Internal Viscosities Research Articles

Reply to the 'Comment on "Dynamics and rheology of vesicles under confined Poiseuille flow"' by G. Coupier and T. Podgorski, Soft Matter, 2024, 20, DOI: 10.1039/D3SM01679J.

In this answer, we provide our arguments in support of the possibility to observe the single file-organization of red blood cells in microvessels and the resulting unexpectedly weak increase of blood viscosity with increasing hematocrit, the physiological relevance of which was questioned in the comment. The key element is that the equivalent diameter in 3D for the maximal hematocrit corresponding to a single file of red blood cells is about 10 µm and not 20 µm, as in 2D. In addition, the viscosity contrast (ratio between the cell internal and external viscosities) value must be chosen in our 2D simulation in a such a way that the effective viscosity (a linear combination of the internal, external and membrane viscosities) be close to that of a real RBC. Taking these two facts into account, we find a reasonable agreement between our 2D viscosity simulations data and experimental data, despite the crude 2D assumption.

Internal Energy Relaxation Processes and Bulk Viscosities in Fluids

Internal energy relaxation processes in fluid models derived from the kinetic theory are revisited, as are related bulk viscosity coefficients. The apparition of bulk viscosity coefficients in relaxation regimes and the links with equilibrium one-temperature bulk viscosity coefficients are discussed. First, a two-temperature model with a single internal energy mode is investigated, then a two-temperature model with two internal energy modes and finally a state-to-state model for mixtures of gases. All these models lead to a unique physical interpretation of the apparition of bulk viscosity effects when relaxation characteristic times are smaller than fluid times. Monte Carlo numerical simulations of internal energy relaxation processes in model gases are then performed, and power spectrums of density fluctuations are computed. When the energy relaxation time is smaller than the fluid time, both the two temperature and the single-temperature model including bulk viscosity yield a satisfactory description. When the energy relaxation time is larger than the fluid time, however, only the two-temperature model is in agreement with Boltzmann equation. The quantum population of a He-H2 mixture is also simulated with detailed He-H2 cross sections, and the resulting bulk viscosity evaluated from the Green–Kubo formula is in agreement with the theory. The impact of bulk viscosity in fluid mechanics is also addressed, as well as various mathematical aspects of internal energy relaxation and Chapman–Enskog asymptotic expansion for a two-temperature fluid model.

Effect of the inlet oil temperature on vibration characteristics of the high-speed turbocharger rotor system

The inlet oil temperature of the rotor system with high-speed and light-load turbocharger will change during operation, which will change the vibration characteristics of the rotor system and even cause vibration accidents. Taking a certain type of high-speed and light-load turbocharger rotor system as the research object, the changes in oil film viscosity, friction power consumption, oil film temperature rise, and ring speed ratio with the inlet oil temperature of floating ring bearings are analyzed. A dynamic finite-element model of the turbocharger rotor–floating-ring-bearing system is constructed, and the finite-element model is verified through the critical speed and colormap spectrogram. The Newmark integral method is used to analyze the nonlinear transient response of the rotor system, and the influence of the inlet oil temperature on the vibration response characteristics of the rotor system is studied. The results show that an increase in the inlet oil temperature leads to a decrease in the internal and external oil film viscosities, frictional power consumption, temperature rise, and an increase in the ring speed ratio. When the inlet oil temperature increases from 50 °C to 130 °C, the amplitude of the inner oil film oscillation will gradually decrease, but the amplitude of the outer oil film vortex will gradually increase, and the journal speed point where the inner oil film oscillation and the outer oil film vortex will appear about 30% in advance. In summary, the rotor vibration is better when the inlet oil temperature is about 90 °C. The conclusion of this paper can provide a theoretical reference for selecting the operating parameters of the rotor system with the least vibration for high-speed light-load turbochargers.

Internal Viscosity-Dependent Margination of Red Blood Cells in Microfluidic Channels.

