Wall Drag Effect Research Articles

Study on wall-slipping mechanism of nano-injection polymer under the constant temperature fields

Abstract Polyphenylene sulfide (PPS) and copper (Cu) were used as the polymer and substrate material to simulate the nano-injection molding process by molecular dynamics method. The results show that the PPS chain obeys Einstein’s diffusion law in the early stage of injection molding then deviates from it in the late stage due to the entanglement and limitation of surrounding nanoparticles. In addition, the process of conformational isomerization of polymer chains is accompanied by the twisting and stretching of fixed chains. There are two kinds of adhesion phenomena, one is the macromolecular slides violently in small areas of some sure nanoscale groove to form multiple anchor points. The other case involves multiple nano-grooves along the metal interface, the polymer chain slides and is bolted as multiple anchors in different grooves due to the exerted wall-drag effect on the neighboring chains. These two slipping and anchoring mechanisms are consistent with de Gennes’ slipping theory. Through the quantitative analysis of the influence of pressure on injection filling, it is found that injection pressure should be kept within a certain range to achieve the positive effect of molding.

Direct observation of submicron Brownian particles at a solid–liquid interface by extremely low coherence dynamic light scattering

The Brownian motion of colloidal particles reduces markedly at a distance of approximately 5 times the particle radius from a solid–liquid interface. This wall-drag effect becomes more prominent for smaller particles. An extremely low coherence dynamic light scattering technique with a supercontinuum source is used to directly observe it. The marked reduction of the diffusion close to the interface can be successfully observed owing to the short temporal coherence length, and the variation of the diffusion coefficient from the region of the constrained diffusion to that of free diffusion can be seamlessly carried out by the path-length-resolved operation.

External mass transfer and hindered diffusion of organic compounds in the adsorption on activated carbon cloth

The overall rate of adsorption of organic compounds on activated carbon cloth (ACC) was interpreted with a diffusional model which takes into account external mass transfer and intrafiber diffusion. It was assumed that the intrafiber diffusion was solely due to pore volume diffusion (Fick diffusion). The effect of molecular size of the organic compounds on the overall rate of adsorption was studied using pyridine (0.49nm), phenol (0.53nm), naphthalenesulfonic acid (NAS) (0.85nm), pentachlorophenol (PCP) (0.87nm) and methylene blue (MB) (1.03nm). The experimental concentration decay data were obtained in a differential column batch adsorber. The overall adsorption rate of pyridine and phenol was controlled by the external mass transfer whereas the intrafiber diffusion was the controlling mechanism in the adsorption rate of NSA, PCP and MB. Additionally, the intrafiber diffusion of NSA, PCP and MB was substantially reduced by hindered diffusion, which was due to steric exclusion, wall drag effects and obstruction caused by the molecules adsorbed on the pore walls. The controlling mechanism in the adsorption rate on ACC is a function of the molecular size of the organic compound.

Hydrodynamic measurement of Brownian particles at a liquid-solid interface by low-coherence dynamic light scattering

The hydrodynamics of Brownian particles close to a wall is investigated using low-coherence dynamic light scattering. The diffusion coefficient of the particles in a suspension is measured as a function of distance from the wall. A sudden reduction in the diffusion coefficient near the interface is clearly observed using this method. The theoretically predicted wall-drag effect is experimentally confirmed when the influence of the spatial resolution due to the finite coherence length of the light source is accounted for. The space-dependent dynamics of Brownian particles under the wall-drag effect is obtained for the first time using our spatially resolved dynamic light scattering technique.

Colloidal dynamics near a wall studied by evanescent wave light scattering: Experimental and theoretical improvements and methodological limitations

The dynamics of colloidal spheres near to a wall is studied with an evanescent wave scattering setup that allows for an independent variation of the components of the scattering wave vector normal and parallel to the wall. The correlation functions obtained with this novel instrumentation are interpreted on the basis of an expression for their short time behavior that includes hydrodynamic interactions between the colloidal spheres and the wall. The combination of the evanescent wave scattering setup and the exact expression for the short time behavior of correlation functions allows for an unambiguous measurement of the particle mobility parallel and normal to the wall by means of light scattering. It is possible to measure the viscous wall drag effect on the dynamics of particles with radii as small as 27 nm, where, however, the method reaches its limits due to the low scattering intensities of such small particles.

