Brownian Motion Of Nanoparticles Research Articles

Heat and mass transfer analysis of s-PTT nanofluid in microchannels under combined electroosmotic and pressure-driven flows with wall slip using the homotopy perturbation method

The heat and mass transfer of the electroosmotic flow in microchannel transporting viscoelastic nanofluid is investigated considering Brownian motion of nanoparticles and slip boundary conditions. The simplified Phan-Thien-Tanner model is employed to describe the rheological behavior of fluid and the nonlinear Navier model with non-zero slip critical shear stress is considered at walls. The governing nonlinear momentum, mass, and heat transfer equations are solved using the Homotopy Perturbation Method. The study reveals that increasing the fluid elasticity, nanoparticle concentration, and size significantly enhances the flow rate, heat and mass transfer. Additionally, elasticity and Reynolds number decrease the friction factor. Reducing the double-layer thickness and increasing the Reynolds number lead to higher flow rates and fluid velocities. Notably, the findings emphasize the critical role of the slip conditions on the Sherwood and Nusselt numbers.

Analysis of entropy generation and MHD thermo‐solutal convection flow of Ellis nanofluid through inclined microchannel

AbstractThis study investigates heat, mass transport, and entropy production in Ellis nanofluid flow through an inclined permeable microchannel, considering Navier's slip effects with convective boundary conditions. It incorporates nanoparticle's thermophoresis and Brownian motion effects under a transverse magnetic field, with fluid suction and injection at microchannel walls. Under appropriate physical assumptions, the problem is presented as nonlinear ordinary differential equations, which are later nondimensionalized. The MATLAB bvp4c solver is used for numerical solutions of the transformed equations. Graphical depictions in the study illustrate how various factors influence velocity, temperature, concentration, Bejan number, and entropy generation. Engineering parameters, affected by changes in critical factors, are presented in tabular format, including the skin friction coefficient, Nusselt number, and Sherwood number. Notably, the enhancement in Ellis fluid parameter has a dual effect, enhancing velocity and Bejan number in the microchannel's lower half, while reversing in the upper half. For the increment in Ellis parameter, the impact on Bejan number for 0.5 is significant and the effect on entropy production contrasts with that of Bejan number. This research offers practical insights for designing efficient microfluidic heat exchangers and developing advanced nanofluids for improved thermal performance while minimizing entropy generation. Additionally, it underscores the potential for innovation within the domain of microfluidics and nanomaterial‐driven heat transfer systems. Furthermore, it should be noted that the flow behavior of Ellis nanofluids within microchannels can closely replicate natural flow patterns found in biological systems, offering insights that could have numerous applications in biology and related fields.

Response surface method and finite element-based investigation of uniform/nonuniform hydromagnetic convection of nanofluids inside a quarter-circular enclosure

Under the influence of magnetohydrodynamics (uniform, periodic, and inclined), the current research evaluates the two-dimensional unsteady dynamics of natural convection flow and heat transportation in the quarter-circular domain considering the Brownian motion of nanoparticles. The nonlinear partial differential equations (PDEs) solver finite element method (FEM) of the Galerkin type is used for the numerical simulation. In addition, the central composite design-based response surface methodology (RSM) is applied to analyze the optimization of the outcomes. To assess the models’ significance in learning the optimum thermal transport efficiency of nanofluids, an analysis of variance is performed. The impacts of several physical characteristics such as Rayleigh number, nanoparticles volume fraction, mean Nusselt number, Brownian effects, size, and shape of the nanoparticles, and magnetic effects (uniform, periodic, and inclined) are examined. The heat transfer rate is significantly influenced by the magnetic field’s period and inclined angle. As an illustration, the optimal heat transmission is noted at λ = 0.75 and γ = 0°. When Brownian effects are included, the heat transfer rate increases by 23.44% and it rises by 39.34% as nanoparticle size drops from 100 nm to 10 nm. Moreover, compared to spherical nano-sized particles, blade-shaped nano-sized particles can improve the transportation of heat by 9.56%. Furthermore, the optimization of the independent factors (Ra, Ha, ϕ, and d p) on the response function Nu (average) is demonstrated by the statistical RSM technique, and a novel correlation is proposed based on FEM numerical data. The optimal thermal transport (Nu av = 24.045) is found when Ra = 10, Ha = 0, ϕ = 0.05, and d p = 10 nm. The model’s average Nusselt number’s R 2-value of 0.9927 indicates that the results are effective.

