Krieger-Dougherty Model Research Articles

Thermal dynamics of nanoparticle aggregation in MHD dissipative nanofluid flow within a wavy channel: Entropy generation minimization

This paper examines how nanoparticle aggregation and a consistent magnetic field influence the peristaltic movement of a dissipative nanofluid, which is caused by the sinusoidal deformation of the boundary. The viscosity of TiO2/H2O nanofluids is accurately determined by the Krieger-Dougherty model with nanoparticle aggregation, while thermal conductivity (TC) is estimated through the Bruggeman model. The set of governing equations are modeled in a fixed frame by utilizing the conservation laws of energy, mass and momentum. Galilean transformation is utilized to transform the system of equations into a wave frame, which is then converted into a dimensionless form. The assumption of a small Reynolds number and long wavelength serve to further simplify the set of equations, which are subsequently addressed through the implementation of the differential quadrature method (DQM), a highly effective numerical technique. Quantities of interest, namely velocity, pressure gradient, temperature, trapping phenomena, heat transfer, and volumetric entropy generation are analyzed across a range of physical parameters, including the solid volume fraction (Φ=0.01−0.04), Eckert number (Ec=0.0−0.1), Hartman number (Mh=0.2−2.2), Grashof number (Gr=1.0−3.0) and temperature ratio parameter (θd=0.5−2.5). A comparative analysis is conducted between the scenario involving aggregation and the one without aggregation. It is observed that nanoparticle aggregation significantly alters these quantities.

Effect of silica nanoparticles on crude oil emulsions stabilized by a natural surfactant from Fenugreek Seeds and polyacrylamide for subsurface oil mobilization applications

Emulsions represent a sustainable method for subsurface resource recovery due to their superior performance in pore plugging, mobility control and interfacial tension reduction. However, the stability of emulsion plays a vital role in determining the success of field implementation. In this work, a novel formulation is reported for emulsions wherein they have been stabilized by natural surfactant extracted from fenugreek seed. In this work, two emulsion systems are reported, that is surfactant polymer and nanoparticle-surfactant-polymer emulsion. Surfactant-polymer emulsions are stabilized by natural surfactant whereas nanoparticle-surfactant-polymer emulsion are stabilized in presence of nanoparticle and natural surfactant. Both the emulsions exhibit shear thinning profile as observed from rheological studies. Nanoparticle-surfactant-polymer emulsions were found to be thermally stable than that of Surfactant-polymer emulsions as evident from microscopic and rheological studies. An increase in temperature has the unfavorable impact on surfactant-polymer emulsion as huge drop in viscosity profile was observed. The viscosity profiles of nanoparticle-surfactant-polymer emulsions were found to be best fitted by the Krieger-Dougherty model with the value of coefficient correlation R2 = 0.99. The contact angle studies showed that NSP solution can reduce the contact angle to much lower value, which is 111˚ to 30˚ whereas surfactant-polymer solution was able to reduce from 116˚ to 57˚ only. Adsorption of silica nanoparticle was also observed in presence of sandstone and decrease in 27.32 % of peak absorbance was observed in span of 20 days. Therefore, finding of the study indicates that nanoparticle-surfactant-polymer emulsions has potential to perform better than surfactant-polymer emulsions, even at elevated temperature, and can be a better and cost-effective alternative to the conventional emulsions used in oilfield applications.

Heat transport analysis of nanoliquid in a microchannel with aggregation kinematics: a modified Buongiorno model approach

ABSTRACT Convective heat transmission of Ti O 2 − EG nanoliquid under slip and convective regime in a microchannel is examined using a modified Buongiorno model. The fractal-based approach is employed to describe the aggregation of nanoparticles. The impact of molecular dynamics, particularly on dynamic viscosity and thermal conductivity due to the aggregation of nano-sized particles, is simulated with the help of two significant models: namely, the Krieger-Dougherty model and the Maxwell-Bruggeman model, respectively. The aspect of the interfacial layer enables us to get a realistic nanoliquid model. The solutions for the designed nondimensional mathematical model are obtained numerically. The variation in flow and thermal distribution for pertinent parameters are visualized graphically. The study reveals that the thermophysical characteristics sturdily depend on nanoparticle concentration and cluster formation. It is emphasized that the viscous dissipation and radiative heat transfer contribute towards magnifying the irreversibilities in a microchannel. The findings are useful in bioconvection and various heat transfer applications.

