Motion and deformation of a droplet in a microfluidic cross-junction.

In this paper we investigate computationally the transient deformation of a droplet flowing along the centerline of a microfluidic cross-junction device. We consider naturally buoyant droplets with size smaller than the cross-section of the square channels comprising the cross-junction, and investigate low-to-strong flow rates and a wide range of fluids viscosity ratio. Our investigation shows that the intersecting flows at the cross-junction act like a constriction, and thus the droplet shows a rich deformation behavior as it passes through the micro-junction. Our work highlights the three-dimensional effects of the asymmetric microfluidic geometry on the droplet deformation, and the different effects of the viscosity ratio on the droplet's overall length scales and the local length scales at the droplet edges. The large edge curvatures and thus the small local length scales developed transiently, especially at the tail of low-viscosity droplets, reveal that the current investigation is a multi-length interfacial dynamics problem.

Determining a membrane's shear modulus, independent of its area-dilatation modulus, via capsule flow in a converging micro-capillary.

Determination of the elastic properties of the membrane of artificial capsules is essential for the better design of the various devices that are utilized in their engineering and biomedical applications. However this task is complicated owing to the combined effects of the shear and area-dilatation moduli on the capsule deformation. Based on computational investigation, we propose a new methodology to determine a membrane's shear modulus, independent of its area-dilatation modulus, by flowing strain-hardening capsules in a converging micro-capillary of comparable size under Stokes flow conditions, and comparing the experimental measurements of the capsule elongation overshooting with computational data. The capsule prestress, if any, can also be determined with the same methodology. The elongation overshooting is practically independent of the viscosity ratio for low and moderate viscosity ratios, and thus a wide range of capsule fluids can be employed. Our proposed experimental device can be readily produced via glass fabrication while owing to the continuous flow in the micro-capillary, the characterization of a large number of artificial capsules is possible.

Intra-specific variation in Ni tolerance, accumulation and translocation patterns in the Ni-hyperaccumulator Alyssum lesbiacum.

A hydroponic experiment was conducted to investigate inter-population variation in Ni tolerance, accumulation and translocation patterns in Alyssum lesbiacum. The in vitro results were compared to field data (soil bioavailable and leaf Ni concentrations) so as to examine any potential relationship between hydroponic and natural conditions. Seeds from the four major existing populations of A. lesbiacum were used for the cultivation of plantlets in solution cultures with incrementally increasing Ni concentrations (ranging from 0 to 250 µmol L(-1) NiSO4). Ni accumulation and tolerance of shoots and roots, along with initial seed Ni concentration for each population were measured. The ratio of root or shoot length of plantlets grown in NiSO4 solutions to root or shoot lengths of plantlets grown in the control solution was used as tolerance index. For the range of metal concentrations used, A. lesbiacum presented significant inter-population variation in Ni tolerance, accumulation and translocation patterns. Initial seed Ni concentration was positively correlated to shoot Ni accumulation. A significant positive relationship between tolerance and accumulation was demonstrated. Initial seed Ni concentration along with physiological differences in xylem loading and Ni translocation of each population, appear to be the determining factors of the significant inter-population variation in Ni tolerance and accumulation. Our results highlight the inter-population variation in Ni tolerance and accumulation patterns in the Ni-hyperaccumulator A. lesbiacum and give support to the suggestion that the selection of metal hyperaccumulator species with enhanced phytoremediation efficiency should be considered at the population level.

Transient dynamics of an elastic capsule in a microfluidic constriction.