Experimental investigation, modelling, and order of magnitude analysis of oxygen mass transfer in pulsed plate column with α‐Fe2O3 nanofluid

AbstractVolumetric oxygen mass transfer coefficient (kLa) is an important parameter in the design of various reactors and bioreactors. In the present work, the influence of α‐Fe2O3 nanofluid on the enhancement of kLa is studied in a pulsed plate column (PPC). An enhancement factor of greater than one showed that the nanofluid is favourable in enhancing the mass transfer rate. The effect of pulsing velocity on kLa is observed to fall under two regimes: the dispersion regime and emulsion regime. The kLa enhancement factor is found to be higher in TiO2 nanofluid than in α‐Fe2O3 nanofluid, indicating that the type of nanofluid influences the enhancement factor. The order of magnitude analysis showed that localized convection triggered by the Brownian motion of nanoparticles is the phenomenon responsible for kLa enhancement. A dimensionless multiple regression analysis (MRA) model was developed to predict kLa in the nanoparticle loading range of 0.003–0.019 (v/v%), relating the Sherwood number with oscillating Reynolds number (1200 ≤ Reo ≤ 20,000), gas flow Reynolds number (0.135 ≤ Reg ≤0.370), Schmidt number (1300 ≤ Sc ≤2700), and Brownian Reynolds number (2.81 × 10−4 ≤ ReB ≤5 × 10−4). The pseudo‐homogeneous model could accurately predict the enhancement until critical loading conditions.

Hydromagnetic Convective Heat Transfer in a Square Cavity Filled with Fe3O4-Water Nanofluid Saturated Porous Medium

A numerical study is carried out to demonstrate the heat transmission events of nanofluid in a square cavity saturated by aluminum foam porous medium under the effect of slanted periodic magnetic field. The cavity wall is heated from left and cooled from right while horizontal walls are supposed to be adiabatic. The Brownian motion of nanoparticle is taken into consideration in the thermal conductivity model construction. The dimensionless governing equations including Darcy-Brinkman model are solved by Galerkin-FEM. The outcomes are exposed with depictions of streamlines, isotherms and average Nusselt numbers. The numerical investigation is performed for parameters: Darcy number, Rayleigh number, Hartmann number, porosity, leaning angle of the periodic magnetic field, period number, and nanoparticle volume fraction. The heat transfer rate upsurges noticeably for the rise of nanoparticle volume fraction, period number, Darcy number and Rayleigh number but the reverse trend is found for the parameter Hartmann number as well as porosity. From the acquired numerical outcomes, the maximum rate of heat transfer is attained at δ=π/4 when λ = 1. Jagannath University Journal of Science, Volume 10, Number II, Dec. 2023, pp. 145-158

Time-dependent stagnation point flow of nano Casson fluid with Joule heating over an elongated surface subjected to viscous heating and exponential space-based heat source/sink: Boungiorno model

The unsteady two-directional flow of a non-Newtonian magneto-Casson nanoliquid flow over an elongated flat surface with the porous matrix is investigated. The flow is subjected to space-based exponential heat generation/absorption (ESHS), thermophoresis, Brownian motion of nanoparticles, and transverse magnetic field. Within the base fluid, the diffusion of chemically reactive nanoparticles is assumed to be highly significant; hence considered. The governing equations of the flow model admit self-similar equations and are numerically solved by employing the Runge-Kutta-based shooting technique (RKSM). The significance of key parameters on the temperature, velocity, friction factor at the surface, heat transfer rate, and mass transfer rate distributions is analyzed. The use of high-Prandtl number base fluid and nanoparticles of high thermal conductivity could be of practical use to increase the heat transfer rate and avoid nanoparticle accumulation. The occurrence of nanoparticles in the operating liquids reduces the shearing stress at the plate surface to avoid backflow.

