Simulation of Polymer Solutions by Dissipative Particle Dynamics

Abstract

Dissipative Particle Dynamics (DPD) is employed to model the dynamics and rheology of polymer solutions, and suspensions of spherical particles with adsorbed polymers. Static and dynamic scaling relationships for the variation of radius of gyration and relaxation time with polymer chain length are reviewed, demonstrating that the DPD polymer solution model correctly represents the effects of hydrodynamic interaction and excluded volume. Rheological simulations for both polymer solutions and polymer-sphere suspensions predict Newtonian viscosities at low shear rate followed by shear-thinning behavior as a reduced shear rate of unity is approached. Both the Newtonian viscosity and the extent of shear-thinning are greatly enhanced in the case of good solvents, compared to the viscosity curves for polymers and polymer-spheres structures dissolved in theta solvents and poor solvents.     

Broth rheology and morphological analysis of Solanum chrysotrichum cultivated in a stirred tank

Solanum chrysotrichum cell cultures were grown in a stirred tank bioreactor and their rheological and morphological behaviour were evaluated. The culture broths exhibited non-Newtonian and shear-thinning characteristics. Pseudoplasticity of the broths was governed by their biomass concentration. The roundness of aggregates measured as the elliptical form factor (EFF) had important changes. At the beginning of the culture the aggregates with an EFF lower than 2 represented 52% of the population, but in stationary phase the proportion increased to 77%. Whereas the size of aggregates did not change 80% of the population had an area lower than 0.1 mm². Overall, these results indicate that the shape of the aggregate therefore needs to be considered when studying plant broth rheology.     

Flush mounted hot film anemometer measurement of wall shear stress distal to a tri-leaflet valve for Newtonian and non-Newtonian blood analog fluids

Wall shear stress has been measured by flush-mounted hot film anemometry distal to an Ionescu-Shiley tri-leaflet valve under pulsatile flow conditions. Both Newtonian (aqueous glycerol) and non-Newtonian (aqueous polyacrylamide) blood analog fluids were investigated. Significant differences in the axial distribution of wall shear stress between the two fluids are apparent in flows having nearly identical Reynolds numbers. The Newtonian fluid exhibits a (peak) wall shear rate which is maximized near the valve seat (30 mm) and then decays to a fully developed flow value (by 106 mm). In contrast, the shear rate of the non-Newtonian fluid at 30 mm is less than half that of the Newtonian fluid and at 106 mm is more than twice that of the Newtonian fluid. It is suggested that non-Newtonian rheology influences valve flow patterns either through alterations in valve opening associated with low shear separation zones behind valve leaflets, or because of variations in the rate of jet spreading. More detailed studies are required to clarify the mechanisms. The Newtonian wall shear stresses for this valve are low. The highest value observed anywhere in the aortic chamber was 2.85 N/m2 at a peak Reynolds number of 3694.     

Hydrodynamic characteristics and mixing behaviour of Sclerotium glucanicum culture fluids in an airlift reactor with an internal loop used for scleroglucan production

The filamentous fungus, Sclerotium glucanicum NRRL 3006, was cultivated in a 0.008 m³ airlift bioreactor with internal recirculation loop (ARL-IL) for production of the biopolymer, scleroglucan. The rheological behaviour of the culture fluid was characterised by measurement of the fluid consistency coefficient (K) and the flow behaviour index (n). Based on these measurements, the culture fluid changed from a low viscosity Newtonian system early in the process, to a viscous non-Newtonian (pseudoplastic) system. In addition, reactor hydrodynamics and mixing behaviour were characterised by measurement of whole mean gas hold-up (ɛ _g), liquid re-circulation velocity (U _ld) and mixing time (t _m). Under identical process conditions, the effects of the viscosity of the culture fluid and air flow rate on ɛ _g, U _ld and t _m were examined and empirical correlations for ɛ _g, U _ld and t _m with both superficial velocity U _g and consistency coefficient K were obtained and expressed separately. The correlations obtained are likely to describe the behaviour of real fungal culture fluids more accurately than previous correlations based on Newtonian or simulated non-Newtonian systems. Journal of Industrial Microbiology & Biotechnology (2001) 27, 208–214. Received 05 June 2000/ Accepted in revised form 18 March 2001     

Axial dispersion in packed bed reactors involving viscoinelastic and viscoelastic non-Newtonian fluids