Cytoplasmic viscosity-dependent margination of red blood cells (RBC) for flow inside microchannels was studied using numerical simulations, and the results were verified with microfluidic experiments. Wide range of suspension volume fractions or hematocrits was considered in this study. Lattice Boltzmann method for fluid-phase coupled with spectrin-link method for RBC membrane deformation was used for accurate analysis of cell margination. RBC margination behavior shows strong dependence on the internal viscosity of the RBCs. At equilibrium, RBCs with higher internal viscosity marginate closer to the channel wall and the RBCs with normal internal viscosity migrate to the central core of the channel. Same margination pattern has been verified through experiments conducted with straight channel microfluidic devices. Segregation between RBCs of different internal viscosity is enhanced as the shear rate and the hematocrit increases. Stronger separation between normal RBCs and RBCs with high internal viscosity is obtained as the width of a high aspect ratio channel is reduced. Overall, the margination behavior of RBCs with different internal viscosities resembles with the margination behavior of RBCs with different levels of deformability. Observations from this work will be useful in designing microfluidic devices for separating the subpopulations of RBCs with different levels of deformability that appear in many hematologic diseases such as sickle cell disease (SCD), malaria, or cancer.

Role of viscosity coefficients during spreading and coalescence of droplets in liquids

Experiments with immersed drops spreading on a surface or with two drops coalescing find that the contact diameter obeys a power law in time and in the internal and external viscosities.

On the anisotropic response of a Janus drop in a shearing viscous fluid

The force and couple that result from the shearing motion of a viscous, unbounded fluid on a Janus drop are the subjects of this investigation. A pair of immiscible, viscous fluids comprise the Janus drop and render it with a ‘perfect’ shape: spherical with a flat, internal interface, in which each constituent fluid is bounded by a hemispherical domain of equal radius. The effect of the arrangement of the internal interface (drop orientation) relative to the unidirectional shear flow is explored within the Stokes regime. Projection of the external flow into a reference frame centred on the drop simplifies the analysis to three cases: (i) a shear flow with a velocity gradient parallel to the internal interface, (ii) a hyperbolic flow, and (iii) two shear flows with a velocity gradient normal to the internal interface. Depending on the viscosity of the internal fluids, the Janus drop behaves as a simple fluid drop or as a solid body with broken fore and aft symmetry. The resultant couple arises from both the straining and swirling motions of the external flow in analogy with bodies of revolution. Owing to the anisotropic resistance of the Janus drop, it is inferred that the drop can migrate lateral to the streamlines of the undisturbed shear flow. The grand resistance matrix and Bretherton constant are reported for a Janus drop with similar internal viscosities.

Gelled Crude Oil Particle Deformation under Hydraulic Suspension Transport Investigated by Numerical Simulation

In hydraulic suspension transport, the gelled crude oil particles are known to change shape in response to local flow conditions. The phase field method is used to simulate the deformation for the gelled crude oil particle with the same internal and external fluid viscosities. For this purpose, an Image Pro Plus software records the major and minor axises and thus, analyzes digitally its deformation degree. Initially spheroidal oil droplet is simulated and it is shown that the gelled crude oil particle exhibits deformation behavior as the movement and its final stable shape close to oval. The deformation behavior is response to shear stress with a time of 0.08s delayed. In the range of delayed time, the gelled crude oil particle deforms with a little degree and after the delayed time, the deformation degree increases seriously.

MRI of adrenal lymphangioma: a case report.

A 42-year-old female admitted with non-specific abdominal pain was evaluated with abdominal sonography which detected a multiloculated cystic lesion in the left perirenal area. Her clinical history was unremarkable. Laboratory examinations revealed no abnormality. The patient was further evaluated with abdominal MR imaging which demonstrated a multiloculated, multicystic lesion at the left adrenal gland with different internal viscosities (Figure 1A). The septations between the cysts showed contrast enhancement but no nodular area was detected at septations or at the wall (Figure 1B). The patient underwent an operation of transperitoneal laparascopic adrenalectomy. The histopathological evaluation of the tumor revealed the diagnosis of lymphangioma (Figure 2).

