Radial Stagnation Point Flow Research Articles

Impact of Reynolds number in modulating wall stresses in radial stagnation-point flow

Wall stresses play a critical role in fluid dynamics and understanding their impact can lead to significant improvements in system performance and efficiency. This article presents a study on the impact of the Reynolds number and magnetic number on wall stresses, energy transport, and thermodynamic irreversibility analysis in axisymmetric flow near the stagnation region. We consider a hybrid nanofluid flow containing titania and silica nanoparticles, using Yamada-Ota and Xue thermal conductivity models. The flow is driven by a cylinder rotating along the z-direction with solar radiation and a magnetic field. To formulate the problem, we use similarity transformation to obtain dimensionless ordinary differential equations and obtain numerical solutions with graphical illustrations by bvp5c in Matlab. The comparison between hybrid nanofluid models indicates a higher rate of heat transformation, with the Yamada-Ota hybrid nanofluid model demonstrating better and faster heat transport properties than the Xue model. This study underlines the importance of understanding the impact of controlled parameters on wall stresses to optimize fluid dynamics system performance and efficiency. Moreover, it highlights the potential of entropy generation analysis to identify changes in thermal processes and reduce the loss of available mechanical power in thermo-fluid systems and provides a foundation for exploring and developing advanced technologies and systems with improved heat transfer performance and energy efficiency.

Thermal case study on linearly twisting cylinder: A radial stagnation point flow of nanofluid

The thermal case study is performed to inspect heat transfer aspects for radial stagnation point flow. For this phenomenon, the study assumes a linear twisting cylinder for the heated viscous nanofluid and the arrangement is investigated among the torsionally rotating cylinders and radial stagnation point flow. The dimensionless torsion rate σ , the volume fraction of nanoparticles φ and the Wangs Reynolds number R are three possible parameters that are articulated in the study. The BVP-Midrch routine integrated with the Maple software is used to obtain numerical results of the governing flow field equations. It is found that the axial wall stress f ″ ( 1 ) is a very weak function of σ , a weak function of φ and a strong function of R . Also, the azimuthal wall stress g ′ ( 1 ) is a strong function of R and shows a practically decreasing behavior and is linear with σ for the starting value g ′ ( 1 ) = 0 at σ = 0 . It is seen that the temperature gradient admits trifling variation for the positive iteration in torsional rate. Furthermore, the heat flux at surface admits direct relation towards volume fraction of nanoparticles.

Self-Similar Solution of Radial Stagnation Point Flow and Heat Transfer of a Viscous, Compressible Fluid Impinging on a Rotating Cylinder

In this study, the radial stagnation point flow of strain rate $$\bar{k}$$ impinging on a cylinder rotating at constant angular velocity ω and its heat transfer are investigated. Reduction in the Navier–Stokes equations and energy equation to primary nonlinear ordinary differential equation systems is obtained by use of appropriate transformations when the angular velocity and wall temperature or wall heat flux all are constant. The impinging free stream is steady and normal to the surface from all sides, and the range of Reynolds number variation ( $$Re = \bar{k}a^{2} /2\upsilon$$ ) is 0.1–1000 in which a and υ are cylinder radius and kinematic viscosity, respectively. Flow results are presented for selected values of compressibility factor and different values of Prandtl numbers along with shear stress and Nusselt number. For all values of Reynolds numbers and surface temperature or surface heat flux, as compressibility factor increases the radial velocity field, the heat transfer coefficient and the wall shear stress increase, whereas the angular velocity field decreases. The rotating movement of the cylinder does not have any effect on the radial component of the velocity, but its increase increases the angular component of the fluid velocity field and the surface shear stress.

Swimming Motility Reduces Deposition to Silica Surfaces.

