Nanoparticle Radius Research Articles

Unsteady mixed convective MHD boundary stagnation point nanofluid flow with multi-slip effects, variable wall temperature and porosity phenomenon

This research highlights the physical significance of nanoparticle in magnetohydrodynamics (MHD) stagnation point flow (SPF) over a stretchable surface with porosity effect and boundary slip phenomenon. The nanoliquid and its advanced thermal activity are shown extra auspicious results when the flow is considered over a permeable (porous) medium. In addition, the nanoparticles of radius size play an important role in the thermal performance of nanofluid. In this work, copper is accounted as a nanoparticle and water as a base fluid. Nanomanufacturing, surface engineering, coatings, nanofabrication and tribology are some of the important and special mechanical characteristics of nanoparticles [D. Guo, G. Xie and J. Luo, J. Phys. D, Appl. Phys. 47, 013001 (2014)]. The flow is electrically conducted in the presence of applied magnetic field. Mixed convection, Joule heating and viscous dissipation effects are accounted in the mathematical modeling. Appropriate similarity variables are used to convert the couple governing system of PDEs into ordinary ones and results are computed through bvp4c via shooting concept. From the obtained results, it is divulged that the velocity field increases against higher estimations of unsteady parameter, while it declines versus larger magnetic parameter and radius of nanoparticles. The engineering interest like skin friction and Nusselt number is mathematically calculated and results are computed in a tabular form, and their obtained outcomes show that the magnitude of skin friction rises against unsteadiness parameter and radius of nanoparticles. This study is an extended work of [Verma et al. Chem. Eng. J. Adv. 12, 100366 (2022)] with some extra flow assumptions like MHD, SPF, Joule heating, heat generation/absorption and viscous dissipation. Obtained results are compared with [Grubka and Bobba J. Heat Transf. 107, 248 (1985)], Verma et al. [Chem. Eng. J. Adv. 12, 100366 (2022)] and [Elbashbeshy and Emam Therm. Sci. 15, 477 (2011)] found 100% accuracy with them. The most important result of the conducted study is that the skin friction coefficient immensely augments subject to larger estimations of radius of nanoparticles when permeability of porosity is less.

Finite element study of nanoparticles spacing and radius on dynamics of water fluid subject to microgravity environment

This communication studies the vital role of particles spacing and radius of nanoparticles subject to microgravity environment, an inclined surface, and magnetic field. The varying particles size and spacing in the microgravity environment is taken into consideration. A mathematical formulation that is based on conservation principles is non-dimensionalized by enforcement of similarity transformation yielding a related set of ordinary differential equations (ODEs). The convective non-linearity and coupling, a finite element (FE) discretization, is implemented and run on the Matlab platform. Then computational endeavor is continued to elucidate the impacts of various inputs of radius, the amplitude of modulation, mixed convection, inclination angle, particles spacing, and magnetic parameter. The increasing inter-particles spacing and radius are directly influence to the fluid velocity and inversely influence to the fluid temperature. The growing strength of frequency of oscillation and incline angle leads to a decline in skin friction and heat transfer coefficients, but an opposite trend is reported when the thermal buoyancy parameter is enhanced. These outcomes would be very useful for researchers to control upper space transportation and devices performance.

Significance of Nanoparticle Radius and Gravity Modulation on Dynamics of Nanofluid over Stretched Surface via Finite Element Simulation: The Case of Water-Based Copper Nanoparticles

This communication studies the importance of varying the radius Dp of Copper nanoparticles for microgravity-modulated mixed convection in micropolar nanofluid flux under an inclined surface subject magnetic field and heat source. In the current era, extremely pervasive modernized technical implementations have drawn attention to free convection governed by g-jitter force connected with microgravity. Therefore, fixed inter-spacing of nanoparticles and effects of g-jitter on the inclined surface are taken into consideration. A mathematical formulation based on conservation principles was non-dimensionalized by enforcement of similarity transformation, yielding a related set of ODEs. The convective non-linearity and coupling, an FE discretization, was implemented and executed on the Matlab platform. The numerical process’ credibility was ensured for its acceptable adoption with the defined outcomes. Then, the computational endeavor was continued to elucidate the impacts of various inputs of Dp, the amplitude of modulation ϵ, material parameter β, mixed convection parameter λ, inclination angle γ, and magnetic parameter M. The enlarging size of nanoparticles accelerated the nanofluid flow due to the depreciation of viscosity and receded the fluid temperature by reducing the surface area for heat transportation. The modulated Nusselt number, couple stress, and skin friction coefficient are significantly affected by the variation of Dp, M, β, λ, and ϵ. These results would benefit experts dealing with upper space transportation and materials’ performance, such as the effectualness of chemical catalytic reactors and crystals.

