Simon L. Goren

Thermophoresis of aerosol particles in the laminar boundary layer on a flat plate

Abstract The thermophoresis of aerosol particles in the laminar compressible boundary layer on a flat plate is considered theoretically. The particles are attracted by a plate colder than the gas and the dust concentration drops monotonically as the wall is approached; in the absence of Brownian diffusion a nonzero concentration at the wall is found. The particles are repelled by a plate hotter than the gas and, in the absence of Brownian diffusion, the aerosol concentration profile exhibits a singularity at which the concentration rapidly approaches zero or infinity. The location of this singularity is taken to be the boundary of the dust-free layer found on heated objects.

Measurements of kinetic energy loss for particles impacting surfaces

Incoming and rebounding particle velocities were measured to within several particle diameters of the impaction surface using laser Doppler velocimetry. Impacts occurred normal to the surface and ranged from 1 m/s, near the threshold for particle bounce, to 100 m/s, well into the plastic damage regime. Monodisperse ammonium fluorescein spheres, 2.6–6.9 μm in diameter, impacted target surfaces including polished molybdenum and silicon, cleaved mica, and a fluorocarbon polymer. The incident kinetic energy recovered on rebound depended on particle size and target composition at low velocity (< 20 m/s), where the adhesion surface energy is important. No dependence on target composition was found at higher velocities where up to half of the impact energy was lost to plastic deformation. Plastic deformation was a significant component of energy loss even at impact velocities near critical velocity. Critical velocities for the onset of bounce decreased with a stronger power-law dependence on particle diameter th...

On the hydrodynamic resistance to a particle of a dilute suspension when in the neighbourhood of a large obstacle

A method is presented for estimating the hydrodynamic force acting on a small particle of a dilute suspension when in a slow streaming motion past a large spherical or cylindrical obstacle for the situation when the particle is moving close to the obstacle. If ap and af denote respectively the radius of the particle and the obstacle, it is shown that the force tangential to the obstacle correct to O(ap/af) and the force normal to the obstacle correct to O(aP2/af2) can be evaluated by using a model in which the particle is in flow of semi-infinite fluid bounded by a rigid plane with the undisturbed flow at infinity determined from the first two non-zero terms in the expansion of the slow motion solution for the flow past the obstacle in a power series about the nearest point of the obstacle to the particle. The deviation of particles from undisturbed flow stream line is shown to be insignificant for particle separations from the obstacle exceeding 2 or 3 particle radii. The mechanical action on the sphere in a semi-infinite fluid, bounded by a plane, whose motion is a general second degree slow flow is also determined.

The shape of low-speed capillary jets of Newtonian liquids

The shape of a jet of Newtonian liquid issuing from a capillary needle into air is considered. The results of two theoretical approaches are presented. One approach is a perturbation analysis about the final state of the jet and the other is a boundary-layer analysis near the point of jet formation. Comparison of the predictions with experimental jet shapes shows them to be in semi-quantitative agreement. Especially interesting is the presence of a ‘discontinuity’ in the empirical exponential decay rate of the jet radius occurring at a Reynolds number somewhere between 14 and 20 and the correspondence of this discontinuity with the peculiar behaviour in this range of the Reynolds number of the theoretical eigenvalue.

On free convection in water at 4°C

Abstract The problem of momentum and heat transfer by free convection from a semi-infinite vertical plate to a liquid at its maximum density is analyzed. It is shown that the magnitude of the convective velocities may be much reduced when operating at this density. For water at 4°C the convective velocities are reduced by about 8- and 80-fold from those in water at 20°C for temperature variations of 1°C and 10 −2 °C respectively.

Improving resolution in coulter counting by hydrodynamic focusing

Abstract A simple technique for improving the resolution of closely sized particles in Coulter counting is described. The method consists of feeding the suspension to be measured from a ∼ 30 μ diameter hole positioned 2 to 4 mm from the aperture of the Coulter device. Both tubes are immersed in a bath of particle-free electrolyte. When the electrolyte is sucked through the sensing aperture in the usual way, the stream tube containing the suspension is accelerated and thinned so that the particles all travel essentially the same streamline, and consequently have uniformity of approach and passage through the sensing aperture. The focusing is found to improve significantly the representation of the particle size distribution as judged from measured distributions of Dow latex microspheres which are known to be extremely uniform in size.

Axial diffusion in a cylinder with pulsed flow

Abstract The theory for the rate of mass transfer through a long tube connecting two reservoirs of constant concentration with oscillatory flow in the tube is developed. The increase in transfer rate relative to that due to molecular diffusion alone is found as a function of three dimensionless groups, an oscillatory Reynolds number ωa2/v, an amplitude parameter A/a and the Schmidt number v/D. An experiment on the mass transfer of HCl in water gave rates increased from 10- to 60-fold and is in good agreement with the theory.

Aerosol Capture in Granular Beds in the Impaction Dominated Regime

Single grain capture efficiencies η for high speed gas flow through clean granular beds are reported. The aerosol particles range in diameter Dp from about 0.6 to 4.5 μm; both liquid (dioctyl phthalate) and solid (potassium biphthalate) aerosol particles were used. The grains used were spheres of diameter D G equal to 2 or 4 mm and pea gravel with an effective diameter of 4 mm. The superficial gas velocity U was varied from about 0.1 to 6 m/sec. Impaction is the dominant capture mechanism for these conditions. Consequently, the Stokes number Stk = p p D p2C p U/18μD G is an important dimensionless group for correlation of the data. Because the gas flow field depends on the fraction solids αG in the bed and the grain Reynolds number Re = iD G U/μ, the single grain capture efficiency η also must depend on these two dimensionless groups. For conditions of greatest practical interest, the Stokes number is much less than unity. Theoretical considerations based on creeping flow and boundary layer flow theory su...

The hydrodynamic forces on touching spheres along the line of centers exerted by a shear field

Abstract The flow near two touching spheres of radius a1 and a2 in a general linear flow is considered. It is shown that the force on either sphere along the line of centers (z direction) is determined by that part of the flow field which is of the form V ∞ = Vi z + G{zi z − 1/2w ∼ i w ∼ } . For a uniform shear flow G is simply related to the shear rate and doublet orientation. For a freely suspended doublet, the force along the line of centers is F 2 = 6πμa 1 2 Gh · ( a 1 a 2 ) = −F 2 , where h is a tabulated function. It is hoped the results will find application to the analysis of floc stability at high shear rates.

The shape of a thread of liquid undergoing break-up

Abstract The shape of a cylindrical or annular thread of liquid which is undergoing break-up has been calculated on the assumption that the surface area of the thread is always a minimum for the given constraints. Measured shapes of annular threads are in good agreement with the calculated ones.