Deep earth recycling in the Hadean and constraints on surface tectonics

The Hadean mantle was efficiently heated from high internal heat production, high rates of impact bombardment, and primordial heat from accretion. As a result a strong case is made for extremely high internal temperatures, low internal viscosities, and extremely vigorous mantle convection. Previous studies of mixing in such high-Rayleigh number convective environments indicate that chemically heterogeneous mantle anomalies should have efficiently remixed into the mantle on timescales of less than 100 Myr. However, ¹⁴²Nd and ¹⁸²W isotope studies indicate that heterogeneous mantle domains survived, without mixing, for over 2 Gyr—at odds with expected mixing rates. Similarly, concentrations of platinum group elements in Archean komatiites, purportedly due to the later veneer of meteoritic addition on the Earth, only achieve current levels at 2.7 Ga—indicating a time lag of almost 1 to 2 Gyr in mixing this material thoroughly into the mantle. Previous studies have sought to explain slow Archean mantle mixing via mantle layering due to endothermic phase changes, or anomalously viscous blobs of material, with limited efficacy. Here we pursue another explanation for inefficient mantle mixing in the Hadean: tectonic regime. A number of lines of evidence suggest that resurfacing in the Archean was episodic, and extending these models to Hadean times implies the Hadean was characterized by long periods of tectonic quiescence. We explore mixing times in 3D spherical-cap models of mantle convection, which incorporate vertically stratified and temperature-dependent viscosities. We show that mixing in stagnant-lid regimes is, at the extreme, over an order of magnitude less efficient than mobile-lid mixing, and for plausible Rayleigh numbers and internal heat production, the lag in Hadean convective recycling can be explained. The attractiveness of this model is that it not only explains the long-lived ¹⁴²Nd and ¹⁸²W anomalies, but also posits an explanation for the delay between accretion of the late veneer—between 4.5 to 3.8 Ga on a stagnant surface—and its fully mixed signature apparent in elevated PGEs in 2.7 Ga komatiites. It also provides an explanation for the 400 Myrs of immobility of the mafic protolith from which the Jack Hill zircons were sourced, and retards early heat loss from the mantle, providing a solution to the “Archean thermal catastrophe” of parameterized Earth evolution models.

How does confinement affect the dynamics of viscous vesicles and red blood cells?

Despite its significance in microfluidics, the effect of confinement on the transition from the tank-treading (steady motion) to the tumbling (unsteady motion) dynamical state of deformable micro-particles has not been studied in detail. In this paper, we investigate the dynamics of a single viscous vesicle under confining shear as a general model system for red blood cells, capsules, or viscous droplets. The transition from tank-treading to tumbling motion can be triggered by the ratio between internal and external fluid viscosities. Here, we show that the transition can be induced solely by reducing the confinement, keeping the viscosity contrast constant. The observed dynamics results from the variation of the relative importance of viscous-, pressure-, and lubrication-induced torques exerted upon the vesicle. Our findings are of interest for designing future experiments or microfluidic devices: the possibility to trigger the tumbling-to-tank-treading transition either by geometry or viscosity contrast alone opens attractive possibilities for microrheological measurements as well as the detection and diagnosis of diseased red blood cells in confined flow.