Unsteady convective ferrohydrodynamic flow of MnZnFe2O4/FeCrNbB - EG hybrid nanofluid in a horizontal channel with porous fins and semi-circular heaters

In this study, we investigate the unsteady incompressible flow of ethylene-glycol (EG) based MnZnFe2O4/ FeCrNbB hybrid nanofluid through a horizontal channel. Three semi-circular heaters are mounted on the lower channel wall, whereas four porous fins are mounted on the upper channel wall. The Forchheimer model is utilized to describe convective nanofluid flow within the porous fins. Also, a variable magnetic field is produced by an electrical wire within each heater and induces motion and heat transfer within the hybrid nanofluid. Governing equations associated with the mathematical model are numerically solved via the mixed finite element technique. Using the computed graphical and tabular results, we examine the effects of the magnetic parameter (105≤Mn≤3×106), size of the porous fins (0.2≤hfin≤0.6), heater radius (0.2≤r0≤0.3), and solid volume fractions of MnZnFe2O4 and FeCrNbB nanoparticles (0≤ϕ1≤0.02 and 0≤ϕ2≤0.02) on the flow velocity, streamlines, isotherms, pressure drop, and heat transfer performance in the channel. The main findings of the study are that increasing the magnetic number and volume fractions of MnZnFe2O4 and FeCrNbB nanoparticles, and decreasing the height of the porous fins and size of the heaters, leads to greater convective heat transfer in the channel. Furthermore, the pressure drop is enhanced when each of the aforementioned parameters is increased.

Subnanometer-Resolution Nanoparticle Sensing through the Strong Coupling between Surface Plasmon Polariton Whispering Gallery Resonances and Localized Surface Plasmon

High-resolution nanoparticle sensing is very important, and many schemes have been proposed to achieve this goal. Circular nanocavities in which surface plasmon polariton (SPP) whispering gallery mode (WGM) resonances were excited were designed to sense particles of ultra-small size and with high resolution. Localized surface plasmon resonances (LSPRs) were excited when a metal particle was set in the circular cavity. The SPP WGM split into symmetric mode (SM) and antisymmetric mode (ASM) due to the LSPRs scattering into the SPPs. The strong coupling between SM resonance and LSPRs generated positive and opposite modes, which were sensitive to the variation in nanoparticle size and position. Even a small nanometer-sized metal particle introduced LSPRs and produced mode splitting. The WGM mode splitting induced by LSPRs reduced the sensing limit. The simulation results show that 1 nm changes in nanoparticle radius and position led to SM 11.8 nm and 10.2 nm wavelength shifts, respectively. This means that variations of 0.09 nm in size and 0.1 nm in position can be sensed with a 1 nm spectral resolution. The strong coupling between SPP WGM and LSPRs can be applied to sense at a subnanometer resolution.

Patterning of Polymer-Functionalized Nanoparticles with Varied Surface Mobilities of Polymers.

The polymers can be either dynamically tethered to or permanently grafted to the nanoparticle to produce polymer-functionalized nanoparticles. The surface mobility of polymer ligands with one end anchored to the nanoparticle can affect the surface pattern, but the effect remains unclear. Here, we addressed the influence of lateral polymer mobility on surface patterns by performing self-consistent field theory calculations on a modeled polymer-functionalized nanoparticle consisting of immobile and mobile brushes. The results show that except for the radius of nanoparticles and grafting density, the fraction of mobile brushes substantially influences the surface patterning of polymer-functionalized nanoparticles, including striped patterns and patchy patterns with various patches. The number of patches on a nanoparticle increases as the fraction of mobile brushes decreases, favored by the entropy of immobile brushes. Critically, we found that broken symmetry usually occurs in patchy nanoparticles, associated with the balance of enthalpic and entropic effects. The present work provides a fundamental understanding of the dependence of surface patterning on lateral polymer mobility. The work could also guide the preparation of diversified nanopatterns, especially for the asymmetric patchy nanoparticles, enabling the fundamental investigation of the interaction between polymer-functionalized nanoparticles.