Empirical investigation of nanofluid performance in a microchannel heat sink for various attributes in low Reynolds number range

Efficient cooling techniques are imperative and present a significant challenge in the electronics industry due to the increasing miniaturization of devices. Elevated temperatures on the surface of components pose a particular concern within the low Reynolds numbers range due to back axial conduction. The current research endeavours to provide an experimental assessment of cooling efficacy, heat transfer coefficient, thermohydraulic performance and loss in concentration utilizing alumina nanofluids with 1–4 % (w/w) concentration in a microchannel heat sink at low Reynolds numbers (10 ≤ Re ≤ 50). The findings indicate notably, the introduction of nanofluids resulted in a 51.54 % reduction in back axial conduction in the microchannel heat sink compared to base fluid, consequently yielding surface temperatures up to 29 % lower in the microchannel heat sink and a substantial enhancement in heat transfer coefficient and Nusselt number up to 43.34 % and 35.85 %, respectively at Reynold number 50. The optimal thermohydraulic performance was noted to be 1.17 at a 3 % (w/w) nanoparticles concentration and Reynold number 50. Correlations have been devised to predict the Nusselt number and friction factor for the microchannel heat sink based on the corresponding nanofluid concentration. The increase in heat transfer coefficient was elucidated by considering thermophoresis and Brownian motion of nanoparticles in the base fluid. In conclusion, this study affirms the potential of nanofluids in efficiently cooling electronic devices, showcasing superior heat transfer performance at low Reynolds number.

Heterogeneity of nanoparticle deposition micro-structure and modeling deposition layer thickness variation underneath periodically growing single boiling bubbles in nanofluids

Nanoparticle deposition in nanofluid boiling can significantly impact heat transfer efficiency. However, there is still much to be uncovered regarding the heterogeneity of micro-structures in nanoparticle deposition and how to quantitatively model variations in deposition layer thickness. To gain a deeper understanding, we conducted experiments where single boiling bubbles were grown from an artificial micro-cavity in SiO2 nanofluids with varying concentrations and durations under a constant heat flux. Our results reveal that the nanoparticle deposition region increases with concentration and boiling duration. Notably, while the deposition morphology is irregular near the bubble nucleation site, it becomes more uniform further away from the bubble nucleation site. We believe that the heterogeneity in the micro-structure of the deposition layer is due to differences in the evaporation time of the liquid microlayer at different positions, variations in its thickness beneath a single boiling bubble, and dependency of nanoparticles Brownian motion on temperature. Additionally, the thickness of the deposition layer decreases as the distance from the nucleation site increases. To accurately describe this variation in thickness, we have proposed a semi-empirical correlation based on the liquid microlayer evaporation theory and the conservation of mass of nanoparticles beneath a single boiling bubble. The thickness of the nanoparticle deposition layer is determined by the number of growing bubbles, liquid density, initial thickness of the liquid microlayer, local nanoparticle concentration, and local nanoparticle stacking density. This study provides valuable insights into optimizing micro-structures or thickness of the deposition layer, leading to improved nanofluid boiling heat transfer.

Cattaneo–Christov double diffusive non-Newtonian nanofluid flow over a rotating disk of variable thickness influenced by swimming microorganisms and velocity slip condition

This exploration examines the effects of the Cattaneo–Christov double diffusion in the Ostwald-de-Waele nanofluid flow on a rotating disk with varying thicknesses. The incorporation of the impacts of the bioconvection microorganisms increases the stability of the nanofluids. The slip boundary constraint is taken at the disk. The flow system is based on the Buongiorno nanofluid model. The envisioned fluid flow model incorporates heat transmission properties that are affected by nanoparticle volume fraction, Brownian motion, and thermophoresis. The numerical software bvp4c method is affianced. The presented diagrams portray the correlation of the protuberant parameters with the associated profiles given with cogent arguments. It is heeded that higher estimates of the thermal and solutal relaxation parameters dwindled the thermal and mass profiles. Furthermore, the motile microorganism distribution is diminished for larger counts of the Peclet number. A comparison table is also included to justify the truthfulness of the proposed model.