Magnitude of weakening during crustal-scale shear zone development

We describe and apply a field-based approach for calculating the bulk strength of a heterogeneous material to a crustal-scale shear zone defining the margin of the Ma Parry Sound domain in the Grenville Province of southeastern Ontario. Using a numerical method, we calculate bulk strength, defined as effective viscosity, as the ratio between the surface traction needed to deform a square block in simple shear and the velocity gradient across that block. We use natural shear zone geometries to define the internal block structure and assign internal relative viscosities based primarily on textural criteria. The margin of the Parry Sound domain developed into the km-scale Twelve Mile Bay shear zone, accommodating several tens of km of transport, while the domain interior remained rigid. Fracturing and fluid infiltration drove development of an amphibolite facies meter-scale shear zone network that evolved into the Twelve Mile Bay structure. We analyzed three sites across the ∼5 km-wide strain gradient from near the granulitic domain to the large scale shear zone. The rocks at the shear zone margin weakened by approximately 30%. Those in the core weakened by at least 77% and probably by an order of magnitude. These values lie between but differ substantively from the isostress and isostrain-rate bounds, indicating that a numerical approach such as presented here markedly improves the accuracy of bulk strength calculations.

EFFECT OF INTERNAL VISCOSITY OF POLYMERIC FLUIDS UNDER STRONG EXTENSIONAL FLOWS

The dumbbell model with internal viscosity for a dilute polymer solution is investigated based on a balance of viscous drag and restoring Brownian forces. An approximate method is used to obtain the solution of extensional stress in closed form in the case of steady flow. For different internal viscosities, this parametric study shows different asymptotic regimes of the extensional viscosity as a function of strain rate. This analysis may explain the attenuation of pressure drop in strong flows from a phenomenological point of view.

Dynamic analysis of polymeric fluid in shear flow for dumbbell model with internal viscosity

The dynamic analysis of semi-flexible polymers, such as DNA molecules, is an important multiscale problem with a wide range of applications in science and bioengineering. In this contribution, a dumbbell model with internal viscosity was studied in steady shear flows of polymeric fluid. The tensors with moments other than second moment were approximated in the terms of second moment tensor. Then, the nonlinear algebraic equation of the second moment conformation tensor was calculated in closed form. Finally, substituting the resulting conformation tensor into the Kramers equation of Hookean spring force, the constitutive equations were obtained. The shear material properties were discussed for different internal viscosities and compared with the results of Brownian dynamics simulation.

The motion of a non-rigid ellipse in a general 2D deformation

A solution for the deformation of a non-rigid viscous elliptical inclusion in a matrix of differing viscosity is developed for the case of a general 2D deformation. A Newtonian rheology is assumed and velocities and stresses are equated at the boundary. An important parameter is the viscosity ratio given by the ratio of the external to the internal viscosities. The dynamics of the behaviour of such inclusions is examined for the cases of pure and simple shear and variable viscosity ratio. In general less viscous inclusions tend to accumulate finite strain more rapidly than more rigid inclusions. Large discordancies between the internal finite strain ellipse orientation and the bulk external finite strain ellipse are to be expected. It is also found that the kinematics of deformation inside an inclusion can often be one of super shear (i.e. kinematic vorticity number, W k, greater than one) even though the external bulk kinematics is one of pure or simple shear ( W k=0 or 1). Objects tend to continuously rotate (the viscosity ratio must be less than 0.5) or asymptotically rotate (i.e. tend to ultimately align parallel to a fixed direction). This solution has many applications, some of which are briefly considered.

Grafting of PVA in Miniemulsion Copolymerizations of n-Butyl Acrylate and Methyl Methacrylate Using Water-Soluble, Partially Water-Soluble, and Oil-Soluble Initiators