Thermophoretic particle deposition in a nanofluid flow across a disc with non-fourier heat flux: An investigation using tangent hyperbolic model

Non-Newtonian nanofluids are attracting the attention of researchers and academics due to the high heat transmission rates that they possess. To improve thermal devices and exchangers, the researchers come up with innovative and expense-effective methods. One of the advanced technological approaches that can be utilized to enhance the thermal performance of devices is the utilization of nanofluids. This non- Newtonian nanofluid possesses the advanced properties of increasing heat transfer and destroying harmful bacteria. For this purpose, the present theoretical work is to explore the heat and thermophoretic particle deposition analysis on the tangent hyperbolic nanofluid flow over the rotating porous disk with presence of non-Fourier heat flux model and nanoparticle aggregation effect. Darcy-Forchheimer fluid model is adopted to develop the fluid flow system. Furthermore, the nanofluid’s viscosity and thermal conductivity are expressed through advanced modeling, employing the modified Krieger-Dougherty model for viscosity and the Maxwell-Bruggeman model for thermal conductivity. The nanoparticles and base fluid involved in this context are Molybdenum disulfide ( Mo S 2 ) and Water/carboxyl-methyl cellulose (CMC) respectively. The mathematical representation of the fluid flow and energy propagation involves a system of coupled partial differential equations (PDEs). The system of partial differential equations (PDEs) is transformed into non-dimensional ordinary differential equations (ODEs), which are then solved both analytically and numerically using the Homotopy Analysis Method(HAM) and Runge-Kutta-Fehlberg (RKF) method along with shooting technique. Exploring the graphical representation reveals a comprehensive analysis of key factors influencing velocity, temperature, and concentration. Through innovative visualization, these parameters take center stage, providing insights into their intricate interplay and dynamic relationships. The heat transfer rate is enhanced 0.24% and 1.4% by rising the values of thermal relaxation parameter and Weissenberg number. Also, the mass transfer rate is accelerated 0.8% and 0.14% due to enhancing the values of thermophoretic coefficient and thermophoresis parameter.

Investigation of entropy generation in the existence of heat generation and nanoparticle clustering on porous Riga plate during nanofluid flow

The objective of this research is to examine the impact of many parameters, including entropy production resulting from nanoparticle aggregation, viscous dissipation, heat source, and buoyancy, on the flow behavior of nanoliquids through a vertical Riga plate made of porous media at the two-dimensional stagnation point. By combining elements of the original Krieger-Dougherty model with the Maxwell-Bruggeman model, a new correlation for the aggregation process may be reached. The PDEs that control the boundary layer area of this problem are changed into a group of nonlinear PDEs using the right non-similarity transformations. The issue may be solved by using the BVP4c MATLAB program, which implements the local non-similarity approach and includes an extra degree of truncation. It was also found that the skin friction coefficient increased by 3.35% to 7.18% for both the aiding and opposing flow zones with the incorporation of a 1% nanoparticle volume fraction. Incorporating the Eckert number resulted in a consistent drop in heat transfer efficiency, from 7.27% to 10.24%. Aggregation of nanoparticles increases the magnitude of velocity and the temperature distribution, as shown by the model of aggregation. The augmentation of the A values is widely acknowledged as a strategy to prolong the initiation of entropy; however, on the contrary, the elevation of the Bejan number helps to expedite it. It has been empirically shown that increasing the ϕ value has a beneficial effect on both the entropy inception field and the Bejan number. An increase in the Brinkman number leads to an acceleration in the rate of entropy generation, concomitantly resulting in a decrease in the Bejan number. The suggested numerical model is validated by comparing it to existing findings that have been made public.

Steady state characteristics and stability limits of oil lubricated journal bearings using titanium dioxide nanoparticles as lubricant additives

The current work is presented to investigate the impact of titanium dioxide (TiO2) nanoparticle volume fraction and the nanoparticle aggregate sizes on the steady state characteristics and stability limits of journal bearings. A modified Krieger-Dougherty model is used to determine the viscosity of a TiO2 dependent nanolubricant with different TiO2 nanoparticle volume concentration and aggregate particle sizes. Dimensionless couple stress parameter values are calculated based on aggregate particle size and bearing radial clearance. The effects of the couple stress parameter on bearing's steady-state characteristics and dynamic response are studied. The results reveal that increasing the couple stress parameter increases the bearing load capacity as well as the bearing's stability limits. The aggregate TiO2 nanoparticle sizes have sensible effects on bearing characteristics and stability limits of the bearing.

