of microbeads was elaborated. When the ratio of Stokes force to centrifugal force mainly acting on a glass bead fell under unity, the glass bead moved out to the wall in spite of the fact that its size was less than the height of the zero velocity position. To examine the separation resolution, the newly designed size-selective separation microchannel with the sheath was fabricated and its separation performance was visualized. The movement of the glass beads showed a good agreement with the separation mechanism explained by the force ratio. The resolution of the separation was visualized to be 10 µm for the size of glass beads used in the experiment. The size-selective separation performance was explained in terms of physical forces and was improved by solving the previous problems. A cascade device for the continuous separation of microbeads of various sizes can improve the separation resolution.

Dependence of the mechanism of solid particle drift in a nonlinear wave field on the time constant and wave front passage time

A criterion that allows determining the prevailing mechanism and direction of the drift of a solid spherical particle in a nonlinear wave field of a closed acoustic resonant cavity, depending on the ratio between the particle time constant, compression wave front growth time, and duration of passage of the acoustic wave, is analyzed. Particle motion is assumed to occur under the action of the Stokes force, buoyancy force, and virtual mass force.

A model for processive movement of single-headed myosin-IX

It is puzzling that in spite of its single-headed structure, myosin-IX can move processively along actin. Here, based on the experimental evidence that the strong binding of myosin to actin in rigor state induces structural changes to several local actin monomers, a Brownian ratchet model is proposed to describe this processive movement. In the model, the actin plays an active role in the motility of single-headed myosin, in contrast to the common belief that the actin acts only as a passive track for the motility of the myosin. The unidirectional movement is due to both the asymmetric periodic potential of the myosin interacting with actin and the forward Stokes force induced by the relative rotation of the neck domain to the motor domain, while the processivity is determined by the binding affinity of the myosin for actin in ATP state. This gives a good explanation to the high processivity of myosin-IX, which results from its high binding affinity for actin in ATP state due to the presence of unique loop 2 insertion or N-terminal extension. The experimental results on the motility of myosin-IX such as the step size, large forward/backward stepping ratio, run length, stall force, etc, are explained well.

On the mechanism of formation of depositional remanent magnetization

Coagulation of particles into aggregates during their settling in an aqueous solution is numerically simulated with regard to Brownian motion, Van der Waals and Stokes's forces, gravitation, and magnetostatic interactions. Clusters obtained have a fractal structure with the average fractal dimension d = 1.83. Magnetic grains do not group until their concentration exceeds at least a few percent. The deposition process obeys a scaling principle: the sizes of clusters arriving at the bottom of a basin do not change if the product of the basin depth H and the concentration of initial material c0 is constant. Attempts at numerical simulations of laboratory redeposition experiments are made. Good agreement between numerical simulations and experimental results by van Vreumingen (1993) demonstrates that the modeling algorithm is based on reasonable physical assumptions. The magnetization of a flocculating suspension is defined by at least seven parameters, which characterize magnetic and nonmagnetic particles, as well as the aqueous medium. This multiparametric dependence hinders estimations of paleofield intensity by the redeposition method because it is practically impossible to reproduce natural conditions in the laboratory. Flocculation influences the magnetization intensity of the settling suspension at concentrations c0 typical for redeposition experiments or natural sedimentation in lakes and shallow seas. Flocculation is of minor importance for deep oceanic regions because of their extremely low sedimentation rate. However, factors like small‐scale turbulence and biotic processes are not taken into account by the model and may require modification of these conclusions. Also, a simple model of pDRM acquisition based on elastic and plastic properties of sediment slurry is proposed.

10.1007/s11455-008-1023-9

A force acting on a nanoparticle occurring in a fluid has been studied by the molecular dynamics method. It is shown that this force is nonstationary and exhibits a relaxation character. At the initial instant, it is two to three times the Stokes force, but then decreases and, outside the first relaxation region, becomes smaller than the Stokes force. A stationary force acting on a nanoparticle is determined by the particle mass and size. Correlation expressions for determining the drag coefficient are constructed. It is established that the drag force is anisotropic.

The process of flushing the gravitational cleaner from pollution cleansers

During the dirt accumulation the operating efficiency of the cleaners is decreasing and can be restored by cleaning the surface of sedimental plates cleaner. The condition of washing cleaner from pollution is excess of stokes forces on sliding friction force and size that characterizes the roll friction. Inequalities for all computed values of stoke strength were arranged and solved relative to waste of certain cleaning fluids. Thus: the flushing gravity cleaner with considered detergents is possible, more efficient process is to wash with detergent that has higher kinematic viscosity coefficient.

Numerical simulation of the process of wave separation of solid particles in resonance gas vibrations in the closed pipe

Drift of solid suspended particles under the action of longitudinal resonance vibrations of the gas column in a closed pipe is studied numerically. Nonlinear gas vibrations with the motion remaining to be laminar are considered. The gas velocity field contains periodic nonlinear waves and an acoustic flow, and the particles move under the action of the Stokes force. For the first, second, and third eigenfrequencies of the longitudinal gas column vibrations, distributions of light and heavy particles observed in the wave field of the closed pipe are obtained.

Computer simulation of the drift of solid particles caused by resonance gas oscillations in the open channel

Computer simulation methods are used to study the drift of solid spherical particles suspended in the open channel due to longitudinal oscillations of the gas column. The gas velocity field consists of periodic nonlinear waves and an acoustic flow. The particles move under the action of the Stokes force. Particle distributions in the wave field of the open channel are obtained in the vicinity of the first, second and third eigen-frequencies of the gas column. The particle’s spatial distribution features attributed to the particle’s drift under the action of acoustic radiation are revealed.