Intelligent computing for MHD radiative Von Kármán Casson nanofluid along Darcy-Fochheimer medium with activation energy

The impact of activation energy in chemical processes, heat radiations, and temperature gradients on non-Darcian steady MHD convective Casson nanofluid flows (NMHD-CCNF) over a radial elongated circular cylinder is investigated in this study. The network of partial differential equations (PDEs) for NMHD-CCNF is developed using the modified Buongiorno framework, and the network of controlling PDEs is then transformed into ordinary differential equations (ODEs) utilizing the Von Karman method. Finally, the resulting non-linear ODEs are computed using the ND-solve approach to produce sets of data to assess the proposed model's skills, which can then be handled using the Bayesian Regularization technique of artificial neural networks (BRT-ANN). A novel stochastic computing-based application is being developed to evaluate the importance of NMHD-CCNF across a spinning disc that is radially stretched. The novelty and significance of results for better understanding, clarity, and highlighting the innovative contributions and significance of the proposed scheme. Further, to check the validity of the defined results for NMHD-CCNF, error charts, validation, and mean squared error suggestions are employed. The impact of multiple physical parameters on concentration, radial and tangential velocities, and temperature profiles is shown via tables and figures. Additionally, the results demonstrate that as the Forchheimer number, Casson nanofluid parameter, magnetic parameter, and porosity parameter are strengthened, the radial and rotational nanofluid mobility drops dramatically. The stretching parameter, on the other hand, has a parallel developmental trend. The heat generation parameter, the thermophoresis process, the thermal radiation parameter, and the Brownian motion of nanoparticles can all be increased to give thermal enhancement. On the other side, with larger estimates in thermophoresis parameters and the activation energy, there is a noticeable increase in the concentration profile.

Bioconvective flow of fourth-grade nanofluid via a stretchable porous surface with microbial activity and activation energy

The current work scrutinizes electro-magnetized mixed convective flow of radiative fourth-grade nanofluid over a stretchable surface with bioconvection mechanism, thermophoretic body force, Brownian motion and activation energy for both nanoparticles (NPs) and motile microorganisms. Also, features of viscous dissipation, fluctuating fluid viscosity, Joule heating, suction/injection, heat source/sink and convective heat-mass-microbial conditions are included in the flow model. By employing suitable dimensionless variables, the set of model equations has been transformed into non-dimensional ordinary differential equations, which are subsequently tackled using quasilinearization-based spectral collocation approach applied in overlapping grids. For different flow parameters, numerical results of flow profiles and quantities of engineering intrigue are discussed. The results reveal that the inclusion of Biot numbers for heat, mass and microbes transfer helps to enhance flow profiles along with quantities of engineering interest. The material parameters enhance the magnitude of velocity, which is also higher for the fourth-grade nanomaterial model. Better heat transfer attributes can be achieved through strong thermophoretic force, thermal radiation, heat generation, viscous dissipation and NP Brownian motion. Activation energy increases NP concentration, while a decreasing trend is notable for higher chemical reaction and NP Brownian diffusion parameters. Bioconvection parameters reduce the motile microbes concentration, while enhancing the rate of motile microbes transfer. Microbial Brownian motion and microbial reaction play a crucial role in the dynamics of microorganisms, and that is confirmed by their noticeable effect on the flow properties.