Three-Dimensional Swirling Flow of Nanofluid with Nanoparticle Aggregation Kinematics Using Modified Krieger–Dougherty and Maxwell–Bruggeman Models: A Finite Element Solution

The current study explores a three-dimensional swirling flow of titania–ethylene glycol-based nanofluid over a stretchable cylinder with torsional motion. The heat transfer process is explored subject to heat source/sink. Here, titania–ethylene glycol–water-based nanofluid is used. The Maxwell–Bruggeman models for thermal conductivity and modified Krieger–Dougherty models for viscosity are employed to scrutinize the impact of nanoparticle aggregation. A mathematical model based on partial differential equations (PDEs) is developed to solve the flow problem. Following that, a similarity transformation is performed to reduce the equations to ordinary differential equations (ODEs), which are then solved using the finite element method. It has been proven that nanoparticle aggregation significantly increases the temperature field. The results reveal that the rise in Reynolds number improves the heat transport rate, whereas an increase in the heat source/sink parameter value declines the heat transport rate. Swirling flows are commonly found in many industrial processes such as combustion, mixing, and fluidized bed reactors. Studying the behavior of nanofluids in these flows can lead to the development of more efficient and effective industrial processes.

Assessment of flow pattern and rheological properties of SF6 hydrate slurry

Sulfur hexafluoride (SF6) has extremely high global warming potential and must be separated and recovered to avoid its emission into the atmosphere. Hydrate-based gas separation, which uses only water as the separation medium and has low environmental impact, is expected to become a new separation and recovery technology for SF6. However, this technique has the drawback that hydrate particles in the slurry can block equipment piping. Therefore, this study investigated the flow pattern and rheological properties of SF6 hydrate slurry using a loop-tube flow apparatus. SF6 hydrate slurry was observed to have three flow patterns as the flow velocity varied: homogeneous flow, heterogeneous flow, and moving-bed flow. We developed experimental relationships based on the Turian–Yuan equation to estimate the flow velocities at which the flow patterns change. These experimental equations were able to predict these velocities within an error of approximately 10%. The rheological properties of SF6 hydrate slurry were found to exhibit Newtonian tendency at low solid fractions and pseudoplastic tendency at high solid fractions. The relative viscosity of the slurry could be estimated within 25% error using the Krieger–Dougherty model.

Elucidating the particle concentration-dependent flow behavior of aqueous TiO2 suspensions based on polymer dispersant structures and interparticle surface distances

Flowing behavior of concentrated aqueous TiO2 suspensions was evaluated in relation to the structure of polymeric dispersants, their adlayer thickness on particle surface, and particle concentrations. Comb-type polymeric dispersants comprising polyethylene glycol-based side chains with different combinations of unit number and side chain length were investigated. Based on particle concentration–apparent viscosity curves of the suspensions with TiO2 nanoparticles saturated with dispersants, maximum packing fraction and polymer adlayer thickness were estimated through the Krieger–Dougherty model. When the steric repulsive force of polymer dispersant dominated van der Waals attractive forces, the flow curves of the suspension exhibited hysteresis characteristics as the average particle surface distance approached the adlayer thickness of polymer dispersants. Additionally, by introducing the concept of relative surface distance, which is the average particle surface distance divided by the adlayer thickness, the particle concentration dependency of the suspension viscosities with different dispersants followed a unified trend.

