Non-interacting Spherical Particles Research Articles

Numerical study of the Poynting vector effect on periodically forced neutrally buoyant spherical particles at low Reynolds numbers — dynamics and rheology

In this paper, the effect of the Poynting vector force field on periodically forced neutrally buoyant spherical particles at low Reynolds numbers is studied numerically. The mathematical formulation of six nonlinear coupled integro–differential equations was obtained by modifying the Lovalenti and Brady formalism for the hydrodynamic force acting on a spherical particle. The governing equations were solved using an adaptive step size Runge–Kutta method by integrating the integral using the trapezoidal rule. The forces acting on the particle-provided phase space trajectories are similar to Jeffery’s orbits. The paper also discusses the possible outcomes of the rheology due to the Poynting vector on the periodically forced neutrally buoyant sparsely spaced non-interacting spherical particles in a fluid at low Reynolds numbers. The computed rheological parameters in this study are first normal stress difference, second normal stress difference, intrinsic pressure and relative viscosity. The study shows that the first normal stress difference is nearly zero and the second normal stress difference is nonzero indicating the dominance of the Poynting vector field over the magnetic field on the bulk stress of the fluid. The intrinsic pressure and the relative viscosity changed due to the stress caused by the electromagnetic force and periodic force on the spherical particles.

Estimation and fingerprinting of the size distribution of non-interacting spherical particles from small-angle scattering data

A new method to estimate the size distribution of non-interacting colloidal particles from small-angle scattering data is presented. The method demonstrates that the distribution can be efficiently retrieved through features of the scattering data when plotted in the Porod representation, thus avoiding the standard fitting procedure of nonlinear least squares. The present approach is elaborated using log-normal and Weibull distributions. The method can differentiate whether the distribution actually follows the functionality of either of these two distributions, unlike the standard fitting procedure which requires a prior assumption of the functionality of the distribution. After validation with various simulated scattering profiles, the formalism is used to estimate the size distribution from experimental small-angle X-ray scattering data from two different dilute dispersions of silica. At present the method is limited to monomodal distributions of dilute spherical particles only.

Raman amplification in the ultra-small limit of Ag nanoparticles on SiO2 and graphene: Size and inter-particle distance effects

Size, shape and hot spots are crucial to optimize Raman amplification from metallic nanoparticle (NPs). The amplification from radius = 1.8 ± 0.4 nm ultra-small silver NPs was explored. Increasing NP density redshifts and widens their plasmon that, according to simulations for NPs arrays, is originated by the reduction of the interparticle distance, d, becoming remarkable for d ≤ R. Inter-particle interaction red-shifts (>130 nm) and widens (>90 nm) the standard plasmon of non-interacting spherical particles. Graphene partly delocalizes the carriers enhancing the NIR spectral weight. Raman amplification of graphene phonons is moderate and depends smoothly on d while that of Rhodamine 6G (R6G) varies almost exponentially due to their location at hot-spots that depend strongly on d. The experimental correlation between amplification and plasmon position is well reproduced by simulations. The amplification originated by the ultra-small NPs is compared to that of larger particles, granular silver films with 7 < R < 15 nm grains, with similar extinction values. The amplification is found to be larger for the 1.8 nm NPs due to the higher surface/volume ration that allows higher density of hot spots. It is demonstrated that Raman amplification can be efficiently increased by depositing low density layers of ultra-small NPs on top of granular films.

Minimization of Hemolysis and Improvement of the Hydrodynamic Efficiency of a Circulatory Support Pump by Optimizing the Pump Flowpath

The present study focuses on the development of methods for design calculation and optimization of the circulatory support pump flowpath. The object of this study is the flowpath of an axial flow pump consisting of a straightener, an impeller, and a diffuser. The working fluid has constant density and viscosity that are close to the physiological parameters of blood of a healthy human. The fluid is considered to be incompressible; the flow is considered steady. Red blood cells in the stream are simulated with non-interacting spherical particles whose trajectories are considered as the trajectories of movement of red blood cells. Equivalent shear stress is calculated at each point of the particle trajectory. The damage parameter is calculated based on the current level of the equivalent shear stress and the time of exposure to shear stress. The criteria of maximum efficiency and minimal hemolysis are used as the optimization criteria. The flowpath is optimized according to these two criteria and local optimum parameters for the suggested initial geometry are determined.