Miniemulsion copolymerizations of methyl methacrylate and n-butyl acrylate initiated with water-soluble (hydrogen peroxide, HPO), partially water-soluble (tert-butyl peroxide, TBHP), and oil-soluble (tert-butyl peroctoate, TBPO) initiators were carried out to study the grafting of poly(vinyl alcohol) (PVA) at the oil/water interface. The amounts of grafted PVA produced in miniemulsion polymerizations initiated with TBHP and TBPO were substantially less than those produced in the corresponding seeded emulsion polymerizations. Differences in the internal viscosities at the respective interfaces were proposed to explain these results. The amount of grafted PVA was determined as a function of the monomer to polymer (M/P) ratio in seeded emulsion polymerizations initiated with TBHP and was found to decrease with increasing M/P ratio. The grafting was followed as a function of conversion in miniemulsion polymerizations initiated with TBPO and where a continuous addition of SFS (sodium formaldehyde sulfoxylate) solution was utilized; the grafting was found to occur mainly in the later stages of the polymerization. Both results strongly support the idea that the different internal viscosities at the interface might affect the termination reactions between primary radicals and PVA macroradicals, thereby resulting in different amounts of grafting. The degree of hydrolysis (DH) of the serum PVA after the miniemulsion polymerizations was determined using FTIR and saponification. On the basis of the results, it was found that aqueous phase and interface grafting occurred in the HPO system; however, interface grafting dominated the TBHP system. In addition, the grafted PVA in the TBHP system was still water-soluble, implying that the grafted chains were short, owing to rapid termination reactions at the interface presumably.

Capillary breakup of a viscous thread surrounded by another viscous fluid

Previous long-wavelength analyses of capillary breakup of a viscous fluid thread in a perfectly inviscid environment show that the asymptotic self-similar regime immediately prior to breakup is given by a balance between surface tension, inertia, and extensional viscous stresses in the thread. In contrast, it is shown here that if viscosity in the external fluid, however small, is included then the asymptotic balance is between surface tension and viscous stresses in the two fluids while inertia is negligible. Scaling estimates for this new balance suggest that both axial and radial scales decrease linearly with time to breakup, so that the aspect ratio remains O(1) with time but scales with viscosity ratio like (μint/μext)1/2 for μint≫μext, where μint and μext are the internal and external viscosities. Numerical solutions to the full Stokes equations for μint=μext confirm the scalings with time and give self-similar behavior near pinching. However, the self-similar pinching region is embedded in a logarithmically large axial advection driven by the increasing range of scales intermediate between that of the pinching region and that of the macroscopic drop. The interfacial shape in the intermediate region is conical with angles of about 6° on one side and 78° on the other.

Large deformation of red blood cell ghosts in a simple shear flow.

Red blood cells are known to change shape in response to local flow conditions. Deformability affects red blood cell physiological function and the hydrodynamic properties of blood. The immersed boundary method is used to simulate three-dimensional membrane-fluid flow interactions for cells with the same internal and external fluid viscosities. The method has been validated for small deformations of an initially spherical capsule in simple shear flow for both neo-Hookean and the Evans-Skalak membrane models. Initially oblate spheroidal capsules are simulated and it is shown that the red blood cell membrane exhibits asymptotic behavior as the ratio of the dilation modulus to the extensional modulus is increased and a good approximation of local area conservation is obtained. Tank treading behavior is observed and its period calculated.

Motion of a deformable capsule through a hyperbolic constriction

A model for the low-Reynolds-number flow of a capsule through a constriction is developed for either constant-flow-rate or constant-pressure-drop conditions. Such a model is necessary to infer quantitative information on the intrinsic properties of capsules from filtration experiments conducted on a dilute suspension of such particles. A spherical capsule, surrounded by an infinitely thin Mooney-Rivlin membrane, is suspended on the axis of a hyperbolic constriction. This configuration is fully axisymmetric and allows the entry and exit phenomena through the pore to be modelled. An integral formulation of the Stokes equations describing the flow in the internal and external domains is developed. It provides a representation of the velocity at any location in the flow as a function of the unknown forces exerted by the boundaries on the fluids. The problem is solved by a collocation technique in the case where the internal and external viscosities are equal. Microscopic quantities (instantaneous geometry, centre of mass velocity, elastic tensions in the membrane) as well as macroscopic quantities (entry time, additional pressure drop or flow rate reduction) are predicted as a function of the capsule intrinsic properties and flow characteristics. The results obtained for a capsule whose initial diameter is larger than that of the constriction throat show that the maximum energy expenditure occurs when the particle centre of mass is still upstream of the throat (typically 1 diameter away), and is thus due to the entry process. For large enough or rigid enough capsules, the model predicts entrance or exit plugging, in agreement with experimental observations. It is then possible to correlate the variation of the pore hydraulic resistance to the flow capillary number (ratio of viscous to elastic forces) and to the size ratio between the pore and the capsule.