Insight into the significance of nanoparticle aggregation and non-uniform heat source/sink on titania–ethylene glycol nanofluid flow over a wedge

The properties of nanoparticles in the working fluid are affected by many external factors and it further influences the effective properties of the resulting nanofluid. To study the heat transference mechanism in nanofluids, the inclusion of such factors is quite important as it provides the exact illustration of the mechanism. One such factor is the nanoparticle aggregation effect. Authors have studied the titania–ethylene glycol nanofluid (TiO2/EG NF) flow over a wedge with nanoparticle aggregation effect. Through this communication, authors have attempted to make a development on the Falkner-Skan problem. The flow is developed in the presence of the suction/injection effects, mixed convection, thermal radiation, porous medium, and non-uniform heat source/sink. To account for the influence of nanoparticle aggregation, revised forms of the Maxwell and Bruggeman models and the Krieger-Dougherty model are employed to estimate the effective thermal conductivity and viscosity of TiO2/EG NF, respectively. The aforementioned modified models developed for TiO2/EG NF gave a soundly close agreement with the experimental data. The governing equations are numerically solved employing the “bvp4c function in MATLAB”. The effect of the primary relevant parameters on the velocity, temperature, and heat transmission rate is depicted graphically. The heat transmission rate at the surface is higher with aggregated nanoparticles in comparison to its absence. The higher NPs volume fraction and the aggregation effect enhance the effective viscosity, the fluid becomes denser, and as a result, the velocity decreases. The outcomes of this study will be useful in many fields that utilize applications of flow over wedge such as in raw oil extraction, storage of nuclear waste, insulating heat exchangers, etc.

Numerical Analysis of Merging Flows of Floc-Forming Fluids in a T-Junction Channel Using a Non-Newtonian Viscous Model Based on a Population

The flow of a floc-forming fluid in a T-junction channel was numerically analyzed using a non-Newtonian viscous model based on the population balance equation (PBE) of the floc size. The finite element method was applied to solve the velocity and pressure fields, and the PBE of the floc size distribution was computed to obtain the effective volume fraction of flocs. The Krieger-Dougherty model was used to evaluate the viscosity of suspension of flocs using the effective volume fraction. The numerical simulation captured the characteristic aggregation-breakage behavior of flocs in the flow. In the region where flows from two entrances merge, the effective volume fraction decreases because the breakage of flocs progresses. In the downstream channel, re-aggregation of flocs occurs near the channel centerline, and the effective volume fraction increases. This aggregation-breakage behavior of flocs was confirmed by the analysis of the floc size distribution.

Heat transfer analysis in magnetohydrodynamic nanofluid flow induced by a rotating rough disk with non-Fourier heat flux: aspects of modified Maxwell-Bruggeman and Krieger-Dougherty models.

Non-Newtonian fluids have unique heat transfer properties compared to Newtonian fluids. The present study examines the flow of a Maxwell nanofluid across a rotating rough disk under the effect of a magnetic field. Furthermore, the Cattaneo-Christov heat flux model is adopted to explore heat transport features. In addition, a comparison of fluid flow without and with aggregation is performed. Using similarity variables, the governing partial differential equations are transformed into a system of ordinary differential equations, and this system is then solved by employing the Runge-Kutta Fehlberg fourth-fifth order method to obtain the numerical solution. Graphical depictions are used to examine the notable effects of various parameters on velocity and thermal profiles. The results reveal that an increase in the value of Deborah number decreases the velocity profile. An increase in the thermal relaxation time parameter decreases the thermal profile. An artificial neural network is employed to calculate the rate of heat transfer and surface drag force. The R values for skin friction and Nusselt number were computed. The results demonstrate that artificial neural networks accurately predicted skin friction and Nusselt number values.

Viscosity transition from dilute to concentrated cementitious suspensions: the effect of colloidal interactions and flocs percolation

The current paper deals with the effect of powder type and chemical admixtures on the rheological properties of mineral suspensions. The plastic viscosity of calcite, cement, and fly ash suspensions with or without superplasticizers (SP) and hydration retarders was characterized in a wide range of solid volume fractions. The results show that the plastic viscosity of suspensions increases with the decrease in particle size, and strongly decreases with the presence of superplasticizers. Besides, for reactive suspensions, hydration retarders decrease the plastic viscosity of the suspension, while competitive adsorption occurs when adding retarders to suspensions containing SP, leading to an increase in the plastic viscosity. Based on the experimental results, a relative plastic viscosity, i.e., the ratio between the total plastic viscosity and the theoretical viscosity contributed by the hard-sphere, is proposed to assess the effect of the contribution of colloidal forces. Moreover, the solid volume fraction of flocs in colloidal suspensions before percolation is identified by comparing the measured plastic viscosity with the Krieger-Dougherty model. Finally, a theoretical approach to determine the percolation packing fraction of minerals powders is further proposed.