Dynamics of blood flow and thrombus formation in a multi-bypass microfluidic ladder network.

The reaction dynamics of a complex mixture of cells and proteins, such as blood, in branched circulatory networks within the human microvasculature or extravascular therapeutic devices such as extracorporeal oxygenation machine (ECMO) remains ill-defined. In this report we utilize a multi-bypass microfluidics ladder network design with dimensions mimicking venules to study patterns of blood platelet aggregation and fibrin formation under complex shear. Complex blood fluid dynamics within multi-bypass networks under flow were modeled using COMSOL. Red blood cells and platelets were assumed to be non-interacting spherical particles transported by the bulk fluid flow, and convection of the activated coagulation factor II, thrombin, was assumed to be governed by mass transfer. This model served as the basis for predicting formation of local shear rate gradients, stagnation points and recirculation zones as dictated by the bypass geometry. Based on the insights from these models, we were able to predict the patterns of blood clot formation at specific locations in the device. Our experimental data was then used to adjust the model to account for the dynamical presence of thrombus formation in the biorheology of blood flow. The model predictions were then compared to results from experiments using recalcified whole human blood. Microfluidic devices were coated with the extracellular matrix protein, fibrillar collagen, and the initiator of the extrinsic pathway of coagulation, tissue factor. Blood was perfused through the devices at a flow rate of 2 µL/min, translating to physiologically relevant initial shear rates of 300 and 700 s-1 for main channels and bypasses, respectively. Using fluorescent and light microscopy, we observed distinct flow and thrombus formation patterns near channel intersections at bypass points, within recirculation zones and at stagnation points. Findings from this proof-of-principle ladder network model suggest a specific correlation between microvascular geometry and thrombus formation dynamics under shear. This model holds potential for use as an integrative approach to identify regions susceptible to intravascular thrombus formation within the microvasculature as well as extravascular devices such as ECMO.

Origin of particle accumulation structures in liquid bridges: Particle–boundary-interactions versus inertia

The formation of particle-accumulation structures in the flow in a cylindrical liquid bridge driven by the thermocapillary effect is studied with the aim of determining the physical mechanism which forms the structures. The flow is modeled using the incompressible Navier–Stokes and energy equations with the assumption of constant fluid properties except for surface tension, which is assumed to depend linearly on temperature. Different models for the motion of small non-interacting spherical particles at low concentration are employed, taking into account particle inertia due to density differences between fluid and particles and the restricted particle motion near the boundaries of the flow domain. Attention is focused on differences in formation time between particle-accumulation structures arising as a result of inertial effects only, particle–boundary-interaction effects only, and a combination of the two.

Anisotropy of the magnetoviscous effect in a cobalt ferrofluid with strong interparticle interaction

The anisotropy of the magnetoviscous effect (MVE) of a cobalt ferrofluid has been studied in a slit die viscometer for three orientations of the applied magnetic field: in the direction of the fluid flow (Δη1), the velocity gradient (Δη2), and the vorticity (Δη3). The majority of the cobalt particles in the ferrofluid exhibit a strong dipole–dipole interaction, which corresponds to a weighted interaction parameter of λw≈10.6. Thus the particles form extended microstructures inside the fluid which lead to enhanced MVE ratios Δη2/Δη1>3 and Δη3/Δη1>0.3 even for strong shearing and weak magnetic fields compared to fluids which contain non-interacting spherical particles with Δη2/Δη1≈1 and Δη3/Δη1=0. Furthermore, a non-monotonic increase has been observed in the shear thinning behavior of Δη2 for weak magnetic fields <10kA/m, which cannot be explained solely by the magnetization of individual particles and the formation and disintegration of linear particle chains but indicates the presence of heterophase structures.