Axial dispersion is an important parameter in the performance of packed bed reactors. A lot of fluids exhibit non-Newtonian behaviour but the effect of rheological parameters on axial dispersion is not available in literature. The effect of rheology on axial dispersion has been analysed for viscoinelastic and viscoelastic non-Newtonian fluids. Aqueous solutions of carboxymethyl cellulose and polyacrylamide have been chosen to represent viscoinelastic and viscoelastic liquid-phases. Axial dispersion has been measured in terms of Bo_L number. The single parameter axial dispersion model has been applied to analyse RTD response curve. The Bo_L numbers were observed to increase with increase in liquid flow rate and consistency index ‘K’ for viscoinelastic as well as viscoelastic fluids. Bodenstein correlation for Newtonian fluids proposed has been modified to account for the effect of fluid rheology. Further, Weissenberg number is introduced to quantify the effect of viscoelasticity.     

Realistic non-Newtonian viscosity modelling highlights hemodynamic differences between intracranial aneurysms with and without surface blebs

Most computational fluid dynamic (CFD) simulations of aneurysm hemodynamics assume constant (Newtonian) viscosity, even though blood demonstrates shear-thinning (non-Newtonian) behavior. We sought to evaluate the effect of this simplifying assumption on hemodynamic forces within cerebral aneurysms, especially in regions of low wall shear stress, which are associated with rupture. CFD analysis was performed for both viscosity models using 3D rotational angiography volumes obtained for 26 sidewall aneurysms (12 with blebs, 12 ruptured), and parametric models incorporating blebs at different locations (inflow/outflow zone). Mean and lowest 5% values of time averaged wall shear stress (TAWSS) computed over the dome were compared using Wilcoxon rank-sum test. Newtonian modeling not only resulted in higher aneurysmal TAWSS, specifically in areas of low flow and blebs, but also showed no difference between aneurysms with or without blebs. In contrast, for non-Newtonian analysis, bleb-bearing aneurysms showed significantly lower 5% TAWSS compared to those without (p=0.005), despite no significant difference in mean dome TAWSS (p=0.32). Non-Newtonian modeling also accentuated the differences in dome TAWSS between ruptured and unruptured aneurysms (p<0.001). Parametric models further confirmed that realistic non-Newtonian viscosity resulted in lower bleb TAWSS and higher focal viscosity, especially when located in the outflow zone. The results show that adopting shear-thinning non-Newtonian blood viscosity in CFD simulations of intracranial aneurysms uncovered hemodynamic differences induced by bleb presence on aneurysmal surfaces, and significantly improved discriminant statistics used in risk stratification. These findings underline the possible implications of using a realistic model of blood viscosity in predictive computational hemodynamics.     

On the relative importance of rheology for image-based CFD models of the carotid bifurcation

BACKGROUND: Patient-specific computational fluid dynamics (CFD) models derived from medical images often require simplifying assumptions to render the simulations conceptually or computationally tractable. In this study, we investigated the sensitivity of image-based CFD models of the carotid bifurcation to assumptions regarding the blood rheology. METHOD OF APPROACH: CFD simulations of three different patient-specific models were carried out assuming: a reference high-shear Newtonian viscosity, two different non-Newtonian (shear-thinning) rheology models, and Newtonian viscosities based on characteristic shear rates or, equivalently, assumed hematocrits. Sensitivity of wall shear stress (WSS) and oscillatory shear index (OSI) were contextualized with respect to the reproducibility of the reconstructed geometry, and to assumptions regarding the inlet boundary conditions. RESULTS: Sensitivity of WSS to the various rheological assumptions was roughly 1.0 dyn/cm(2) or 8%, nearly seven times less than that due to geometric uncertainty (6.7 dyn/cm(2) or 47%), and on the order of that due to inlet boundary condition assumptions. Similar trends were observed regarding OSI sensitivity. Rescaling the Newtonian viscosity based on time-averaged inlet shear rate served to approximate reasonably, if overestimate slightly, non-Newtonian behavior. CONCLUSIONS: For image-based CFD simulations of the normal carotid bifurcation, the assumption of constant viscosity at a nominal hematocrit is reasonable in light of currently available levels of geometric precision, thus serving to obviate the need to acquire patient-specific rheological data.     