Effects of Brownian Motions and Fractal Structure of Nanoparticles on Natural Convection

The study simulated heat transfer in alumina-water nanofluid in a natural convection flow and Rayleigh-Benard configuration considering the Brownian motions and fractal structure of the nanofluids. The simulations were based on a two-dimensional, Eulerian-Eulerian method. Many simulations have been performed to examine the effect of aspect ratio, heat flux, and para-meters related to the structure of the nanoclusters including size, fractal dimension, and volume fraction on the natural convective heat transfer coefficient. The comparison between the simulation results and the experimental data of heat transfer coefficient indicates a good agreement. The simulation results indicated that the enhancement of aspect ratio, heat flux, and fractal dimension increases the heat transfer coefficient. On the other hand, the reduction of nanoclusters and nanoparticle size decreased this coefficient. Moreover, the simulation results showed that in high heat transfer fluxes, the heat transfer coefficient first increases by increasing the nanoparticles solid volume fraction and then decreases. However, heat transfer coefficient decreased steadily with the increase in the nanoparticles solid volume fraction in low heat transfer fluxes. The results suggested that using the nanoparticles Brownian motion mechanism along with their fractal structure can be well-applied in natural-convection heat transfer modelling of nanofluids.

Numerical simulation for a Casson nanofluid over an inclined vessel surrounded by hot tissue at the microscale

This study presents a theoretical model to mimic heat transfer and nanoparticle transport through the tumour interstitium surrounding an inclined cylindrical blood vessel exposed to an alternating magnetic field. Using similarity transformations, we convert the governing equations (partial differential equations) into a system of ordinary differential equations, which we solve numerically with a MATLAB built-in solver (bvp4c). The converence of the numerical solution is proved using the mesh convergence test. All parameters and their effects on fluid flow, heat, and mass transfer in the interstitium are studied and investigated. For instance, the nanoparticle penetration into the deep tissue can be enhanced by exposing the tumour to a magnetic field, increasing the tumour temperature and the nanoparticle Brownian motion, which is a consequence of increasing the tumour temperature. Moreover, we consider the case of non-Newtonian interstitial fluid in the tumour to mimic the nonlinearity of the fluid flow in the tumour tissue. The findings of this manuscript may optimise tumour ablation using hyperthermia by optimising nanoparticle delivery to deep tumour tissue and tumour temperature.

Vortex Dynamo in Rotating Media

The review highlights the main achievements in the theory of the vortex dynamo in rotating media. Various models of a vortex dynamo in rotating media are discussed: a homogeneous viscous fluid, a temperature-stratified fluid, a moist atmosphere, and a stratified nanofluid. The main analytical and numerical results for these models obtained by the method of multiscale asymptotic expansions are presented. The main attention is paid to models with a non-spiral external force. For a rotating moist atmosphere, characteristic estimates of the spatial and temporal scales of the generated vortex structures are obtained. New effects of the vortex dynamo in a rotating stratified nanofluid, which arise due to thermophoresis and Brownian motion of nanoparticles, are shown. The results of the analysis of the nonlinear equations of the vortex dynamo in the stationary regime are presented in the form of spiral kinks, periodic nonlinear waves, and solitons.

Thermal Convection of Rivlin-Ericksen Fluid Governed by the Brownian Motion and Thermophoresis of Nanoparticles with Passive Behaviour of Nanoparticles at the Parallel Boundaries

Stability of Rivlin-Ericksen category of nanofluid saturated in a continuous medium bounded by infinite horizontal plates has been studied. Energy equation has been supplemented with the variables belonging to the Brownian motion and thermophoresis of nanoparticles. For the linear and the non-linear stability analyses, other than the specific boundary conditions appraised with the physical situation, the boundary conditions for the flux of nanoparticle mass, in analogy with the passive behaviour of temperature at the boundaries have been explored. The novelty of the paper is that the stationary convection exists for both positive as well as negative Rn (concentration Rayleigh number) and the convection sets in earlier in comparison to a porous medium. It is also shown that the non-existence of the oscillatory convection in a Newtonian nanofluid has been ruled out for Rivlin-Ericksen nanofluid, though it exists only for negative Rn, the situation when the density of the fluid is greater than the density of nanoparticle. The viscoelastic parameter of Rivlin-Ericksen nanofluid annihilates the instability of oscillatory convection. Under non-linear stability analysis, the truncated representation of Fourier series approach has been used and the parameters belonging to the heat and mass transfer have been evaluated. It is shown that corresponding to certain parameters, the rate of heat and mass transfer rises rapidly. The valuable results are shown graphically and verified numerically.