In this paper we investigate computationally the transient dynamics of an elastic capsule flowing in a square microchannel with a rectangular constriction, and compare it with that of a droplet. The confinement and expansion dynamics of the fluid flow results in a rich deformation behavior for the capsule, from an elongated shape at the constriction entrance, to a flattened parachute shape at its exit. Larger capsules are shown to take more time to pass the constriction and cause higher additional pressure difference, owing to higher flow blocking. Our work highlights the effects of two different mechanisms for non-tank-treading transient capsule dynamics. The capsule deformation results from the combined effects of the surrounding and inner fluids' normal stresses on the soft particle's interface, and thus when the capsule viscosity increases, its transient deformation decreases, as for droplets. However, the capsule deformation is not able to create a strong enough inner circulation (owing to restrictions imposed by the material membrane), and thus the viscosity ratio does not affect much the capsule velocity and the additional pressure difference. In addition, the weak inner circulation results in a positive additional pressure difference ΔP+ even for low-viscosity capsules, in direct contrast to low-viscosity droplets which create a negative ΔP+. Our findings suggest that the high cytoplasmatic viscosity, owing to the protein hemoglobin required for oxygen transport, does not affect adversely the motion of non-tank-trading erythrocytes in vascular capillaries.

Deformation of an elastic capsule in a rectangular microfluidic channel.

In the present study we investigate computationally the deformation of an elastic capsule in a rectangular microfluidic channel and compare it with that of a droplet. In contrast to the bullet or parachute shape in a square or cylindrical channel where the capsule extends along the flow direction, in a rectangular channel the capsule extends mainly along the less-confined lateral direction of the channel cross-section (i.e. the channel width), obtaining a pebble-like shape. The different shape evolution in these two types of solid channels results from the different tension development on the capsule membrane required for interfacial stability. Furthermore, in asymmetric channel flows, capsules show a different deformation compared to droplets with constant surface tension (which extend mainly along the flow direction) and to vesicles which extend along the more-confined channel height. Therefore, our study highlights the different stability dynamics associated with these three types of interfaces. Our findings suggest that the erythrocyte deformation in asymmetric vessels (which is similar to that of capsules) results from the erythrocyte's inner spectrin skeleton rather than from its outer lipid bilayer.

Analysis of the variation in the determination of the shear modulus of the erythrocyte membrane: Effects of the constitutive law and membrane modeling.

Despite research spanning several decades, the exact value of the shear modulus Gs of the erythrocyte membrane is still ambiguous, and a wealth of studies, using measurements based on micropipette aspirations, ektacytometry systems and other flow chambers, and optical tweezers, as well as application of several models, have found different average values in the range 2-10µN/m. Our study shows that different methodologies have predicted the correct shear modulus for the specific membrane modeling employed, i.e., the variation in the shear modulus determination results from the specific membrane modeling. Available experimental findings from ektacytometry systems and optical tweezers suggest that the dynamics of the erythrocyte membrane is strain hardening at both moderate and large deformations. Thus the erythrocyte shear modulus cannot be determined accurately using strain-softening models (such as the neo-Hookean and Evans laws) or strain-softening/strain-hardening models (such as the Yeoh law), which overestimate the erythrocyte shear modulus. According to our analysis, the only available strain-hardening constitutive law, the Skalak et al. law, is able to match well both deformation-shear rate data from ektacytometry and force-extension data from optical tweezers at moderate and large strains, using an average value of the shear modulus of Gs=2.4-2.75µN/m, i.e., very close to that found in the linear regime of deformations via force-extension data from optical tweezers, Gs=2.5±0.4µN/m. In addition, our analysis suggests that a standard deviation in Gs of 0.4-0.5µN/m (owing to the inherent differences between erythrocytes within a large population) describes well the findings from optical tweezers at small and large strains as well as from micropipette aspirations.

Tank-treading of swollen erythrocytes in shear flows.