Significance of nanoparticle radius and inter-particle spacing toward the radiative water-based alumina nanofluid flow over a rotating disk

Abstract The study of nanofluid flow over a rotating disk has significant importance because of its enormous range of implementations, including cancer treatments, chemotherapy, nanomedicines, fermentation sciences, selective drug delivery, food sciences, biosensors, biomedicines, and electronics. Due to these applications of nanofluid, the present problem investigates the magnetohydrodynamic flow of nanofluid with nonlinear thermal radiation and viscous dissipation. In this analysis, the aluminum oxide nanoparticles are mixed with water. Furthermore, the mechanism for inter-particle spacing and radius of aluminum oxide nanoparticles on the dynamics of the two-dimensional flow of nanofluid are investigated. The present problem is modeled in the form of partial differential equations (PDEs), and these PDEs are converted into ordinary differential equations with the help of suitable similarity transformations. The analytical solution to the current modeled problem has been obtained by using the homotopy analysis technique. The main purpose of the present research work is to analyze the behavior of the velocity and temperature of the nanofluid for small and large radius of the aluminum oxide nanoparticles and inter-particle spacing. Also, the role of heat transport is computed for linear and nonlinear thermal radiation cases. The major findings and principal results of this investigation are concluded that the primary velocity of nanoliquid is augmented due to the intensification in suction parameter for both the small and larger radius of aluminum oxide nanoparticles. Furthermore, it is perceived that the heat rate transfer is larger when the Eckert number and nanoparticle volume fraction are higher for both nonlinear and linear thermal radiation cases.

STUDY OF VARYING CONCENTRATION AND SIZE OF NANOPARTICLES IN A CATHETERIZED ARTERY WITH CLOT AND STENOSIS

This mathematical study comprising of a catheterized artery with clot and stenosis is conducted to highlight the usage of nanoparticles in treatment of thrombosis. Catheter coated with silver nanoparticles is inserted in the lumen of artery having clot and stenosis. The behavior of blood with nanoparticles is described using nanofluid. Navier-Stokes equation and diffusion equation for temperature as well as concentration are used to model the flow problem. Our prime intention is to study how concentration and nanoparticle size effect nanofluid flow considering the influence of various thermal features like thermal conductivity, specific heat capacity and thermal expansion. Solution has been obtained for concentration, temperature and velocity is obtained using finite difference method. The effects of radius of nanoparticle, Brownian motion parameter, stenosis depth, Grashof number and Darcy number have been examined graphically using MATLAB. It has been concluded that nanoparticles highly concentrate on the clot and stenosis and thus point to possible signicant use of nanoparticles in antithrombotic therapy. This model can be, thus, utilized in thrombolytic therapies by proper optimization of concentration of nanoparticles as well as their geometries.

Multiscale bridging method to characterize elasto-plastic properties of polymer nanocomposites

A multiscale bridging method is proposed to describe the elasto-plastic behavior of polymer nanocomposites affected with the interphase elasto-plastic constitutive law (near the nanoparticle). The inverse characterization method of the interphase elasto–plastic constitutive law was proposed by combining full atomistic molecular dynamics and finite element homogenization. Based on the proposed multiscale bridging method, the influences of the crosslink ratio of the epoxy network and radius of nanoparticles on the elasto-plastic behavior of the interphase were investigated. Additionally, a multiscale homogenization analysis of the representative volume element of the multi-particulate systems was conducted using the elasto–plastic constitutive law of interphase.

Depletion Interactions between Nanoparticles: The Effect of the Polymeric Depletant Stiffness.

A Density Functional Theory is employed to study depletion interactions between nanoparticles mediated by semiflexible polymers. The four key parameters are the chain contour length and the persistence length of the polymeric depletant, its radius of gyration, and the nanoparticle radius. In the Density Functional Theory calculation of the depletion interaction between the nanoparticles mediated by semiflexible polymers, the polymer gyration radius is kept constant by varying the contour length and the persistence length simultaneously. This makes it possible to study the effect of the chain stiffness on the depletion potential of mean force between the nanoparticles for a given depletant size. It is found that the depletion attraction becomes stronger for stiffer polymer chains and larger colloids. The depletion potential of mean force is used as input to compute the phase diagram for an effective one-component colloidal system.