Examination of effective strategies on changing the amount of heat transfer and entropy during non-Newtonian magneto-nanofluid mixed convection inside a semi-ellipsoidal cavity

Due to the application importance of convection flows under the impact of external fields such as magnetic field for non-Newtonian nanofluids, in cases such as nuclear processes, technologies related to lubrication, production and processing of food products, the modeling of these types of currents is very important. The existing research inquires the influence of heat production/absorption on the characteristics of non-Newtonian flow and entropy formation caused by convection heat transfer. For this purpose, the phenomenon of mixed convection inside the semi-elliptical chamber containing a power-law nanofluid is presumed in such a way that the Brownian motion of nanoparticles is considered. The curved and vertical walls of the enclosure are cold and under three different types of heating, respectively. The cold wall has no speed while the chamber vertical wall has a non-uniform velocity distribution (cosine) with a phase difference. The main goal of the research is to depict the impact of changing the position of applying the magnetic field and changing the phase difference of wall movement on the fluid flow. Flow modeling was accomplished via the utilization of lattice Boltzmann method and the accuracy of the findings was affirmed by comparing previous related studies. According to the research findings, enhancing the mean Nusselt number has a direct relationship with enhancing the phase difference. In addition, by enhancing the phase difference to 180, the mean Nusselt number up to 46% more is acquired, the influence of magnetic field applying becomes more conspicuous. In addition to the fact that the enhancing in Richardson number leads to increment of in the mean Nusselt number value and flow power, the effect of varying the phase difference becomes more noticeable with the enhancing in Richardson number. Enhancing in the Hartmann number, index of power-law and decreasing in the heat production/absorption coefficient lead to decrease in the entropy value and the average Nusselt number. By changing the position of applying the magnetic field, a current with various features can be acquired. Based on the results, it was demonstrated that changing the type of wall heating along with changing the heat absorption/production coefficient are very useful strategies in controlling the system thermal characteristics.

Solidification performance improvement of phase change materials for latent heat thermal energy storage using novel branch-structured fins and nanoparticles

In the present study, we propose the combination of novel branch-structured fins and Al2O3 nanoparticles to enhance the performance of a phase change material (PCM) during the solidification process in a triple-tube heat exchanger. The inevitable drawback of PCMs is their lower heat conductivity, which can result in a long response time during the phase change process in latent heat thermal storage systems. Therefore, any serious improvement strategy needs an optimized phase change process. A mathematical model for a two-dimensional structure composed of a PCM with paraffin RT82 and Al2O3 nanoparticles that considers the thermal conduction in metal fins, Brownian motion of nanoparticles, and natural convection in a liquid phase PCM is proposed and verified based on experimental results. The impact of various volume fractions and fin layouts on the solidification process is discussed, involving the evolution and deformation of solid–liquid interfaces and distribution of isotherms and average temperature and liquid fraction curves. The results imply that the solidification behaviour can be significantly enhanced by the application of nanoparticles and metal fins. Compared with the inherent structure of the heat exchanger, the solidification time is decreased by 8.5%, 9.3%, and 10.3% for Al2O3 nanoparticles (at 2%, 5%, and 8%, respectively) only and by 83.0%, 80.7%, 80.8%, and 82.9%, respectively, for various fin layouts only. This is attributed to increased heat transfer by thermal conduction and natural convection. It can be concluded that the impact of the use of fins is preferable compared to that for nanoparticles, and the benefit of nanoparticles is limited.