ISDD: A computational model of particle sedimentation, diffusion and target cell dosimetry for in vitro toxicity studies

BackgroundThe difficulty of directly measuring cellular dose is a significant obstacle to application of target tissue dosimetry for nanoparticle and microparticle toxicity assessment, particularly for in vitro systems. As a consequence, the target tissue paradigm for dosimetry and hazard assessment of nanoparticles has largely been ignored in favor of using metrics of exposure (e.g. μg particle/mL culture medium, particle surface area/mL, particle number/mL). We have developed a computational model of solution particokinetics (sedimentation, diffusion) and dosimetry for non-interacting spherical particles and their agglomerates in monolayer cell culture systems. Particle transport to cells is calculated by simultaneous solution of Stokes Law (sedimentation) and the Stokes-Einstein equation (diffusion).ResultsThe In vitro Sedimentation, Diffusion and Dosimetry model (ISDD) was tested against measured transport rates or cellular doses for multiple sizes of polystyrene spheres (20-1100 nm), 35 nm amorphous silica, and large agglomerates of 30 nm iron oxide particles. Overall, without adjusting any parameters, model predicted cellular doses were in close agreement with the experimental data, differing from as little as 5% to as much as three-fold, but in most cases approximately two-fold, within the limits of the accuracy of the measurement systems. Applying the model, we generalize the effects of particle size, particle density, agglomeration state and agglomerate characteristics on target cell dosimetry in vitro.ConclusionsOur results confirm our hypothesis that for liquid-based in vitro systems, the dose-rates and target cell doses for all particles are not equal; they can vary significantly, in direct contrast to the assumption of dose-equivalency implicit in the use of mass-based media concentrations as metrics of exposure for dose-response assessment. The difference between equivalent nominal media concentration exposures on a μg/mL basis and target cell doses on a particle surface area or number basis can be as high as three to six orders of magnitude. As a consequence, in vitro hazard assessments utilizing mass-based exposure metrics have inherently high errors where particle number or surface areas target cells doses are believed to drive response. The gold standard for particle dosimetry for in vitro nanotoxicology studies should be direct experimental measurement of the cellular content of the studied particle. However, where such measurements are impractical, unfeasible, and before such measurements become common, particle dosimetry models such as ISDD provide a valuable, immediately useful alternative, and eventually, an adjunct to such measurements.

Physicochemical study of aggregation in silver colloids

Characterization of particles in the Carey Lea silver hydrosol [ Amer. J. Sci. 37, 476 (1889)], has been carried out by various techniques (electron microscopy, X-ray diffraction, analytical ultracentrifugation, light scattering, photon correlation spectroscopy). Existence of noninteracting spherical particles (5–6 nm in diameter) in equilibrium with agglomerates (of various size) made up of chained elementary particles has been demonstrated. Physicochemical studies have allowed a description of the surface shell as adsorbed citrate on charged Ag + sites. It has been shown that sol evolution governed by citrate desorption enhances the particle clustering and coalescing phenomena.

Small-Angle X-Ray-Scattering Determination of Diameter Distributions

Test calculations have been carried out to develop a practical method of using small-angle x-ray-scattering data to determine the particle-diameter distribution in polydisperse suspensions of noninteracting spherical particles. A new method has been developed for extrapolating the scattering curve for scattering angles beyond the largest angles at which data can be obtained. This extrapolation technique is shown to be an improvement over an earlier method [J. H. Letcher and P. W. Schmidt, J. Appl. Phys. 37, 649 (1966)] by being less sensitive to uncertainties in the data and to choices of the constants used in the extrapolation.

Small-Angle X-Ray Scattering Determination of Particle-Diameter Distributions in Polydisperse Suspensions of Spherical Particles

A scheme is developed for using small-angle x-ray-scattering data to find the distribution of the particle diameters in dilute colloidal suspensions of noninteracting spherical particles. No assumptions need to be made about the form of the distribution function. An investigation is made of the errors likely to be introduced in the numerical operations on the data. The method was tested on theoretical scattering curves for which the calculations could be done both numerically and analytically. After these tests showed the feasibility of the calculation, diameter distributions were computed from the x-ray small-angle scattering data from some polydisperse colloidal samples composed of spherical particles. The results suggest that this technique may often be a useful procedure for analysis of small-angle x-ray-scattering data.