Anisotropy of Brownian motion caused only by hydrodynamic interaction with a wall

The diffusivity of spherical colloidal particles close to a planar hard wall is studied by dynamic light scattering with evanescent illumination. A novel setup allows us to independently vary the scattering vector components parallel Q parallel and normal Q perpendicular to the wall. An expression for the initial decay rate Gamma of the time autocorrelation functions is derived as a function of both Q parallel and Q perpendicular, as well as the penetration depth of the evanescent wave, where hydrodynamic interactions of particles with the wall are included. This makes it possible to study the viscous wall drag effect quantitatively for particles as small as 85 nm in radius.

A high-temperature and -pressure microscope cell to observe colloidal behaviors in subcritical and supercritical water: Brownian motion of colloids near a wall

A high-temperature and -pressure cell for in situ optical microscopy was constructed, and used to study behavior of polystyrene latex ( d = 2.092 μm) in water at temperatures between 298 and 573 K at constant pressure of 24.6 MPa. Measured diffusion coefficients of the latex near the quartz surface were smaller than those predicted by Stokes–Einstein equation, and the deviation became larger as temperature was raised. Analysis considering the wall drag effect revealed that the colloids get closer to the wall as temperature is increased. This was ascribed to reduction of buoyant force due to decrease of water density at high temperatures (from 1008 kg/m 3 at 298 K to 742.7 kg/m 3 at 573 K at 24.6 MPa).

Mathematical analysis of coaxial disk cellular shear loading devices

Coaxial disk devices are widely used at low Reynolds numbers to simulate cellular shear loading. Here, we develop a mathematical theory for analyzing fluid behavior in these instruments. It improves upon classical results by accounting for both unsteady dynamics and wall drag effects. All previous models are shown to be special cases of the present one. Most devices utilize a low aspect ratio, for which we find wall effects to be limited to small regions near the periphery. In these cases, classical theory yields acceptable precision over most of the domain. Investigators commonly simulate pulsatile effects using low-frequency sinusoidal forcing. Results indicate that fluid motion remains essentially harmonic, permitting the exact solution to be approximated by a simple separable expression. This approximation should be useful in analyzing specific configurations. A wavelike flow mode conjectured to exist at high Strouhal numbers is also discussed.

Tracking a colloidal particle for the measurement of dynamic entropies

The paper describes the apparatus and measurement procedure for tracking long time trajectories of a single colloidal particle undergoing Brownian motion in water. The bulk motion obeys the Einstein–Stokes formulation, while sedimented motion is slowed by an additional drag known as the wall-drag effect. The sedimented particle trajectory is long enough to show diffusive motion spanning four decades in time. We describe the sample preparation, tracking routine, data-acquisition and noise. The experiment shows that Brownian motion exhibits a positive dynamic entropy consistent with microscopic chaos. The theoretical relevance of the experimental results is discussed.

Direct measurements of constrained brownian motion of an isolated sphere between two walls

We report the results of direct measurements, using video microscopy in combination with optical tweezers, of constrained diffusion of an isolated uncharged PMMA sphere in a density-matched fluid confined between two parallel flat walls. Our experimental methodology allows us to study the hindered diffusion of the sphere as an explicit function of its distance from the walls, without interference from sedimentation or from electrostatic interaction between the particle and the walls. The measured diffusion coefficients are used to test the predictions of the wall drag effect predicted by several approximate theoretical analyses. We find a quantitative agreement with the behavior predicted using a hydrodynamic analysis that independently superimposes the wall drag effects arising from each wall. Our results imply, indirectly, that neglect of multiple interactions with the colloid sphere of the perturbations of the pressure and velocity fields induced by each wall leads to an underestimate of the influence of the wall on the drag force experienced by the particle.

Diffusion of an isolated colloidal sphere confined between flat plates

Constrained diffusion of an isolated uncharged PMMA sphere (∼1 μm diameter) confined between two parallel flat walls was studied using video microscopy in combination with optical tweezers. This technique allows us to measure directly the hindered diffusive motion of the sphere as an explicit function of the distance of the sphere from a wall without interference of electrostatic interaction between the sphere and the walls, nor interference from sedimentation. The measured diffusion coefficients are used to test the predictions of the wall drag effect predicted by several approximate theoretical analyses. We find quantitative agreement with the behavior predicted using a hydrodynamic analysis that independently superposes the wall drag effects arising from each wall.