Investigation of Nanofluid Natural Convection Inside a Square Cavity for Two Orientations Using Lattice Boltzmann Method

In this study, natural convection heat transfer of a water based nanofluid inside a square cavity is numerically investigated for two different orientations of a wall-heated cavity. The enclosure is heated by applying a constant heat flux while cooled at ambient conditions. Lattice Boltzmann method (LBM) is used to simulate nanofluid natural convection. The Brownian motion of nanoparticles is considered. LBM simulation is validated by comparison with experimental and numerical results of the literature. The effect of Rayleigh number (Ra = 103, 104, 105, 106), Biot number (Bi = 0.1, 1, 10, 100) and volume fraction of nanoparticles (Φ = 0, 1, 3 and 5%) on the isotherms, streamlines, velocity components, local and Nusselt number is analyzed for two oriented cavities. The bottom-heated cavity shows higher heat transfer rate than that of the cavity heated from the sidewall. The average Nusselt number increases by up to 6.81%. Furthermore, Biot number, Rayleigh number, and volume fraction of nanoparticles show significant effects on the heat transfer rate.

Nanoparticle-induced drag reduction for polyacrylamide in turbulent flow with high Reynolds numbers

• Nanoparticles enhance the drag reduction effect of polyacrylamide solution. • The drag reduction of nanoparticles and polyacrylamide is observed at Re over 6000. • The combination of nanoparticles with cationic polyacrylamide is optimized. • Nanoparticles act as nodes to protect the polymer chain from shear breaking. Although having been increasingly studied, there is still controversy as to when the addition of nanoparticles could improve the drag reduction performance of polymer drag reducer and particularly what is the underlying mechanism from the fluid dynamics viewpoint. The drag reduction effects of adding SiO 2 nanoparticles to various polymer polyacrylamide (PAM) solutions were examined in this work. The optimal combination of SiO 2 nanoparticles with cationic polyacrylamide was confirmed. Interestingly, the addition of SiO 2 nanoparticles to cationic polyacrylamide solution was shown to be quite efficient for reducing drag, but only at higher flow rates with Reynolds numbers more than 6000, below which the nanoparticle addition is even negative. The addition of SiO 2 nanoparticles to the PAM solution is supposed to play a dual role. The first is an increase in flow resistance caused by the Brownian motion of nanoparticles, while the second is a decrease in flow resistance caused by acting as nodes to protect the polymer chain from shear-induced breaking under high shear action. At optimal nanoparticle concentration and under higher Reynolds numbers, the later effect is dominant, which could improve the drag reduction performance of polymer drag reducers. Our work should serve as a guide for the application of natural gas fracturing, where the flow rate is frequently very high.

Chaotic Model of Brownian Motion in Relation to Drug Delivery Systems Using Ferromagnetic Particles

Deterministic and stochastic models of Brownian motion in ferrofluids are of interest to researchers, especially those related to drug delivery systems. The Brownian motion of nanoparticles in a ferrofluid environment was theoretically analyzed in this research. The state of the art in clinical drug delivery systems using ferromagnetic particles is briefly presented. The motion of the nanoparticles in an external field and as a random variable is elaborated by presenting a theoretical model. We analyzed the theoretical model and performed computer simulation by using Maple software. We used simple low-dimensional deterministic systems that can exhibit diffusive behavior. The ferrofluid in the gravitational field without the presence of an external magnetic field in the xy plane was observed. Control parameter p was mapped as related to the fluid viscosity. Computer simulation showed that nanoparticles can exhibit deterministic patterns in a chaotic model for certain values of the control parameter p. Linear motion of the particles was observed for certain values of the parameter p, and for other values of p, the particles move randomly without any rule. Based on our numerical simulation, it can be concluded that the motion of nanoparticles could be controlled by inherent material properties and properties of the surrounding media, meaning that the delivery of drugs could possibly be executed by a ferrofluid without an exogenous power propulsion strategy. However, further studies are still needed.