The transport and fate of bacteria in porous media is influenced by physicochemical and biological properties. This study investigated the effect of swimming motility on the attachment of cells to silica surfaces through comprehensive analysis of cell deposition in model porous media. Distinct motilities were quantified for different strains using global and cluster-based statistical analyses of microscopic images taken under no-flow condition. The wild-type, flagellated strain DJ showed strong swimming as a result of the actively swimming subpopulation whose average speed was 25.6 μm/s; the impaired swimming of strain DJ77 was attributed to the lower average speed of 17.4 μm/s in its actively swimming subpopulation; and both the nonflagellated JZ52 and chemically treated DJ cells were nonmotile. The approach and deposition of these bacterial cells were analyzed in porous media setups, including single-collector radial stagnation point flow cells (RSPF) and two-dimensional multiple-collector micromodels under well-defined hydrodynamic conditions. In RSPF experiments, both swimming and nonmotile cells moved with the flow when at a distance ≥20 μm above the collector surface. Closer to the surface, DJ cells showed both horizontal and vertical movement, limiting their contact with the surface, while chemically treated DJ cells moved with the flow to reach the surface. These results explain how wild-type swimming reduces attachment. In agreement, the deposition in micromodels was also lowest for DJ compared with those for DJ77 and JZ52. Wild-type swimming specifically reduced deposition on the upstream surfaces of the micromodel collectors. Conducted under environmentally relevant hydrodynamic conditions, the results suggest that swimming motility is an important characteristic for bacterial deposition and transport in the environment.

Flagella-Mediated Differences in Deposition Dynamics for Azotobacter vinelandii in Porous Media

A multiscale approach was designed to study the effects of flagella on deposition dynamics of Azotobacter vinelandii in porous media, independent of motility. In a radial stagnation point flow cell (RSPF), the deposition rate of a flagellated strain with limited motility, DJ77, was higher than that of a nonflagellated (Fla(-)) strain on quartz. In contrast, Fla(-) strain deposition exceeded that of DJ77 in two-dimensional silicon microfluidic models (micromodels) and in columns packed with glass beads. Both micromodel and column experiments showed decreasing deposition over time, suggesting that approaching cells were blocked from deposition by previously deposited cells. Modeling results showed that blocking became effective for DJ77 strain at lower ionic strengths (1 mM and 10 mM), while for the Fla(-) strain, blocking was similar at all ionic strengths. In late stages of micromodel experiments, ripening effects were also observed, and these appeared earlier for the Fla(-) strain. In RSPF and column experiments, deposition of the flagellated strain was influenced by ionic strength, while ionic strength dependence was not observed for the Fla(-) strain. The observations in all three setups suggested flagella affect deposition dynamics and, in particular, result in greater sensitivity to ionic strength.

Transport of Cryptosporidium parvum Oocysts in a Silicon Micromodel

Effective removal of Cryptosporidium parvum oocysts by granular filtration requires the knowledge of oocyst transport and deposition mechanisms, which can be obtained based on real time microscopic observation of oocyst transport in porous media. Attachment of oocysts to silica surface in a radial stagnation point flow cell and in a micromodel, which has 2-dimensional (2-D) microscopic pore structures consisting of an array of cylindrical collectors, was studied and compared. Real time transport of oocysts in the micromodel was recorded to determine the attached oocyst distributions in transversal and longitudinal directions. In the micromodel, oocysts attached to the forward portion of clean collectors, where the flow velocity was lowest. After initial attachment, oocysts attached onto already attached oocysts. As a result, the collectors ripened and the region available for flow was reduced. Results of attachment and detachment experiments suggest that surface charge heterogeneity allowed for oocyst attachment. In addition to experiments, Lattice-Boltzmann simulations helped understanding the slightly nonuniform flow field and explained differences in the removal efficiency in the transversal direction. However, the hydrodynamic modeling could not explain differences in attachment in the longitudinal direction.

Composition and Conformation of Cryptosporidium parvum Oocyst Wall Surface Macromolecules and Their Effect on Adhesion Kinetics of Oocysts on Quartz Surface

We characterized the composition and conformation of Cryptosporidium parvum ( C. parvum ) oocyst wall surface macromolecules and studied their effect on interactions between C. parvum oocyst and quartz surface. Proteinase K and mixed glycosidases were used to modify C. parvum oocyst surface macromolecules. The peptides released by proteinase K and carbohydrates hydrolyzed by mixed glycosidases were respectively analyzed with liquid chromatography/nanoelectrospray ionization tandem mass spectrometry (LC-MS/MS) and phenol-sulfuric acid assay to determine the composition of C. parvum oocyst wall surface macromolecules. Surface potential and polarity of the untreated and proteinase treated C. parvum oocysts revealed information about the conformation of oocyst wall surface macromolecules. The results illustrated that C. parvum oocyst wall is covered by a fluffy layer of glycoproteins. Adhesion kinetics of untreated and proteinase K treated C. parvum oocysts on quartz surface were studied in a radial stagnation point flow cell over a wide range of ionic strength to investigate the effect of C. parvum oocyst wall surface macromolecules on oocysts-quartz interactions. The adhesion rate coefficient of proteinase K treated C. parvum oocysts significantly decreased compared to that of untreated oocysts. This observation indicated that the fluffy layer on C. parvum oocysts wall leads to weaker van der Waals interaction and stronger steric repulsion.