Rheological properties of <Emphasis Type="Italic">Chlorella pyrenoidosa</Emphasis> culture grown heterotrophically in a fermentor

Rheological properties of Chlorella pyrenoidosa culture grown heterotrophically in a 14 L fermentor were investigated. It was found that the fluid viscosity was rather low and remained almost unchanged during the cultivation, implying that no (or very few) viscous substances were excreted into the medium. Investigation of the condensed suspension of C. pyrenoidosa showed that for biomass concentration under 150 g.L⁻¹, the suspension of C. pyrenoidosa exhibited Newtonian behavior, and the fluid viscosity was rather low (about 40 mPa·s) and increased very slowly with the increase in cell concentration. With further increase in biomass concentration however, the fluid rheological behavior changed to non-Newtonian, and the fluid viscosity increased rapidly with the increase in cell concentration. From the viewpoint of rheology, C. pyrenoidosa is an excellent organism for high-cell-density culture, and there will be no rheological problems at cell densities under 150 g.L⁻¹.     

Fracture of DNA in transient extensional flow. A numerical simulation study

Using the Brownian dynamics simulation technique, we studied the fracture process of DNA chains subjected to transient extensional flow, letting the solution with DNA molecules pass through a very small orifice (radius = 0.0065 cm), thus experiencing extensional flow of the convergent (sink) type. The DNA molecules were modeled as FENE bead-spring chains with the springs obeying a modified Warner force law, as proposed by Reese and Zimm. The fracture yield was strongly dependent on flow rate and molecular weight, reaching, in our setup, a level of 100% at a flow rate of around 0.001 cm³/s for DNA with molecular weight 26 × 10⁶ (T7 DNA). There was found to exist a critical flow rate (Q_crit) below which fracture did not occur, in accordance with what was observed in studies on polystyrene in transient extensional flow. We found that for DNA, the critical flow rate depended on the molecular weight as Q_crit ∼ M⁻¹⁴ when the hydrodynamic interaction effect (HI) was not included in the simulations. When HI was accounted for, the relation was found to be Q_crit ∼ M^−1.1, close to the theoretical prediction for fracture of partly extended chains in transient extensional flow. © 1996 John Wiley & Sons, Inc.     

Numerical study of the impact of non-Newtonian blood behavior on flow over a two-dimensional backward facing step

Endothelial cell (EC) responsiveness to shear stress is essential for vasoregulation and plays a role in atherogenesis. Although blood is a non-Newtonian fluid, EC flow studies in vitro are typically performed using Newtonian fluids. The goal of the present study was to determine the impact of non-Newtonian behavior on the flow field within a model flow chamber capable of producing flow disturbance and whose dimensions permit Reynolds and Womersley numbers comparable to those present in vivo. We performed two-dimensional computational fluid dynamic simulations of steady and pulsatile laminar flow of Newtonian and non-Newtonian fluids over a backward facing step. In the non-Newtonian simulations, the fluid was modeled as a shear-thinning Carreau fluid. Steady flow results demonstrate that for Re in the range 50-400, the flow recirculation zone downstream of the step is 22-63% larger for the Newtonian fluid than for the non-Newtonian fluid, while spatial gradients of shear stress are larger for the non-Newtonian fluid. In pulsatile flow, the temporal gradients of shear stress within the flow recirculation zone are significantly larger for the Newtonian fluid than for the non-Newtonian fluid. These findings raise the possibility that in regions of flow disturbance, EC mechanotransduction pathways stimulated by Newtonian and non-Newtonian fluids may be different.     

The influence of the non-Newtonian properties of blood on the flow in large arteries: unsteady flow in a 90 degrees curved tube.

A numerical and experimental investigation of unsteady entry flow in a 90 degrees curved tube is presented to study the impact of the non-Newtonian properties of blood on the velocity distribution. The time-dependent flow rate for the Newtonian and the non-Newtonian blood analog fluid were identical. For the numerical computation, a Carreau-Yasuda model was employed to accommodate the shear thinning behavior of the Xanthan gum solution. The viscoelastic properties were not taken into account. The experimental results indicate that significant differences between the Newtonian and non-Newtonian fluid are present. The numerical results for both the Newtonian and the non-Newtonian fluid agree well with the experimental results. Since viscoelasticity was not included in the numerical code, shear thinning behavior of the blood analog fluid seems to be the dominant non-Newtonian property, even under unsteady flow conditions. Finally, a comparison between the non-Newtonian fluid model and a Newtonian fluid at a rescaled Reynolds number is presented. The rescaled Reynolds number, based on a characteristic rather than the high-shear rate viscosity of the Xanthan gum solution, was about three times as low as the original Reynolds number. Comparison reveals that the character of flow of the non-Newtonian fluid is simulated quite well by using the appropriate Reynolds number.     