In this paper, we investigate computationally the oscillatory tank-treading motion of healthy swollen human erythrocytes (owing to lower than physiological plasma osmolarity) in shear flows with capillary number Ca=O(1) and small to moderate viscosity ratios 0.01≤λ≤2.75. Swollen cells show similar shear flow dynamics with normal cells but with significantly higher inclination and tank-treading speed owing to the higher cell thickness. For a given viscosity ratio, as the flow rate increases, the steady-state erythrocyte length L (in the shear plane) increases logarithmically while its depth W (normal to the shear plane) decreases logarithmically; increase of the viscosity ratio results in lower cell deformation. The erythrocyte width S, which exists in the shear plane, is practically invariant in time, flow rate, and viscosity ratio and corresponds to a real cell thickness of about 2.5 µm at physiological osmolarity (300 mO) and 3.4 µm at an osmolarity of 217 mO. The erythrocyte inclination decreases as the flow rate increases or as the surrounding fluid viscosity decreases, owing to the increased inner rotational flow which tends to align the cell toward the flow direction. The ektacytometry deformation of swollen cells increases logarithmically with the shear stress but with a slower slope than that for normal cells owing mainly to the higher orientation of the more swollen cells. As the cell swelling increases, the tank-treading period decreases owing to the higher thickness of the actual cell which overcomes the opposite action of the reduced shape-memory effects (i.e., the more spherical-like erythrocyte's reference shape of shearing resistance). The local area incompressibility tensions from the lipid bilayer increase with the cell swelling and cause a higher cytoskeleton prestress; this increased prestress results in smaller, but still measurable, local area changes on the spectrin skeleton of the more swollen erythrocytes. Our work provides insight on the effects of clinical syndromes and biophysical processes associated with lowered plasma osmolarity (and thus higher cell swelling) such as inappropriate antidiuretic hormone secretion and diuretic therapy.

Local social capital and the acceptance of Protected Area policies: an empirical study of two Ramsar river delta ecosystems in northern Greece.

Managing Protected Areas (PAs) is a challenging task, and globally many instruments have been utilised for this purpose. Existing research demonstrates that the effectiveness of these instruments is highly dependent on their social acceptability among local communities resident within PAs. Consequently, investigating local attitudes and perceptions of Protected Area (PA) policies has been emphasised in recent studies. Drawing on empirical work conducted in two National Parks including river delta ecosystems designated as Ramsar wetlands in northern Greece, this paper examines local residents' perceptions of three hypothesized policy options (regulatory, market-based and participatory) for Park management. The influence of social capital elements (social trust, institutional trust and social networks) on residents' perceptions is explored. The findings reveal a high degree of importance attached by resident communities to Park designation in both PAs, though residents' perceptions of the proposed management options varied. The regulatory option was regarded as the least restrictive, while the most restrictive was perceived to be the market-based option. However, greater benefits were identified by residents from the market-based option, while the fewest benefits were considered to arise from the proposed regulatory option. Furthermore, local residents' perceptions were significantly shaped by the proposed management and decision-making structure offered under each policy option. The influence of different social capital elements on residents' perceptions also varied in the study sample, with social trust and institutional trust positively correlated with the benefits that were perceived to arise from the different policy options. Moreover, when social capital was measured as an aggregate indicator at the level of the individual, it was positively correlated with perceived environmental benefits.

Comment on "Tank-treading and tumbling frequencies of capsules and red blood cells".

In a recent computational investigation, Yazdani et al. [Phys. Rev. E 83, 046305 (2011)] reported an exponential (logarithmic) dependence of the tank-treading frequency F(tt) with the viscosity ratio λ at low (moderate) viscosity ratios for erythrocytes in shear flows. We argue that the authors misinterpreted the inverse linear dependence on λ of the tank-treading frequency F(tt), as found by Wodson and Dimitrakopoulos [Biophys. J. 99, 2906 (2010)], owing to the fact that Yazdani et al. plotted their frequency-versus-λ results in a log-log plot.

Motion of an elastic capsule in a square microfluidic channel.