Investigation of the stability of a plane-channel suspension flow with account for finite particle volume fraction

Within the framework of the two-fluid approach, a variant of a heterogeneous-medium model which takes into account a finite volume fraction of the inclusions and a small but finite phase velocity slip is proposed. The interphase momentum exchange is described by the Stokes force with the Brinkman correction for the finite particle volume fraction. The suspension viscosity depends on the particle volume fraction in accordance with the Einstein formula. Within the framework of the model constructed, a formulation of the problem of linear stability of plane-parallel two-phase flows is proposed. As an example, the stability of a channel suspension flow is considered. The system of equations for small disturbances with the boundary conditions is reduced to an eigenvalue problem for a fourth-order ordinary differential equation. Using the orthogonalization method, the dependence of the critical Reynolds number on the governing nondimensional parameters of the problem is studied numerically. It is shown that taking a finite volume fraction of the inclusions into account significantly affects the laminar-turbulent transition limit.

Aerosol focusing in micro-capillaries: Theory and experiment

A combined theoretical and experimental study is presented where we illustrate the focusing influence of Saffman force upon the fluid dynamics of aerosol flows through micro-capillaries. It is shown that under proper conditions, the Saffman force acting on aerosol particles in gas flowing through a micro-capillary causes migration of particles toward the center line of the capillary. This approach is in stark contrast to the classical aerodynamic focusing methodologies where only particle inertia and the Stokes force of gas–particle interaction are typically considered. A new mathematical model for aerosol flow through a micro-capillary accounting for complicated interactions between particles and carrier gas is presented and this model describes the experimental observables obtained via imaging microscopy of a beam of aerosol particles ( d ∼ 1 μ m ). In general, this study affords a method for controlling and optimizing focused aerosol beams by appropriate modification of process variables such as the micro-capillary geometry, the carrier gas composition and the nature of the aerosol particles.

Force acting on a nanoparticle in a fluid

A force acting on a nanoparticle occurring in a fluid has been studied by the molecular dynamics method. It is shown that this force is nonstationary and exhibits a relaxation character. At the initial instant, it is two to three times the Stokes force, but then decreases and, outside the first relaxation region, becomes smaller than the Stokes force. A stationary force acting on a nanoparticle is determined by the particle mass and size. Correlation expressions for determining the drag coefficient are constructed. It is established that the drag force is anisotropic.

Effect of gravity convection on interface morphology during solidification

An experimental apparatus consisting of a crystal growth room and a crystal growth observation system was developed for the study of the effect of the gravity convection perpendicular to the growth direction on the growth process by use of model alloy succinonitrile (SCN)-5wt%ethanol. It was found that the convection improves the stability of the interface and causes the downstream alternation of the cell growth direction because of the dual effect of the Stokes force and the gravity. The second dendrite arm facing the flow comes into being earlier than that at another side when the interface transforms cell to dendrite. Then the dendrite at the side facing the flow comes into being earlier. The second dendrite arm facing the flow grows faster and is more developed than that at another side. In addition, the primary dendrite arm spacing increases and the dendrite tip radius decreases under the gravity convection.

자기영동을 이용한 자성입자 분리 마이크로 칩 제작 및 성능평가

We developed a microfluidic platform able to control the trap and release of magnetic beads used for separation of a specific biomolecules. The magnetic beads can be trapped and released conditionally by controlling the difference between the Stokes force induced by the fluid flow and magnetic force resulting from a permanent magnet. The permanent magnet of CoNiP alloy is electroplated. It is characterized to have the 1369 Oe of coercivity, 1762 Gauss of remanence, and 0.603MGOe of (BH)max. Through the experimental and numerical investigation, the magnetic beads are trapped under the flow velocity of 17 ㎛/s and are released perfectly above the velocity of 174 ㎛/s.

Generalization of the theory of thermophoresis for a doublet of solid particles experiencing a temperature step on the surface

Using the linear operator approach, a theory of thermophoresis is constructed for the case of two homogenous solid spherical aerosol particles moving parallel to their center line. Formulas for the Stokes force, force of thermophoresis, and rate of thermophoresis of an aerosol particle with regard to a temperature step on its surface and the effect of the other particle are derived. Approximate engineering formulas are presented.

Model for helicase translocating along single-stranded DNA and unwinding double-stranded DNA

A model is proposed for non-hexameric helicases translocating along single-stranded (ss) DNA and unwinding double-stranded (ds) DNA. The translocation of a monomeric helicase along ssDNA in weakly-ssDNA-bound state is driven by the Stokes force that is resulted from the conformational change following the transition of the nucleotide state. The unwinding of dsDNA is resulted mainly from the bending of ssDNA induced by the strong binding force of helicase with dsDNA. The interaction force between ssDNA and helicases in weakly-ssDNA-bound state determines whether monomeric helicases such as PcrA can unwind dsDNA or dimeric helicases such as Rep are required to unwind dsDNA.

Gravity-Induced Convection during Directional Solidification of Hypermonotectic Alloys

A two-phase volume-averaging model developed for the simulation of the dynamic decomposition and solidification of hypermonotectic alloys was used to study the occurrence of convection phenomena during directional solidification of a hypermonotectic alloy (Al-10 wt.%Bi) under terrestrial condition. The model accounts for nucleation and growth of secondary phase droplets, Marangoni and Stokes forces, solute partitioning, heat release due to decomposition and solidification. It is shown that the appearance and growth of secondary droplets is accompanied with a continuous downwards motion of droplets, which rapidly becomes unstable. After relaxation of this dynamic motion the advancing solidification front freezes in the resulting non-uniform droplet distribution.