A study of the rheological properties of a non-Newtonian fermentation broth

Polysaccharide was synthesized by Aureobasidium pullulans (or Pullularia pullulans) 2552 in a sucrose medium. The field apparent viscosity of the culture medium from shake flask experiments rose to 24,500 cP and then dropped toward its initial value as the fermentation progressed. The magnitude of the maximum apparent viscosity depended on the initial pH of the fermentation broth. The inoculum age influenced the cultivation period before which the maximum viscosity was reached. Rheograms of the fermentation broths showed a change in viscosity behavior from Newtonian to pseudoplastic, and then toward Newtonian characteristics during the fermentation. The calculated non-Newtonian index was found to be a sensitive factor for the indication of the non-Newtonian behavior. Such behavior could not be detected from rheograms. Viscosity profiles of polysaccharide isolated from various stages of the fermentation showed a change from Newtonian to pseudoplastic behavior depending on the concentration (0–2%) of polysaccharide.     

Influence of culture vessel characteristics and agitation rate on gaseous exchange,hydrodynamic stress,and growth of embryogenic cork oak (<Emphasis Type="BoldItalic">Quercus suber</Emphasis> L.) cultures

Somatic embryogenesis can be induced in the leaves of cork oak (Quercus suber L.) trees. The use of this propagation system in multivarietal forestry requires the mass production of cloned plants at low cost. Investigations were made into the influence of three types of Erlenmeyer flask and three orbiting speeds (60, 110, and 160 rpm) on oxygen transfer rate (K_L a), the shear force index (SFI), biomass production, and the proliferation of embryogenic clumps (EMCs) in cultures during the proliferation phase. K_L a varied between 0.11 and 1.47 h⁻¹ without biomass production being limited by oxygen availability. The EMCs grew even in hypoxic conditions, although the suppression of gaseous exchange strongly reduced biomass production. Cultures with different levels of hydrodynamic stress and SFI values (1.4·10⁻³–8.8·10⁻³ cm min⁻¹) were obtained. Proliferation rates of EMCs increased with agitation rate and the SFI. The largest number of EMCs was obtained in baffled flasks agitated at 160 rpm (K_L a of 1.47 h⁻¹, and SFI of 8.8·10⁻³ cm min⁻¹) with mild hydrodynamic stress enhancing growth. Biomass production increased with agitation and hydrodynamic stress, but only when the SFI value was below 5·10⁻³ cm min⁻¹. The greatest biomass production was obtained in smooth 100 ml flasks agitated at 160 rpm. The differentiation of embryos was favoured by the lowest K_L a (0.11 h⁻¹) and SFI (1.40·10³ cm min⁻¹) values, achieved using these flasks when agitated at 60 rpm.     

Droplets motion on chemically/topographically heterogeneous surfaces

We present a numerical study of droplets sliding across chemically heterogeneous surfaces formed by a periodic pattern of alternating hydrophobic and hydrophilic stripes, or topographically heterogeneous surfaces which are microgrooved. The numerical simulation performed by using a particle-based numerical method, Many-body Dissipative Particle Dynamics (MDPD), is adopted to observe the stick-slip motion of droplets driven by a constant body force. The fractions of two types of surfaces are varied from 0.3 to 0.7 to investigate their influence on stick-slip motion of droplets. The dynamic contact angles and the variation in distance D_fr between the front and the rear contact points are shown for different fractions. The jerky motion characterised by stick-slip motion can be found on chemically heterogeneous surfaces for all fractions we choose and the partial stick-slip motion can also be discovered on topographically heterogeneous surfaces except for fraction Φ_s = 0.3. The snapshots of droplet show that stick-slip motion is the consequence of the periodic deformation of droplet interface during crossing heterogeneous surfaces and can be controlled by fractions.     

Shape optimization in unsteady blood flow: a numerical study of non-Newtonian effects

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.     