Molecular dynamics simulation of thermal behavior of nanofluid flow in a nanochannel with Cetryltrimethylammoniu Bromide surfactant molecules

The poor heat transfer properties of the base fluid are the first effective obstacle to improving heat exchangers' efficiency. The key point of using very high conductivity of solid particles (in nanometer dimension) is hundreds of times more than common fluids in heat transfer in the composition of these fluids. Therefore, adding nanoparticles (NPs) to base fluids has been a solution to increase the heat transfer (HT) properties of common energy-carrying fluids. On the other hand, adding surfactants prevents the sedimentation and instability of NPs and improves the thermal performance of nanofluids (NF). So, this study surveyed the thermal properties of water-copper NF with/without surfactant molecules in a rectangular nanochannel using molecular dynamics (MD) simulation. Cetryltrimethylammoniu Bromide (CTAB) molecules were used as surfactants, copper structure as NPs, and water molecules as a base fluid in this simulation. In the present study, the effect of nanochannel wall temperature, copper nanoparticle (NP) size, and force field type (DREIDING, Universal Force-Field (UFF), and CHARM) on thermal conductivity (Knf) of water-copper NF were studied. The results show that as the wall temperature decreased from 80 to 30 K, Knf decreased from 0.783 to 0.753 Wm-1K−1. On the other hand, by increasing the radius of NPs from 0.5 to 2 nm, Knf and heat flux (HF) increase from 0.77 to 0.798 Wm-1K−1 and 5734 to 6352 W.m−2, respectively. One of the important purposes of researchers and engineers in various industries is to increase efficiency and reduce the systems' size. Therefore, it is expected that the results of this study will be effective in many different thermal industries.

Flexible and Transparent Ceramic Nanocomposite for Laboratory X-ray Imaging of Micrometer Resolution.

Transparent nanocomposites have attracted considerable attention in many areas including X-ray imaging, wearable electronics, and volumetric display. However, both the transparency and the flexibility were largely jeopardized by the loading content of functional nanoparticles (NPs), posing a major challenge to material engineering. Herein, an ultra-high-loading-ceramic nanocomposite film was fabricated by a blade-coating technique. The film exhibited a high transparency over ∼89% in the whole visible region even with a fluoride-ceramic content up to ∼83 wt %. Based on a real-time investigation on the formation process of the film, the refractive-index difference between the nanoparticles and matrix was identified as the dominating factor to transparency. The transmittance spectra based on Rayleigh scattering theory were simulated to screen both nanoparticle radius and loading content, leading to the discovery of a transparency zone for film making. As a proof-of-concept experiment, the transparent film was used as an X-ray scintillation screen, which exhibited a comparable light yield to that of LYSO owing to the mitigated self-absorption effect. The homemade imager demonstrated a spatial resolution of 122 lp/mm, representing a record resolution of 4.1 μm for laboratory X-ray photography. Our work not only provided an experimental procedure to make high-loading functional films but also demonstrated a theoretical model to guide the search for gradients of transparent composites.

Shear induced fractionalized dispersion during Magnetic Drug Targeting in a permeable microvessel

Solute dispersion is a significant phenomenon during drug targeting to estimate the accumulation of drug particles at the tumour region with the capture efficiency. In this present study, we aim to predict the effective dispersion and saturated concentration of drug carriers during magnetic drug targeting in a microvessel with a time fractional derivative based dispersion model. The magnetic nanoparticles are bound with the non-magnetic materials/microgels with the therapeutic agents to prepare the drug carriers. A magnetic field is created outside the body to control and accelerate the trajectories of the drug carriers. The nature of the blood flow into the vessel is considered as Casson fluid. The velocity of the drug carriers is solved analytically, while the fractional-order dispersion equation is computed numerically using the finite difference technique with the forward time and central space discretization. The influence of fractional-order parameter and model biological parameters such as rheological parameter, permeability parameter related to hydraulic conductivity, magnetization, volume fraction of nanoparticles, tumour-magnet distance, nanoparticle radius, drug elimination, and source term on the relative effective dispersion are discussed. The outcomes showed that both rheological parameters and volume fraction increase drug carrier particle concentration, and that saturating occurs at a later time as they increase. Higher magnetization, permeability parameter related to the hydraulic conductivity, and source term are associated with faster transportation of drug carriers to the tumour site. In addition, we note that by using small particle sizes, a high concentration of the drug-coated nanoparticles will be expected in the tumour area, and this slows the rate at which it reaches the saturation point.