Effusive silicic volcanism in the Central Andes: The Chao dacite and other young lavas of the Altiplano‐Puna Volcanic Complex

The largest known Quaternary silicic lava body in the world is Cerro Chao in north Chile, a 14‐km‐long coulée with a volume of at least 26 km3. It is the largest of a group of several closely similar dacitic lavas erupted during a recent (< 100,000 year old) magmatic episode in the Altiplano‐Puna Volcanic Complex (APVC; 21‐24°S) of the Central Andean Volcanic Zone. The eruption of Chao proceeded in three phases. Phase 1 was explosive and produced ∼1 km3 of coarse, nonwelded dacitic pumice deposits and later block and ash flows that form an apron in front of the main lava body. Phase 2 was dominantly effusive and erupted ∼22.5 km3 of magma in the form of a composite couleé covering ∼53 km2 with a 400‐m‐high flow front and a small cone of poorly expanded pumice around the vent. The lava is homogeneous with rare flow banding and vesicular tops and selvages. Ogives (flow ridges) reaching heights of 30 m form prominent features on its surface. Phase 3 produced a 6‐km‐long, 3‐km‐wide flow that emanated from a collapsed dome. Ogives are subdued, and the lava is glassier than that produced in previous phases. All the Chao products are crystal‐rich high‐K dacites and rhyodacites with phenocrysts of plagioclase, quartz, hornblende, biotite, sphene, rare sanidine, and oxides. Phenocryst contents reach 40–60 vol % (vesicle free) in the main phase 2 lavas but are lower in the phase 1 (20–25%) and phase 3 (∼40%) lavas. Ovoid andesitic inclusions with vesicular interiors and chilled margins up to 10 cm are found in the later stages of phase 2 and compose up to 5% of the phase 3 lava. There is little evidence for preemptive zonation of the magma body in composition, temperature (∼840°C), ƒO2 (10−11), or water content, so we propose that eruption of the Chao complex was driven by intrusion of fresh, hot andesitic magma into a crystallizing and largely homogeneous body of dacitic magma. Morphological measurments suggest that the Chao lavas had internal plastic viscosities of 1010 to 1012Pa s, apparent viscosities of 109 Pa s, surface viscosities of 1015 to 1024 Pa s, and a yield strength of 8×105 Pa. These estimates indicate that Chao would have exhibited largely similar rheological properties to other silicic lava extrusions, notwithstanding its high phenocryst content. We suggest that Chao's anomalous size is a function of both the relatively steep local slope (20° to 3°) and the available volume of magma. The eruption duration for Chao's emplacement is thought to have been about 100 to 150 years, with maximum effusion rates of about 25 m3 s−1 for short periods. Four other lavas in the vicinity with volumes of ∼5 km3 closely resemble Chao and are probably comagmatic. The suite as a whole shares a petrologic and chemical similarity with the voluminous regional Tertiary to Pleistocene ignimbrites of the APVC and may be derived from a zone of silicic magmatism that is thought to have been active since the late Tertiary. Chao and the other young lavas may represent either the waning of this system or a new episode fueled by intrusions of mafic magma.

Flow of a capsule through a constriction : application to cell filtration

The motion of a freely suspended capsule (liquid drop surrounded by a deformable membrane) forced to squeeze through an axisymmetric constriction smaller than its initial dimensions is studied by means of a numerical model based on boundary integrals. The flow is driven by a constant pressure difference. The suspending liquid and internal capsule viscosities are equal. It is found that the maximum energy loss is due to entrance effects rather than to the flow in the pore itself. The role of the membrane rigidity can be predicted