The numerical study of nanofluid flow with energy and mass transfer over a stretching/shrinking wedge

For nanomaterials aggregation impacts, the Falkner–Skan problem for shrinking/stretching wedge is generalized. The simulation is performed in the presence of a heat source, magnetic field, chemical reaction, suction/injection, and thermal radiation effects. Modifications of the Krieger–Dougherty model, as well as the Bruggeman and Maxwell models, are developed to approximate the thermal conductivity and viscosity of TiO2/ethylene glycol (EG) nanofluid (NF) to accommodate for nanoparticle (NP) aggregation influences. The system of equations describing the Falkner–Skan dilemma for wedges with NP aggregation impacts is translated using resemblance substitution and computed using the “parametric continuation method (PCM)” algorithm. The outcomes are justified by comparing them to the existing literature and the “bvp4c” package. The NP aggregation consequences are seen to be significantly strong even when the NP concentration is modest, as prior published experimental research has revealed. In comparison to the lack of NP aggregation effects, the heat transference rate of TiO2/EG NF is greater. The velocity, thermal efficiency, and mass transition rate of TiO2/EG NF boost with the inclusion of titanium dioxide NPs in the working fluid EG.

Falkner–Skan Problem for a Stretching or Shrinking Wedge With Nanoparticle Aggregation

Abstract The Falkner–Skan problem for stretching or shrining wedge is generalized for nanoparticle aggregation effects. The model is developed in the presence of the magnetic field, thermal radiation, and suction/injection effects. For the inclusion of nanoparticle aggregation effects, modifications of the Krieger-Dougherty model and Maxwell and Bruggeman models are used to predict effective viscosity and thermal conductivity of titania–ethylene glycol (TiO2/EG) nanofluid, respectively. These models are already tested experimentally in the past and are known to predict the true values for the TiO2/EG nanofluid with aggregated nanoparticles. The system of equations depicting the Falkner–Skan problem for a wedge with nanoparticle aggregation effects is transformed via similarity transformations and solved via the “bvp4c” function, which is accessible by matlab software. The validation of results is done through a comparison of results with published literature and a comparison of present results with the “bvp5c” function and RKF-Shooting Technique. As suggested by the previously published experimental studies, it is observed that the nanoparticle aggregation effects are strong even when the nanoparticle concentration is low. The heat transmission rate of TiO2/EG nanofluid is seen as higher with nanoparticle aggregation effects in comparison to its absence. The streamlines become denser and more intense with the presence of a magnetic field. The results of this study apply to several thermal systems, engineering, and industrial process, which utilize nanofluid for cooling, and heating processes.

A two-phase design strategy based on the composite of mortar and coarse aggregate for 3D printable concrete with coarse aggregate

In this investigation, a two-phase design strategy based on the composite of mortar phase and coarse aggregate phase is proposed for designing 3D printable concrete (3DPC) with coarse aggregate. Coussot model and Krieger-Dougherty model were utilized to establish a quantitative relationship between the rheological property of 3DPC and the volume fraction of coarse aggregate, aiming to design 3DPC with coarse aggregate based on the mix proportion of printable mortar and thus facilitate the mixture design. It is found that the plastic viscosity of 3DPC with coarse aggregate is excessively high when the volume fraction of coarse aggregate reaches to a certain value, which is the main reason restricting the printability of 3DPC with coarse aggregate. The printability of 3DPC with coarse aggregate cannot be solely evaluated by yield stress, the plastic viscosity should be taken into consideration together with yield stress for evaluation as well.

