The viscous drag of three-dimensional model fibrous filters

Dependences of the viscous drag of the model filter consisting of two parallel cylinder rows arranged perpendicular to the Stokes flow and to each other, on a step and a distance between rows are found. The approximation formula for the drag force of a cylinder in contacting rows is obtained. The drag was calculated for the three-dimensional model filter where two hexagonal grids of cylinders are inserted into each other at a right angle. The drag force of a cylinder for this model is close to that for the fan model filter.     

Assembling and orientation of polyfluorenes in solution controlled by a focused near-infrared laser beam

Ordered fibril- and particle-like assemblies of poly(2,7-(9,9-bis(2-ethylhexyl)fluorene)) can be formed by photon force of a focused near-infrared laser beam during the drying process of its tetrahydrofuran solution on a glass substrate. These formations have been achieved controllably by combining laser irradiation with convection in the cast solution; that is, when viscous drag of the solution in the convection is stronger than the photon force, the fibril-like assemblies can be formed. Molecular orientation in the assemblies differs from that in self-assembled fibril-like structures, and maybe it can be controlled by the polarization direction of the focused laser beam. We have demonstrated that the length and width of the assemblies can be controlled by the irradiation time, the laser power, the concentration of the solution, and the convection rate in the solution. On the other hand, when the viscous drag of the solution in the convection is weak compared to the photon force, particle-like assemblies in which molecular orientation is controlled by polarization direction are formed.     

Capillary impregnation into cylinder banks

The capillary rise of liquid in a cylinder bank is examined in order to study the capillary pressure variation perpendicular to the direction of the cylinders. The calculations consider the local geometric variation of the flow channel and the position-dependent capillary pressure. The capillary flow around each cylinder is calculated by balancing the capillary pressure and the viscous drag along the flow path. The rate of filling for several layers of cylinders is used to estimate the equivalent capillary pressure. The method is also applied to the underfill of a flip chip system, which is modeled as a cylinder bank between parallel plates.     

Equilibrium theory for a particle pulled by a moving optical trap

The viscous drag on a colloidal particle pulled through solution by an optical trap is large enough that on experimentally relevant time scales the mechanical force exerted by the trap is equal and opposite the viscous drag force. The rapid mechanical equilibration allows the system to be modeled using equilibrium theory where the effects of the energy dissipation (thermodynamic disequilibrium) show up only in the coordinate transformations that map the system from the laboratory frame of reference, relative to which the particle is moving, to a frame of reference in which the particle is, on average, stationary and on which the stochastic dynamics is governed by a canonical equilibrium distribution function. The simple equations in the stationary frame can be analyzed using the Onsager-Machlup theory for stochastic systems and provide generalizations of equilibrium and near equilibrium concepts such as detailed balance and fluctuation-dissipation relations applicable to a wide range of systems including molecular motors, pumps, and other nanoscale machines.     

Drag force on a rigid spheroidal particle in a cylinder filled with Carreau fluid

The boundary effect on the drag acting on a rigid particle is investigated by considering a spheroid on the axis of a cylinder filled with a Carreau fluid. The result of numerical simulation reveals that the ratio (drag coefficient in Carreau fluid/drag coefficient in Newtonian fluid) has a maximum as the ratio (semiaxis in radial direction/radius of cylinder) varies. The presence of a wall has the effect of enhancing the convective motion in the rear part of a particle, and therefore, the formation of wakes. The influence of the shape of a particle on the drag force acting on it can be decreased either by increasing the shear-thinning effect of the fluid or by increasing the Reynolds number. The Reynolds number at which flow separation occurs is found to increase roughly linearly with the increase in the power-law exponent of the Carreau fluid.     

Modelling a flow of a highly viscous liquid with the boundary layer of low viscosity in an extruder

Features of the flow of a highly viscous liquid in an extruder with boundary layer of low viscosity liquid at the cylinder wall and at the endless screw surface are considered. The liquid flow is modeled under conditions of isothermal simple shift using cylindrical model of a screw canal. The profiles of rates for the stream of a highly viscous liquid with the ring boundary layer of low-viscous liquid at the cylinder wall and at screw in the both presence and absence of a counter pressure are calculated. Consideration of computer calculations shows that increase in the flow rate is possible when the counter pressure tends to zero and the low-viscous liquid forms a ring boundary layer at the cylinder wall.     

Viscoelastic Drag of Particles Settling in Wormlike Micellar Solutions of Varying Surfactant Concentration

Wormlike micellar octadecyl trimethyl ammonium chloride (OTAC) solution is a self-assembled fracturing fluid used to carry proppants into fractures in oil recovery. Slow settling velocity of proppant is desirably resulted from the viscoelastic drag with low viscosity of fracturing fluids for fracturing work. Steel spheres, as a substitute for proppants, fall into three semi-dilute OTAC solutions. The steady rheology demonstrates that OTAC solutions are divided into shear-thickening and shear-thinning regimes by the critical shear rate. The applied steel spheres always lie in the shear-thickening regime of the 2.8 wt% OTAC solution with aggregated micelles as their characteristic shear rates are less than the critical shear rate of the solution. Strong shear-thickening viscous drag results in lower settling velocity of steel spheres. Most of the applied steel spheres, on the other hand, lie in the shear-thinning regime of the 4 wt% OTAC solution with orientated micelles. Although the latter solution has small dissipation coefficient, high Weissenberg number, and consequently high elastic effect, the shear-thinning viscosity results in higher settling velocity of steel spheres.     