In the present study we investigate computationally the steady-state motion of an elastic capsule along the centerline of a square microfluidic channel and compare it with that in a cylindrical tube. In particular, we consider a slightly over-inflated elastic capsule made of a strain-hardening membrane with comparable shearing and area-dilatation resistance. Under the conditions studied in this paper (i.e., small, moderate, and large capsules at low and moderate flow rates), the capsule motion in a square channel is similar to and thus governed by the same scaling laws with the capsule motion in a cylindrical tube, even though in the channel the cross section in the upstream portion of large capsules is nonaxisymmetric (i.e., square-like with rounded corners). When the hydrodynamic forces on the membrane increase, the capsule develops a pointed downstream edge and a flattened rear (possibly with a negative curvature) so that the restoring tension forces are increased as also happens with droplets. Membrane tensions increase significantly with the capsule size while the area near the downstream tip is the most probable to rupture when a capsule flows in a microchannel. Because the membrane tensions increase with the interfacial deformation, a suitable Landau-Levich-Derjaguin-Bretherton analysis reveals that the lubrication film thickness h for large capsules depends on both the capillary number Ca and the capsule size a; our computations determine the latter dependence to be (in dimensionless form) h ~ a(-2) for the large capsules studied in this work. For small and moderate capsule sizes a, the capsule velocity Ux and additional pressure drop ΔP+ are governed by the same scaling laws as for high-viscosity droplets. The velocity and additional pressure drop of large thick capsules also follow the dynamics of high-viscosity droplets, and are affected by the lubrication film thickness. The motion of our large thick capsules is characterized by a Ux-U ~ h ~ a(-2) approach to the undisturbed average duct velocity and an additional pressure drop ΔP+ ~a(3)/h ~ a(5). By combining basic physical principles and geometric properties, we develop a theoretical analysis that explains the power laws we found for large capsules.

Oscillatory tank-treading motion of erythrocytes in shear flows.

In this paper, we investigate the oscillatory dynamics of the tank-treading motion of healthy human erythrocytes in shear flows with capillary number Ca = O(1) and small to moderate viscosity ratios 0.01 ≤ λ ≤ 1.5. These conditions correspond to a wide range of surrounding medium viscosities (4-600 m Pa s) and shear flow rates (2-560 s(-1)), and match those used in ektacytometry systems. For a given viscosity ratio, as the flow rate increases, the steady-state erythrocyte length L (in the shear plane) increases logarithmically while its depth W (normal to the shear plane) decreases logarithmically. In addition, the flow rate increase dampens the oscillatory erythrocyte inclination but not its length oscillations (which show relative variations of about 5-8%). For a given flow rate, as the viscosity ratio increases, the erythrocyte length L contracts while its depth W increases (i.e., the cell becomes less deformed) with a small decrease in the length variations. The average orientation angle of the erythrocyte shows a significant decrease with the viscosity ratio as does the angle oscillation while the oscillation period increases. These trends continue in higher viscosity ratios resulting eventually in the transition from a (weakly oscillatory) tank-treading motion to a tumbling motion. Our computations show that the erythrocyte width S, which exists in the shear plane, is practically invariant in time, capillary number, and viscosity ratio, and corresponds to a real cell thickness of about 2.5 µm. Comparison of our computational results with the predictions of (low degree-of-freedom) theoretical models and experimental findings, suggests that the energy dissipation due to the shape-memory effects is more significant than the energy dissipation due to the membrane viscosity. Our work shows that the oscillatory tank-treading motion can account for more than 50% of the variations found in ektacytometry systems; thus, researchers who wish to study inherent differences between erythrocytes within a population must devise a way of monitoring individual cells over time so that they can remove the oscillation effects.

Tank-treading of erythrocytes in strong shear flows via a nonstiff cytoskeleton-based continuum computational modeling.

We develop a computationally efficient cytoskeleton-based continuum erythrocyte algorithm. The cytoskeleton is modeled as a two-dimensional elastic solid with comparable shearing and area-dilatation resistance that follows a material law (Skalak, R., A. Tozeren, R. P. Zarda, and S. Chien. 1973. Strain energy function of red blood cell membranes. Biophys. J. 13:245-264). Our modeling enforces the global area-incompressibility of the spectrin skeleton (being enclosed beneath the lipid bilayer in the erythrocyte membrane) via a nonstiff, and thus efficient, adaptive prestress procedure which accounts for the (locally) isotropic stress imposed by the lipid bilayer on the cytoskeleton. In addition, we investigate the dynamics of healthy human erythrocytes in strong shear flows with capillary number Ca =O(1) and small-to-moderate viscosity ratios 0.001 ≤ λ ≤ 1.5. These conditions correspond to a wide range of surrounding medium viscosities (4-600 mPa s) and shear flow rates (0.02-440 s(-1)), and match those used in ektacytometry systems. Our computational results on the cell deformability and tank-treading frequency are compared with ektacytometry findings. The tank-treading period is shown to be inversely proportional to the shear rate and to increase linearly with the ratio of the cytoplasm viscosity to that of the suspending medium. Our modeling also predicts that the cytoskeleton undergoes measurable local area dilatation and compression during the tank-treading of the cells.