Investigation of phase change and heat transfer in water/copper oxide nanofluid enclosed in a cylindrical tank with porous medium: A molecular dynamics approach

In this study, the thermal behavior of atomic structures has been studied by examining factors as adding nanoparticles (NPs), increasing the radius of NPs and the atomic percentage of copper oxide (CuO) NPs, heat flux and temperature difference in simulated samples. First, the equilibrium of atomic samples has been examined by examining the physical quantities of total energy, potential energy, kinetic energy, and temperature. Second, to investigate thermal behavior of atomic structures, the physical quantities of the thermal conductivity coefficient (TCC) and phase change duration (PCD) were calculated. The obtained outcomes proved by adding NPs, increasing radius of NPs and their atomic percentage, the TCC increases and PCD in the structures decreases. Addition of copper oxide NPs into the basefluid leads to an increase in atomic mobility in the structure and the amount of heat transfer (HT) in the structures increases. This increase causes more oscillation range in the structures and as a result more effective HT of nanofluid as well as phase change in atomic samples. Examining the heat flux shows that its excessive increase leads to a decrease in the duration of NPs clumping.

Fractal flow model for cluster interfacial nanolayer of magnetized metallic oxides nanomaterials

In this paper, we investigate the novel properties of the cluster interfacial nanolayer theory for a thermal conductivity-based model. Under the influence of magnetohydrodynamics, the interaction of nanomaterials aggregation of metallic oxide nanomaterials with base fluid is explored. This paper discusses a specific form of new low permeability Reynolds number connected with an injection/suction factor related to an absorbent channel. A numerical simulation of higher-order nonlinear differential equations reveals the momentum flow and energy fields predicted by single-phase nanofluid simulations. Shear stress and Nusselt numbers were used to determine the effect of nanoparticle radius and diameter. Insertion of the metallic nanoparticles volume fraction level from 1% to 8% enhances the thermal performance at lower and upper porous walls respectively. Injection/suction and MHD have to decrease and increase behavior respectively in the presence of spherical nanoparticles. Interfacial nanolayer formation has a substantial impact on thermal conductivity performance. Comparing calculated findings to published literature validates their correctness. Graphs are generated to analyze the impact of flow parameters on velocity and temperature profiles. In tabular and graphical style, the effects of all physical factors are explored on the skin friction coefficient and the local Nusselt number.

Dynamics of Polymer Chains in Poly(ethylene oxide)/Silica Nanocomposites via a Combined Computational and Experimental Approach.

The dynamics of polymer chains in poly(ethylene oxide)/silica (PEO/SiO2) nanoparticle nanohybrids have been investigated via a combined computational and experimental approach involving atomistic molecular dynamics simulations and dielectric relaxation spectroscopy (DRS) measurements. The complementarity of the approaches allows us to study systems with different polymer molecular weights, nanoparticle radii, and compositions across a broad range of temperatures. We study the effects of spatial confinement, which is induced by the nanoparticles, and chain adsorption on the polymer's structure and dynamics. The investigation of the static properties of the nanocomposites via detailed atomistic simulations revealed a heterogeneous polymer density layer at the vicinity of the PEO/SiO2 interface that exhibited an intense maximum close to the inorganic surface, whereas the bulk density was reached for distances ∼1-1.2 nm away from the nanoparticle. For small volume fractions of nanoparticles, the polymer dynamics, probed by the atomistic simulations of low-molecular-weight chains at high temperatures, are consistent with the presence of a thin adsorbed layer that exhibits slow dynamics, with the dynamics far away from the nanoparticle being similar to those in the bulk. However, for high volume fractions of nanoparticles (strong confinement), the dynamics of all polymer chains were predicted slower than that in the bulk. On the other hand, similar dynamics were found experimentally for both the local β-process and the segmental dynamics for high-molecular-weight systems measured at temperatures below the melting temperature of the polymer, which were probed by DRS. These differences can be attributed to various parameters, including systems of different molecular weights and nanoparticle states of dispersion, the different temperature range studied by the different methods, the potential presence of a reduced-mobility PEO/SiO2 interfacial layer that does not contribute to the dielectric spectrum, and the presence of amorphous-crystalline interfaces in the experimental samples that may lead to a different dynamical behaviors of the PEO chains.