The drag of the row of parallel chains of spherical particles in the Stokes flow

The drag of thin-layered porous deposit consisting of dendrites of identical spherical particles with respect to the flow of viscous incompressible liquid is calculated. The deposit is approximated by a model system, a row of parallel chains of particles oriented perpendicular to a flow direction. The expression is derived for the dimensionless drag force acting on the unit chain length as a function of the ratio of a particle radius to a half-distance between chain axes, a/h. It is shown that, at a/h < 0.5, the hydrodynamic equivalent of the chains is the smooth cylinder whose radius is 1.16 times smaller than the particle radius that agrees with the experiment. It is also shown that, at a/h = 1, the drag force of a particle contacting with four adjacent particles in the layer with square packing is equal to F = 44F _St, where F _St is the Stokes drag force of a spherical particle. The pressure drop in this single layer is by 3.5% higher than in the layer of spherical particles with cubic packing. At a/h = 2/√3, drag force F of the particle contacting with six particles in a single layer with hexagonal packing is equal to 340F _St.     

EFFECT OF INTERNAL VISCOSITY OF POLYMERIC FLUIDS UNDER STRONG EXTENSIONAL FLOWS

The dumbbell model with internal viscosity for a dilute polymer solution is investigated based on a balance of viscous drag and restoring Brownian forces.An approximate method is used to obtain the solution of extensional stress in closed form in the case of steady flow.For different internal viscosities,this parametric study shows different asymptotic regimes of the extensional viscosity as a function of strain rate.This analysis may explain the attenuation of pressure drop in strong flows from a phenom...     

Coating functional sol–gel films inside horizontally-rotating cylinders by rimming flow/state

The fabrication of uniform sol–gel coatings with embedded functional nanomaterials inside cylinders requires detailed understanding of the gelation behavior. For sol–gel systems the viscosity is a function of gelation time that affects sol–gel coatings on the inside of a slowly, horizontally rotating cylinder. Therefore the angular velocity has to be adjusted to this time dependence. The higher the viscosity the more liquid is dragged along with the moving cylinder wall while the balance of gravity and drag limits the layer thickness. In addition, inertial forces and surface tension can create instabilities within the coated layer. Here, we show that it is important to suppress these instabilities by transitioning the viscous sol directly to a velocity that allows for the formation of an almost uniform layer. In this regime, which is the so-called rimming state, the recirculation of the gel precursor solution is strongly reduced which allows to fabricate coatings with shear sensitive sol–gel chemistries. Here, we tested this approach with 4 different aerogel systems, with low-density CH-based-, TiO₂-, SiO₂- and Fe₂O₃-aerogels, that represent a wide variety of different sol–gel behaviors. We show that the required rotational velocities for these aerogel systems can be predicted with a simple analytical approximation, and we performed computational fluid dynamics simulations to predict local shear and thickness uniformity.     

On the Flow of a Viscous Liquid around a Heated Spheroidal Particle

An expression is derived for the viscous drag of a spheroidal particle whose temperature differs from that of the carrier liquid. Calculations are performed for the case where the temperature dependence of the liquid viscosity may be represented by an exponential power series.     

Electrokinetic lift force for a charged particle moving near a charged wall — a modified theory and experiment

We present the refined theory of the electrokinetic lift force for a charged particle moving at a charged wall at the distance much larger than the double layer thickness. The theory is based on the lubrication approximation for the solution of the Stokes equation for the flow around a long cylinder moving near a solid wall. The “thin double layer” approximation is used to solve the ionic balance and electro-osmotic flow equations. The electrokinetic lift force is then obtained by integration of the viscous stress tensor as well as the Maxwell stress tensor over the particle surface. The resulting lift force for the cylinder translating, rotating at the wall as well as for the stationary cylinder in the wall shear flow, is considered. Following this, we apply the Derjaguin approximation to transform the obtained results to the sphere–wall geometry and we compare our theoretical predictions with the measurements of the electrokinetic lift force performed in the “colloidal particle collider” apparatus for the latex particles suspended in the glycerol–water solutions. Our theoretical results for the electrokinetic lift force exceeds by several orders of magnitude one obtained from the previously developed theory and are in a good agreement with experimental findings.     

A capsule with a fractal shell in a uniform liquid flow

The problem of a liquid flow, which is uniform at infinity, around a capsule comprising a fractal shell filled with a liquid identical to the ambient liquid has been solved. The flow in the fractal layer is described by the Brinkman equation, assuming that the viscosity of the effective medium differs from the viscosity of the pure liquid. Velocity and pressure distributions have been found, and the viscous drag force applied to the capsule has been calculated.     