General stabilizing effects of plant diversity on grassland productivity through population asynchrony and overyielding.

Insurance effects of biodiversity can stabilize the functioning of multispecies ecosystems against environmental variability when differential species' responses lead to asynchronous population dynamics. When responses are not perfectly positively correlated, declines in some populations are compensated by increases in others, smoothing variability in ecosystem productivity. This variance reduction effect of biodiversity is analogous to the risk-spreading benefits of diverse investment portfolios in financial markets. We use data from the BIODEPTH network of grassland biodiversity experiments to perform a general test for stabilizing effects of plant diversity on the temporal variability of individual species, functional groups, and aggregate communities. We tested three potential mechanisms: reduction of temporal variability through population asynchrony; enhancement of long-term average performance through positive selection effects; and increases in the temporal mean due to overyielding. Our results support a stabilizing effect of diversity on the temporal variability of grassland aboveground annual net primary production through two mechanisms. Two-species communities with greater population asynchrony were more stable in their average production over time due to compensatory fluctuations. Overyielding also stabilized productivity by increasing levels of average biomass production relative to temporal variability. However, there was no evidence for a performance-enhancing effect on the temporal mean through positive selection effects. In combination with previous work, our results suggest that stabilizing effects of diversity on community productivity through population asynchrony and overyielding appear to be general in grassland ecosystems.

Spindles, cusps, and bifurcation for capsules in Stokes flow.

Interfacial dynamics of membrane-enclosed fluid volumes in viscous flows is complicated due to the coupling of the fluid dynamics with the membrane properties. Based on computational investigation via our interfacial spectral boundary element algorithm, our study shows that a (strain-hardening) Skalak-type capsule in a planar extensional Stokes flow develops steady-state shapes whose edges from spindled become cusped with increasing flow rate owing to a transition of the edge tensions from tensile to compressive. A bifurcation in the steady-state shapes is also found (i.e., existence of both spindled and cusped edges for a range of high flow rates) by implementing different transient processes, owing to the different evolution of the membrane tensions.

Hypotheses, mechanisms and trade-offs of tolerance and adaptation to serpentine soils: from species to ecosystem level.

Understanding the relative importance of the abiotic environment and species interactions in determining the distribution and abundance of organisms has been a challenge in ecological research. Serpentine substrata are stressful environments for plant growth due to multiple limitations, collectively called the "serpentine syndrome". In the present review, our aim is not only to describe recent work in serpentine ecology, but also to highlight specific mechanisms of species tolerance and adaptation to serpentine soils and their effects on community structure and ecosystem functioning. We present hypotheses of the development of serpentine endemism and a description of functional traits of serpentine plants together with a synthesis of species interactions in serpentine soils and their effects on community structure and ecosystem productivity. In addition, we propose hypotheses about the effects of the 'serpentine syndrome' on ecosystem processes including productivity and decomposition.

Stress, birefringence, and conformational relaxation of an initially straight stiff bead-rod polymer.