Wall-drag effect on diffusion of colloidal particles near surfaces: A photon correlation study.

The reduction of the diffusion coefficient of latex spheres near glass surfaces was measured by photon correlation spectroscopy. Theory and experiment are not in agreement; possible causes for the discrepancy are discussed. In addition, the diffusion coefficient of sedimented latex spheres on a glass surface decreases with decreasing Debye length of the solution. This shows that the mean particle-surface separation distance decreases as the strength of the double-layer repulsion between the latex spheres and the glass surface is weakened. The utility of photon correlation spectroscopy for studies of interactions between colloidal particles and surfaces is discussed.

SOLUTE REJECTION IN THE ULTRAFILTRATION OF POLYDISPERSE ORGANICS FROM NATURAL PRODUCTS

Abstract Solute rejection in the ultrafiltration of solutions containing polydisperse solutes was modeled using a spherical solute/cylindrical capillary model, accounting for steric hindrance and wall drag effects. A power law relationship was used for the solute radius-molecular weight relationship. The three parameters in the nondimensional model are the ratio of mean pore radius/solute radius coefficient, the exponent in the solute radius versus molecular weight relationship, and the standard deviation of the logarithms of the pore diameters. Values of the parameters, obtained by fitting the model to rejection coefficient data for solutions containing dissolved organics from wood, were self-consistent and made physical sense. The model provides a useful tool for evaluating ultrafiltration membranes for specific solute fractionation applications.

The diffusive conductance of slits between endothelial cells in muscle capillaries

A computerized random-walk method was developed to simulate three-dimensional diffusion through intercellular slits in capillary walls. This method was employed to analyze a population of 25 such slits in the dog gastrocnemius. Each slit consisted of three distinct segments, whose dimensions were obtained from Casley-Smith et al. [(1975) Microvasc. Res. 10, 43–64]. From the computer simulations a diffusive conductance factor ( G D ) was calculated for each slit segment and for each complete slit. By using the Faxén formula for the wall drag effect, the analysis was extended to spherical solute molecules with diameters up to 30 Å. For any solute within this range, the logarithm of the slit conductance was found to display an approximately normal distribution. For molecules of zero diameter, the coefficient of variation of the slit conductance was 0.34. These three-dimensional estimates of slit conductance and resistance were compared with one-dimensional approximations computed by the method of Perl (1971). In this set of slits, the 1-D method yielded a mean slit resistance that was 60% too high and a mean slit conductance that was 22% too low. An approximate concordance between experimental [Pappenheimer et al., (1951) Amer. J. Physiol. 167, 13–46] and theoretical (3-D conductance) values of the capillary diffusion capacity supports the hypothesis that small hydrophilic solutes traverse muscle capillary walls by restricted diffusion through water-filled slits between endothelial cells.

Wall Drag On Free-Moving Ciliated Micro-Organisms

ABSTRACT It is generally assumed that wall drag on free-moving, self-propelled or passively moving micro-organisms is not significant under normal observation conditions. Yet the point at which such drag becomes significant has not been determined quantitatively. By comparing the relative velocities of sinking as well as swimming ciliates in tubes of various bore widths it has been determined that wall drag on sinking cells is about 8 % significant at 10–132 body radii (or minor semi-axes) from the cell surface while the corresponding range for swimming cells is less than 1–4·2 body radii. These results are compared with the mathematical approximations for Stokes radius Rs and depth of penetration of diffusing vorticity δ which characterize steady and quasi-steady Stokes flow respectively around a solid body. It is found that the asymptotic nature of the velocity profile of steady flow is reflected in the lack of agreement between Rs and the measured distance for 8 % drag. Conversely, the sharp gradient (or propulsive envelope) of the quasi-steady velocity profile is reflected in the substantial agreement between 8 and the measured distance for > 0 % drag. It is suggested that the given formula for 8 which includes allowance for a propagated wave is a valid measure of the thickness of the quasi-steady region and that observations on motile ciliates be restricted to organisms at least 4 cell radii from the nearest wall if measurements free of wall-drag effects are to be obtained.