Role of Divalent Cations on Deposition of Cryptosporidium parvum Oocysts on Natural Organic Matter Surfaces

A Radial Stagnation Point Flow (RSPF) system coupled with a microscope was used to study deposition of Cryptosporidium parvum oocysts on quartz and Suwannee River Natural Organic Matter (SRNOM)-coated surfaces in solutions with different Ca(2+) or Mg(2+) concentrations. Both untreated and proteinase K-treated oocysts were used. Deposition of oocysts on a SRNOM surface in Ca(2+) solution was higher than in Mg(2+) solution, even though the energy barriers calculated from Derjaguin-Landau-Verwey-Overbeek (DLVO) theory for Ca(2+) solution were higher than for Mg(2+) solution. On the other hand, the attachment of oocysts on a quartz surface was the same in both Ca(2+) and Mg(2+) solution and in qualitative agreement with the DLVO energy profiles. Inductive coupled plasma (ICP) was employed to measure the free divalent cation concentration in solutions containing oocysts. ICP data showed more Ca(2+) bound to oocyst surface than Mg(2+). Moreover, proteinase K treatment of oocysts led to a significant decrease in deposition rate due to less binding of Ca(2+) to the surface of the treated oocysts as shown by the ICP data. The deposition and ICP results suggested that inner-sphere complexation of Ca(2+) with carboxylate groups on both SRNOM and oocyst surfaces enhanced deposition of oocysts on a SRNOM surface.

Identifying the Role of Flagella in the Transport of Motile and Nonmotile Salmonella enterica Serovars

The influence of bacterial flagella on cell transport has been examined using three Salmonella enterica serovars with different motility phenotypes. Both a packed bed (PB) column and radial stagnation point flow system (RSPF) were employed to investigate bacterial deposition kinetics onto quartz over a range of conditions. The aim of this study was to better understand the role of motility on the deposition behavior of Salmonella, an important food- and waterborne pathogen. In both the PB column and RSPF systems, flagellated strains showed higher deposition, indicating the nonmotile cells can be transported further than the motile. At late-exponential growth phase, the deposition of the functional flagellated motile strain was enhanced, much more so than the dysfunctionally flagellated nonmotile and nonflagellated strains, highlighting the role of flagellar motion in cellular deposition and retention through available pore spaces and irregularities on quartz surfaces.

Impact of Higher Alginate Expression on Deposition of Pseudomonas aeruginosa in Radial Stagnation Point Flow and Reverse Osmosis Systems

Extracellular polymeric substances (EPS) have major impact on biofouling of reverse osmosis (RO) membranes. On one hand, EPS can reduce membrane permeability and on the other, EPS production by the primary colonizers may influence their deposition and attachment rate and subsequently affect the biofouling propensity of the membrane. The role of bacterial exopolysaccharides in bacterial deposition followed by the biofouling potential of an RO membrane was evaluated using an alginate overproducing (mucoid) Pseudomonas aeruginosa. The mucoid P. aeruginosa PAOmucA22 was compared with its isogenic nonmucoid prototypic parent PAO1 microscopically in a radial stagnation point flow (RSPF) system for their bacterial deposition characteristics. Then, biofouling potential of PAO1 and PAOmucA22 was determined in a crossflow rectangular plate-and-frame membrane cell, in which the strains were cultivated on a thin-film composite, polyamide, flat RO membrane coupon (LFC-1) under laminar flow conditions. In the RSPF system, the observed deposition rate of the mucoid strain was between 5- and 10-fold lower than of the wild type using either synthetic wastewater medium (with ionic strength of 14.7 mM and pH 7.4) or 15 mM KCl solution (pH of 6.2). The slower deposition rate of the mucoid strain is explained by 5- to 25-fold increased hydrophilicity of the mucoid strain as compared to the isogenic wild type, PAO1. Corroborating with these results, a significant delay in the onset of biofouling of the RO membrane was observed when the mucoid strain was used as the membrane colonizer, in which the observed time for the induced permeate flux decline was delayed (ca. 2-fold). In conclusion, the lower initial cell attachment of the mucoid strain decelerated biofouling of the RO membrane. Bacterial deposition and attachment is a critical step in biofilm formation and governed by intimate interactions between outer membrane proteins of the bacteria and the surface. Shielding these interactions by a hydrated and hydrophilic alginate capsule is shown to dramatically lessen the biofouling potential of the membrane colonizers.