Real-time fluid dynamics investigation and physiological response for erythromycin fermentation scale-up from 50 L to 132 m<Superscript>3</Superscript> fermenter

The physiological response of erythromycin fermentation scale-up from 50 L to 132 m³ scale was investigated. A relatively high oxygen uptake rate (OUR) in early phase of fermentation was beneficial for erythromycin biosynthesis. Correspondingly, the maximal consistency coefficient (K) reflecting non-Newtonian fluid characteristics in 50 L and 132 m³ fermenter also appeared in same phase. Fluid dynamics in different scale bioreactor was further investigated by real-time computational fluid dynamics modeling. The results of simulation showed that the impeller combination in 50 L fermenter could provide more modest flow field environment compared with that in 132 m³ fermenter. The decrease of oxygen transfer rate (OTR) in 132 m³ fermenter was the main cause for impairing cell physiological metabolism and erythromycin biosynthesis. These results were helpful for understanding the relationship between hydrodynamic environment and physiological response of cells in bioreactor during the scale-up of fermentation process.     

Comparison between a generalized Newtonian model and a network-type multiscale model for hemodynamic behavior in the aortic arch: Validation with 4D MRI data for a case study

Blood is a complex fluid in which the presence of the various constituents leads to significant changes in its rheological properties. Thus, an appropriate non-Newtonian model is advisable; and we choose a Modified version of the rheological model of Phan-Thien and Tanner (MPTT). The different parameters of this model, derived from the rheology of polymers, allow characterization of the non-Newtonian nature of blood, taking into account the behavior of red blood cells in plasma. Using the MPTT model that we implemented in the open access software OpenFOAM, numerical simulations have been performed on blood flow in the thoracic aorta for a healthy patient. We started from a patient-specific model which was constructed from medical images. Exiting flow boundary conditions have been developped, based on a 3-element Windkessel model to approximate physiological conditions. The parameters of the Windkessel model were calibrated with in vivo measurements of flow rate and pressure. The influence of the selected viscosity of red blood cells on the flow and wall shear stress (WSS) was investigated. Results obtained from this model were compared to those of the Newtonian model, and to those of a generalized Newtonian model, as well as to in vivo dynamic data from 4D MRI during a cardiac cycle. Upon evaluating the results, the MPTT model shows better agreement with the MRI data during the systolic and diastolic phases than the Newtonian or generalized Newtonian model, which confirms our interest in using a complex viscoelastic model.     

Liquid saturation in concurrent gas-liquid downflow through packed beds

The total and dynamic liquid saturation under concurrent gas-liquid downflow through packed beds were experimentally measured for non-foaming, foaming Newtonian and non-Newtonian liquids. The variables include the column diameter, packing size and shape, flow rate of the phases, and physical properties. Correlations were presented in terms of Lockhart-Martinelli parameter, χ for non-foaming Newtonian and non-Newtonian liquids and in terms of modified Lockhart-Martinelli parameter, χ′ for foaming Newtonian liquids.     

Rheology and Hydrodynamic Properties of Tolypocladium inflatum Fermentation Broth and Its Simulation

A physico-chemical, two phase simulated pseudoplastic fermentation (SPF) broth was investigated in which Solka Floc cellulose fibre was used to simulate the filamentous biomass, and a mixture of 0.1% (w/v) carboxymethyl cellulose (CMC) and 0.15 M aqueous sodium chloride was used to simulate the liquid fraction of the fermentation broth. An investigation of the rheological behaviour and hydrodynamic properties of the SPF broth was carried out, and compared to both a fungal Tolypocladium inflatum fermentation broth and a CMC solution in a 50 L stirred tank bioreactor equipped with conventional Rushton turbines. The experimental data confirmed the ability of the two phase SPF broth to mimic both the T. inflatum broth bulk rheology as well as the mixing and mass transfer behaviour. In contrast, using a homogeneous CMC solution with a similar bulk rheology to simulate the fermentation resulted in a significant underestimation of the mass transfer and mixing times. The presence of the solid phase and its microstructure in the SPF broth appear to play a significant role in gas holdup and bubble size, thus leading to the different behaviours. The SPF broth seems to be a more accurate simulation fluid that can be used to predict the bioreactor mixing and mass transfer performance in filamentous fermentations, in comparison with CMC solutions used in some previous studies.