The stress and optical relaxation of an initially straight stiff polymer chain are studied through Brownian dynamics simulations (based on a semiflexible bead-rod model) covering a broad range of time scales and polymer lengths. The strong stress component sigma11 (where "1" is the direction of the original alignment) is shown to be associated with the chain's longitudinal relaxation while the weak stress component sigma22 = sigma33 is shown to depend on the chain's transverse relaxation. The two independent stress components follow a different relaxation; this anisotropy is shown to result from the participation of the different relaxation modes in the transverse direction. The chain's optical relaxation is shown to be affected by the longitudinal dynamics only. The early relaxation of the strong stress component sigma11 and that of the chain's optical properties constitute a universal behavior--i.e., valid for any stiffness of the bead-rod chain, since at the early times the bending forces do not affect the longitudinal dynamics. Based on the knowledge of the physical mechanism and the chain's conformational behavior, we predict and explain the polymer stress and optical relaxation. A nonlinear stress-optic law (valid for any time and chain stiffness) is derived based on the identified relation of the chain configuration with the optical properties and the polymer stress. A coarse-grain model describing extended semiflexible bead road chains is also derived.

Normal force exerted on vascular endothelial cells.

Hemodynamic forces play an important role in the normal and pathological behavior of vascular endothelial cells as recent studies on the shear stress over the endothelium have shown. Based on computational investigation and scaling analysis, our study shows that the normal force contributes significantly to the total force on the endothelial cells even in large vessels. Therefore, our study suggests that the functions of endothelial cells are also affected by the normal forces exerted on them. The effects of the normal force are more pronounced for smaller vessels and/or less spread cells.

Longitudinal relaxation of initially straight flexible and stiff polymers.

The relaxation mechanism of an initially straight flexible or stiff polymer chain of length N in a viscous solvent is studied through Brownian dynamics simulations covering a broad range of time scales. After the short-time free diffusion, the chain's longitudinal reduction R2(0)-R2 approximately Nt1/2 at early intermediate times is shown to constitute a universal behavior for any chain stiffness caused by a quasisteady T approximately Nt(-1/2) relaxation of tensions associated with the deforming action of the Brownian forces. Stiff chains with a persistence length E > or = N are shown to exhibit a late intermediate-time longitudinal reduction R2(0)-R2 approximately N2E(-3/4)t1/4 associated with a T approximately N2E(-3/4)t(-3/4) relaxation of tensions affected by the deforming Brownian and the restoring bending forces.

Short- and intermediate-time behavior of the linear stress relaxation in semiflexible polymers.

The linear viscoelasticity of semiflexible polymers is studied through Brownian Dynamics simulations covering a broad range of chain stiffness and time scales. Our results agree with existing theoretical predictions in the flexible and stiff limits; however, we find that over a wide intermediate-time window spanning several decades, the stress relaxation is described by a single power law t(-alpha), with the exponent alpha apparently varying continuously from 1/2 for flexible chains, to 5/4 for stiff ones. Our study identifies the limits of validity of the t(-3/4) power law at short times predicted by recent theories. An additional regime is identified, the "ultrastiff" chains, where this behavior disappears. In the absence of Brownian motion, the purely mechanical stress relaxation produces a t(-3/4) power law for both short and intermediate times.

PROFILE: Tourism Contribution to Agro-Ecosystems Conservation: The Case of Lesbos Island, Greece.

/ The modernization of agriculture and the development of other economic sectors have prompted the abandonment of cultivated areas, which are marginally productive. Specifically, olive groves in Greece are transformed into pastures due to their location in inaccessible mountainous regions where breeding and raising of sheep and goats are the main economic activities. Overgrazing degrades the environment, exhausts natural resources, and prevents natural regeneration. The Greek islands have limited possibilities of development, except for their coastal areas where the growth of tourism is possible.The objective of this study was to investigate the impact of tourism activities on olive tree cultivation and the human population of the island of Lesbos. The presence or absence of tourism is related with the maintenance or abandonment of olive tree cultivation and population changes for each community. A spatial segregation of the island is evident, related to tourist development, olive tree cultivation, and population change. The results of the study demonstrate that in communities where tourism plays an important role olive tree cultivation is preserved and the population is stable. The preservation of the agro-ecosystem is assured while the olive groves remain productive. Simultaneously, the landscape, which provides specific attractions for tourism, is not altered.