Deposition kinetics of bacteriophage MS2 to natural organic matter: Role of divalent cations

The role of divalent cations (i.e. Ca 2+ and Mg 2+) in the deposition kinetics of the bacteriophage MS2 onto flat bare silica surfaces and Suwannee River Natural Organic Matter (SRNOM)-coated silica surfaces was investigated using a Quartz Crystal Microbalance (QCM) coupled with a radial stagnation point flow (RSPF) system. Experimental results demonstrated that attachment efficiencies of MS2 onto the SRNOM surface were seven to seventeen times higher in the presence of Ca 2+ than in the presence of Mg 2+. A similar trend was observed for the adsorption of polyglutamic acid, which is one of the carboxylate-containing amino acid residues found on the surface of MS2 capsids present on SRNOM-coated surfaces. The difference in attachment rates in a solution containing either Ca 2+ or Mg 2+ can be explained by a stronger tendency of Ca 2+ compared to Mg 2+ to form cation bridges by binding to carboxylate groups of both the SRNOM and the MS2 capsids. Moreover, higher attachment efficiencies of MS2 onto the SRNOM-coated silica surfaces compared to those on bare silica surfaces in the presence of either Ca 2+ or Mg 2+ at concentrations higher than 0.3 mM emphasized the important role of SRNOM carboxylate groups. Experimental data also showed reduced attachment efficiency of MS2 to SRNOM-coated surfaces in solution containing 1 mg/L SRNOM.

Deposition of Cryptosporidium parvum Oocysts on Natural Organic Matter Surfaces: Microscopic Evidence for Secondary Minimum Deposition in a Radial Stagnation Point Flow Cell

A radial stagnation point flow (RSPF) system combined with a microscope was used to determine the deposition kinetics of Cryptosporidium parvum oocysts on quartz surfaces and silica surfaces coated with Suwannee River natural organic matter (SRNOM) in solutions with different ionic strengths. Microscopic evidence of C. parvum oocysts entrapped in the secondary minimum energy well was presented to show that among the entrapped C. parvum oocysts some were washed away by the radial flow and some were able to transfer to deep primary minima and become irreversibly deposited. Experimental data were compared with simulation results obtained by the convective-diffusion equation and Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. The experimental results suggested that surface charge heterogeneity led to a higher attachment efficiency at low ionic strength. In addition, the maximum attachment efficiency was less than 1 at high ionic strength due to steric interaction.

Deposition Kinetics of Bacteriophage MS2 on a Silica Surface Coated with Natural Organic Matter in a Radial Stagnation Point Flow Cell

A quartz crystal microbalance (QCM) coupled with a radial stagnation point flow (RSPF) cell was used to study deposition kinetics of bacteriophage MS2 on silica surface coated with Suwannee River natural organic matter (SRNOM). Three stocks of MS2 stored in 1 mM NaHCO3, deionized (DI) water or phosphate buffer saline (PBS) solution were studied. MS2 stored in PBS solution were found to aggregate at all studied ionic strengths from 3 mM to 200 mM, while MS2 stored in DI water and bicarbonate solutions remained monodispersed. Isoelectric points of MS2 storedin PBS solution were lower than for those stored in DI water and 1 mM NaHCO3 solution. Nonrepulsive deposition rates of MS2 on silica surface coated with poly-L-lysine (PLL) were independent of ionic strength. In contrast MS2 deposition rates on bare silica surface or silica surface coated with SRNOM increased gradually and stabilized at an ionic strength of 60 mM. MS2 deposition rates on bare silica surface were higher than those on silica surface coated with SRNOM at low ionic strengths. Deposition rates on these two surfaces were similar at high ionic strengths. Experimental data suggest that electrostatic and steric interactions were the two main deposition mechanisms of MS2 on either bare silica or silica surface coated with SRNOM.