Thermal analytical model of size reduction (fragmentation) of colloidal metal nanoparticles by short laser pulses

Theoretical investigations and estimations of significant size reduction of the metal spherical nanoparticles by the laser pulses in a liquid medium have been carried out. Thermal analytical model has been developed for this purpose. The conservation energy law is used for the estimations of the threshold laser fluencies leading to the nanoparticle size reduction. The analytical dependencies of threshold fluencies on pulse durations, laser wavelengths and nanoparticle radii have been established and discussed for nanosecond and picosecond laser pulses. Comparison of some predicted values of the threshold laser parameters for the wavelength 532 nm for size reduction of gold spherical nanoparticle in water with the experimental data is given and satisfactory agreement of these results validates the model developed. These model and results can be used for the investigation of the thermal processes of the nanoparticle processing and the applications in various laser technologies.

The numerical simulation of nanoparticle size and thermal radiation with the magnetic field effect based on tangent hyperbolic nanofluid flow

Tiny particles have extraordinary thermal conductivity due to their unusual characteristics, making them crucial in materials science, nanotechnology, heat exchangers, and electronics. When there is the inclusion of thermal radiation, a heat source, and a convective boundary, magnetohydrodynamic (MHD) micropolar, tangent hyperbolic flow for water-based Al2O3 nanofluid over a stretching sheet, this work intends to investigate the significance of a nanoparticle's radius. The mathematically described ordinary differential system is created by transforming a set of partial differential equations via similarity transformations. The bvp4c approach is used to solve the problem numerically (MATLAB built-in function). In this comprehensive study, the main objective is to improve heat transformation under the impact of various parameters. The velocity profiles, temperature distribution, micro-rotation distribution, and the local skin friction factor, along with the rate of heat transfer, have been displayed with several physical parameters. It is observed that the variation in velocity and the temperature profiles is the cause of increasing the size of the nanoparticles and the involving parameters that caused an increase in the rate of heat transfer. Graphs and tables have then been used to demonstrate the consequences of these physical parameters. The enhancement in the radius of nanoparticles causes a decrease in the skin friction factor, thermal layer, and micro-rotation. As the Biot number increased, the thermal layer became thicker. The impact of influential parameters on physical quantities is illustrated using three-dimensional graphs.

The Dynamics of Water-Based Nanofluid Subject to the Nanoparticle’s Radius with a Significant Magnetic Field: The Case of Rotating Micropolar Fluid

This article investigates the significance of varying radius of copper nanoparticles for non-Newtonian nanofluid flow due to an extending sheet in the presence of a magnetic field and porous medium. The modern technological applications of non-Newtonian nanofluids have attracted researchers in the current era. So, the impacts of the radius of nanoparticles with micropolar fluid have been taken into consideration. Three-dimensional leading equations (PDEs) for momentum, concentration, and temperature are transformed into ODEs by applying the appropriate similarity transformation. The numerical approach bvp4c is applied to obtain the problem’s solution numerically. The influence of the nanoparticles’ radius and various physical parameters on the microrotation, velocity, and temperature profile are analyzed. The velocity profile decreases against the magnetic field (M), rotational parameter (Γ), and Forchheimer number (Fr), but the temperature distribution has increasing behavior for these parameters, and the microrotation is augmented for rising inputs of the magnetic parameter and boundary parameter (β). It is also observed that the temperature reduces against the material parameter (∇) and Forchheimer number (Fr). The skin friction coefficients and Nusselt number decrease against the growing strength of the Forchheimer number (Fr). At the stretching surface, the skin friction factor and Nusselt number are numerically and graphically calculated.

Spatial and temporal characteristics of a four-wave radiation converter with due regard for Earth's gravity field acting on nanoparticles dissolved in a transparent liquid

A theoretical analysis of the dynamics of the spatial spectrum of the object wave in a degenerate four-wave mixing in a transparent solution of nanoparticles in the classical scheme with counterpropagating pump waves is carried out. It is shown that when pump waves propagate orthogonally to the gravity force, a dip arises in the modulus of the spatial spectrum of the object wave, with its half-width nonmonotonically decreasing over time and increasing in the direction of gravity force with increasing radius of the nanoparticles. There is an optimal time over which the half-width of the dip in the direction of the gravity force reaches the lowest value. This time decreases monotonically with increasing nanoparticle radius, as well as with a decrease in the solution thickness.