Stokes flow in periodic systems of parallel cylinders with porous permeable shells

The problem solved in this study concerns steady-state flow of a viscous incompressible liquid at low Reynolds numbers in a model filter consisting of parallel cylinders with porous permeable shells. Both a separate row and lattices (square and hexagonal) of cylinders directed perpendicularly to the flow are considered. The flow field outside and inside the porous shell is found from the solutions to the Stokes and Brinkman equations. The drag force and the filtration efficiency are determined both as functions of the ratio between the cylinder diameter and the distance between the axes of adjacent cylinders and as functions of the thickness and permeability of the shells. The cell model is shown to be applicable for describing the flow field in a hexagonal lattice of cylinders with porous shells within a wide range of packing densities. Original Russian Text ? V.A. Kirsh, 2006, published in Kolloidnyi Zhurnal, 2006, Vol. 68, No. 2, pp. 198–206.     

Diffusion of liquid domains in lipid bilayer membranes

We report diffusion coefficients of micron-scale liquid domains in giant unilamellar vesicles of phospholipids and cholesterol. The trajectory of each domain is tracked, and the mean square displacement grows linearly in time, as expected for Brownian motion. We study domain diffusion as a function of composition and temperature and measure how diffusion depends on domain size. We find mechanisms of domain diffusion which are consistent with membrane-dominated drag in viscous L(o) phases and bulk-dominated drag for less viscous L(alpha) phases. Where applicable, we obtain the membrane viscosity and report activation energies of diffusion.     

Electroviscous Forces on a Charged Cylinder Moving Near a Charged Wall

The refined theory of the electroviscous lift forces is presented for the case when the separation distance between the particle and the wall is larger than the double-layer thickness. The theory is based on the lubrication approximation for motion of a long cylinder near a solid wall in creeping flow. The approximate analytical formula for the lift force valid for Pe相似文献   

Nanoparticle deposition in granular filters at Reynolds numbers higher than unity

The influence of the inertia of a viscous incompressible liquid flow on the viscous drag and diffusion deposition of particles in model granular filters at Reynolds numbers higher than unity, Re > 1, has been considered. The granule drag forces and particle-collection efficiencies in isolated layers with square and hexagonal packings of granules have been calculated. The influence on each other of approaching monolayers of granules on pressure drop and nanoparticle deposition has been studied. It has been shown that, at Re > 1, the collection efficiency dramatically increases due to the effect of interception.     

Capillary forces between spherical particles floating at a liquid-liquid interface

We study the capillary forces acting on sub-millimeter particles (0.02-0.6 mm) trapped at a liquid-liquid interface due to gravity-induced interface deformations. An analytical procedure is developed to solve the linearized capillary (Young-Laplace) equation and calculate the forces for an arbitrary number of particles, allowing also for a background curvature of the interface. The full solution is expressed in a series of Bessel functions with coefficients determined by the contact angle at the particle surface. For sub-millimeter spherical particles, it is shown that the forces calculated using the lowest order term of the full solution (linear superposition approximation; LSA) are accurate to within a few percents. Consequently the many particle capillary force is simply the sum of the isolated pair interactions. To test these theoretical results, we use video microscopy to follow the motion of individual particles and pairs of interacting particles at a liquid-liquid interface with a slight macroscopic background curvature. Particle velocities are determined by the balance of capillary forces and viscous drag. The measured velocities (and thus the capillary forces) are well described by the LSA solution with a single fitting parameter.     

Direct measurement of the viscous force between two spherical particles trapped in a thin wetting film

Here we present the first direct measurement of the viscous drag force between two spherical particles of millimeter size trapped in a thin wetting film. Each particle is constrained by the liquid/air interface and the solid substrate. The viscous force is counterbalanced by another known force, the attractive capillary immersion force between identical particles protruding from the film surface. The results of the measurements provide evidence for an increased hydrodynamic force due to a non-Stokesian resistance to the particle motion. Our findings can be applied to the self-assembly of colloidal particles in a two-dimensional array for coating and to the friction between small species and a solid. Received: 19 March 1999 Accepted in revised form: 11 May 1999     

Drag on a nanotube in uniform liquid argon flow

In this work, nonequilibrium molecular dynamics (MD) simulations were performed to investigate uniform liquid argon flow past a carbon nanotube. In the simulation, nanotubes were modeled as rigid cylinders of carbon atoms. Both argon-argon and argon-carbon interactions were calculated based on Lennard-Jones potential. Simulated drag coefficients were compared with (i) published empirical equation which was based on experiments conducted with macroscale cylinders and (ii) finite element (FE) analyses based on Navier-Stokes equation for flow past a circular cylinder using the same dimensionless parameters used in MD simulations. Results show that classical continuum mechanics cannot be used to calculate drag on a nanotube. In slow flows, the drag coefficients on a single-walled nanotube calculated from MD simulations were larger than those from the empirical equation or FE analysis. The difference increased as the flow velocity decreased. For higher velocity flows, slippage on the surface of the nanotube was identified which resulted in lower drag coefficient from MD simulation. This explains why the drag coefficient from MD dropped faster than those from the empirical equation or FE simulation as the flow velocity increased. It was also found that the drag forces are almost equal for single- and double-walled nanotubes with the same outer diameter, implying that inner tubes do not interact with fluid molecules.