Bacterial Swimming Motility Enhances Cell Deposition and Surface Coverage

The influence of bacterial motility on cell transport and deposition was investigated in a well-characterized radial stagnation point flow (RSPF) chamber. Deposition experiments were conducted with nonmotile (PA01 deltafliC deltapilA) and motile (PA01 deltapilA) strains of Pseudomonas aeruginosa, and oppositely (positively) charged modified quartz surfaces. Deposition dynamics ofthe two bacterial strains were determined over a wide range of solution ionic strengths and at two flow velocities. The observed deposition dynamics were modeled using a modified expression of the random sequential adsorption (RSA) blocking function accounting for the impacts of hydrodynamic and electrostatic interactions on cell deposition. Results for the nonmotile bacteria indicated that the changes in blocking rate and surface coverage with ionic strength and flow rate were similar to those expected for nonbiological, "soft" particles, for which the coupling of hydrodynamic interactions and electrostatic repulsion governs the deposition dynamics. In contrast deposition dynamics of the motile bacterial cells reduced blocking rates and enhanced maximum coverages, approaching the jamming limit predicted for "hard" ellipsoids of 0.583. We hypothesized that cell motility allows the upstream swimming of bacteria and subsequent cell deposition on regions which are otherwise inaccessible to nonmotile cell deposition due to the "shadow effect".

Calcium and Magnesium Cations Enhance the Adhesion of Motile and Nonmotile Pseudomonas aeruginosa on Alginate Films

We investigated the impact of calcium and magnesium ions on the deposition kinetics of flagellated and nonflagellated Pseudomonas aeruginosa onto an alginate conditioning film in a radial stagnation point flow system. The bacterial deposition/adhesion behavior was related to structural changes of the alginate film in the presence of the divalent cations. Our results showed that adhesion of nonmotile bacteria was governed by cation bridging interactions between high-affinity sites at the bacterial surface and either clean or alginate-conditioned substrate surfaces. For motile bacteria, the adhesion onto clean quartz was governed by electrostatic interactions while adhesion onto alginate-conditioned quartz was dependent on the structure and viscoelastic properties of the alginate film in the presence of calcium or magnesium. We demonstrate that bacterial adhesion behavior is governed both by the effects of divalent cations on the surface properties of the bacteria and the substrate and by the type of specific interactions occurring between these two surfaces.

Adhesion of Nonmotile Pseudomonas aeruginosa on “Soft” Polyelectrolyte Layer in a Radial Stagnation Point Flow System: Measurements and Model Predictions

Prediction of bacterial deposition rates onto substrates in natural aquatic systems is quite challenging because of the inherent complexity of such systems. In this study, we compare experimental deposition kinetics of nonmotile bacteria (Pseudomonas aeruginosa) on an alginate-coated substrate in a radial stagnation point flow (RSPF) system to predictions based on DLVO theory. The "softness" of the surface layer of the bacteria and alginate-coated substrate was considered in the calculations of their electrokinetic surface properties, and the relevance of both the classical zeta potential and the outer surface potential as surrogates for surface potential was investigated. Independent of the used electrical potentials, we showed that significant discrepancies exist between theory and experiments. Analysis of microscopic images in the RSPF system has demonstrated, for the first time, that irreversible deposition of particles or cells entrapped in the secondary energy minimum can occur on the alginate layer, despite the hydrodynamic forces resulting from the radial flow in the RSPF system. It is suggested that polymeric structures associated with the surface of the particle/cell and the alginate-coated substrate are responsible for the transition between the secondary minimum and primary energy well. This mode of deposition is likely to be important in the deposition of microorganisms in complex aquatic systems.