Significance of aggregation of nanoparticles, activation energy, and Hall current to enhance the heat transfer phenomena in a nanofluid: a sensitivity analysis

The mechanisms involved in the heat transport enhancement due to suspended nanoparticles are still unclear. Many studies have shown that nanoparticle aggregation is a key aspect of increasing nanofluid thermal conductivity. Nevertheless, the fractal dimension of nanoparticle aggregation will have a substantial impact on the nanofluid’s thermal conductivity. Therefore, the present study examines the influence of nanoparticle aggregation and Hall current on the nanoliquid flow past a spinning disk. The importance of Arrhenius activation energy is also investigated. A revised correlation for the aggregation mechanism is attained using the modified Krieger-Dougherty model (KD-model) and the Maxwell-Bruggeman model (MB-model). A similarity technique and finite difference method are used to construct the numerical solutions for the boundary value problem. The 2D plots and 3D surface plots are shown to investigate how different key parameters impact the velocity, temperature, and concentration fields. The study highlights that the Hall current has a beneficial effect on the fluid flow field. Higher activation energy leads to a productive chemical reaction which, improves the concentration layer. The thermal boundary for NPs aggregation is superior than to that without NPs aggregation, and the suspension of nanoparticles will have a favorable impact on the thermal layer.

A thermodynamics-guided framework to design lightweight aggregate from waste coal combustion fly ash

A systematic thermodynamics-based framework was applied to recycle waste low and high-calcium coal combustion Fly Ash (FA) into synthetic lightweight aggregates (LWA) through sintering. The process to successfully manufacture synthetic LWA was investigated, which requires a delicate balance among three phenomena: (i) sufficient liquid phase formation during sintering, (ii) appropriate viscosity for the liquid-solid phase, and (iii) sufficient amount of gas emission to form pores in the LWA. Thermodynamics modeling was used to quantify the formation of the liquid phase during sintering while the fluxing agent and the temperature change. The Urbain- Kalmanovitch, Browning, and Krieger-Dougherty models were used to quantify the viscosity of the liquid and liquid-solid phase, respectively. A lower bound of 100 Pa•s for the viscosity was found to ensure spherical shape of the LWA. Using thermogravimetric analysis, it was shown that the LWA had a notable gas release potential, owing to the presence of anhydrite and hematite, which could create gas-filled pores in the LWA macro-microstructure. X-ray computed tomography (X-CT) observation revealed the formation of a porous structure for the produced LWA where high calcium FA LWA generally had larger pores compared with low calcium FA LWA. By correlating the X-CT and scanning electron microscopy (SEM) observations and thermodynamic modeling results, it was found that a minimum of 40% liquid phase content (% by mass) is necessary for the formation of gas-filled pores in FA-LWA.

Optimization of UV-curable alumina suspension for digital light processing of ceramic membranes

Herein a novel method was proposed for the fabrication of ceramic membranes by digital light processing (DLP) three-dimensional (3D) printing. The UV-curable alumina suspension was optimized by tuning the solid content, grading ratio, and temperature to achieve low viscosity. The Krieger-Dougherty model and the Vogel-Fulcher-Tammann equation were employed to describe and predict the changing trends of viscosity. The effects of the sintering process on the microstructures, mechanical strength, and permeability of the ceramic membranes were also studied. Under the optimized conditions, ceramic membranes were obtained with uniform pore size distribution, high porosity of 42.6%, an average pore size of 0.9 μm, and a pure water flux of 2.66 m3 m-2 h-1 bar-1. Therefore, DLP 3D printing demonstrates good prospects for application in the fabrication of ceramic membranes.

Droplet-Based Microfluidic Tool to Quantify Viscosity of Concentrating Protein Solutions.

Measurement of the viscosity of concentrated protein solutions is vital for the manufacture and delivery of protein therapeutics. Conventional methods for viscosity measurements require large solution volumes, creating a severe limitation during the early stage of protein development. The goal of this work is to develop a robust technique that requires minimal sample. In this work, a droplet-based microfluidic device is developed to quantify the viscosity of protein solutions while concentrating in micrometer-scale droplets. The technique requires only microliters of sample. The corresponding viscosity is characterized by multiple particle tracking microrheology (MPT). We show that the viscosities quantified in the microfluidic device are consistent with macroscopic results measured by a conventional rheometer for poly(ethylene) glycol (PEG) solutions. The technique was further applied to quantify viscosities of well-studied lysozyme and bovine serum albumin (BSA) solutions. Comparison to both macroscopic measurements and models (Krieger-Dougherty model) demonstrate the validity of the approach. The droplet-based microfluidic device provides accurate quantitative values of viscosity over a range of concentrations for protein solutions with small sample volumes (~ μL) and high compositional resolution. This device will be extended to study the effect of different excipients and other additives on the viscosity of protein solutions.