Impact of Alginate Conditioning Film on Deposition Kinetics of Motile and Nonmotile Pseudomonas aeruginosa Strains

The initial deposition of bacteria in most aquatic systems is affected by the presence of a conditioning film adsorbed at the liquid-solid interface. Due to the inherent complexity of such films, their impact on bacterial deposition remains poorly defined. The aim of this study was to gain a better understanding of the effect of a conditioning film on the deposition of motile and nonmotile Pseudomonas aeruginosa cells in a radial stagnation point flow system. A well-defined alginate film was used as a model conditioning film because of its polysaccharide and polyelectrolyte nature. Deposition experiments under favorable (nonrepulsive) conditions demonstrated the importance of swimming motility for cell transport towards the substrate. The impact of the flagella of motile cells on deposition is dependent on the presence of the conditioning film. We showed that on a clean substrate surface, electrostatic repulsion governs bacterial deposition and the presence of flagella increases cell deposition. However, our results suggest that steric interactions between flagella and extended polyelectrolytes of the conditioning film hinder cell deposition. At a high ionic strength (100 mM), active swimming motility and changes in alginate film structure suppressed the steric barrier and allowed conditions favorable for deposition. We demonstrated that bacterial deposition is highly influenced by cell motility and the structure of the conditioning film, which are both dependent on ionic strength.

Role of Solution Chemistry and Ion Valence on the Adhesion Kinetics of Groundwater and Marine Bacteria

The role of solution chemistry on bacterial adhesion has been investigated using a radial stagnation point flow (RSPF) system. This experimental system utilized an optical microscope and an image-capturing device to directly observe the deposition kinetics of a groundwater bacterium, Burkholderia cepacia G4g, and a marine bacterium, Halomonas pacifica g. Experiments were carried out under well-controlled hydrodynamic and solution chemistry conditions, allowing for the sensitivity of bacterial adhesion behavior to be examined under a range of ionic strength and valence (KCl vs CaCl2) simulating groundwater and marine environments. Complimentary cell characterization techniques were conducted to evaluate the electrophoretic mobility, hydrophobicity, surface charge density, and viability of the bacteria under the same range of conditions. Solution chemistry was found to have a marked effect on the electrokinetic and surface properties of bacteria and the quartz collector, as well as on the resulting rate of bacterial deposition. Comparable adhesion trends were observed for B. cepacia G4g and H. pacifica g. Specifically, the deposition rates of the two bacteria species in both KCl and CaCl2 solutions increased with ionic strength, a trend consistent with traditional Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, which considers the combination of van der Waals and electrostatic double-layer interaction forces. However, in some cases, experimental results showed bacterial deposition behavior to deviate from DLVO predictions. On the basis of the systematic investigation of bacterial cell characteristics, it was found that Ca2+ ions play a distinct role on bacterial surface charge, hydrophobicity, and deposition behaviors. It is further suggested that bacterial adhesion is determined by the combined influence of DLVO interactions, electrosteric interactions associated with solution chemistry, and the hydrodynamics of the deposition system.

Influence of Growth Phase on Bacterial Deposition: Interaction Mechanisms in Packed-Bed Column and Radial Stagnation Point Flow Systems

Influence of Growth Phase on Bacterial Deposition: Interaction Mechanisms in Packed-Bed Column and Radial Stagnation Point Flow Systems

CryptosporidiumOocyst Surface Macromolecules Significantly Hinder Oocyst Attachment

The role Cryptosporidium parvum oocyst surface macromolecules play in controlling oocyst adhesion (deposition) kinetics to quartz surfaces has been investigated utilizing a radial stagnation point flow system. Deposition kinetics and corresponding attachment efficiencies of viable oocysts were compared with those after treatment with a digestive enzyme (proteinase K) to cleave these surface macromolecules. Low deposition rates were observed with viable oocysts over the entire range of ionic strengths (KCl) investigated, even at ionic strengths as high as 100 mM where the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal stability predicts the absence of an electrostatic energy barrier. "Electrosteric" repulsion between the oocyst surface macromolecules and the quartz surface is surmised to cause these low deposition rates and attachment efficiencies. However, after removal of these surface macromolecules by the digestive enzyme, increased attachment efficiencies were observed over the entire range of ionic strengths. This significant increase in the deposition kinetics was seen despite the oocysts having a more negative zeta potential following the removal of the surface macromolecules. After treatment with proteinase K, the oocysts no longer experienced electrosteric repulsive forces, and their deposition kinetics followed the general behavior predicted by DLVO theory.