German Drazer

Lattice Boltzmann method for non-Newtonian (power-law) fluids.

We study an ad hoc extension of the lattice Boltzmann method that allows the simulation of non-Newtonian fluids described by generalized Newtonian models. We extensively test the accuracy of the method for the case of shear-thinning and shear-thickening truncated power-law fluids in the parallel plate geometry, and show that the relative error compared to analytical solutions decays approximately linear with the lattice resolution. Finally, we also tested the method in the reentrant-flow geometry, in which the shear rate is no longer a scalar and the presence of two singular points requires high accuracy in order to obtain satisfactory resolution in the local stress near these points. In this geometry, we also found excellent agreement with the solutions obtained by standard finite-element methods, and the agreement improves with higher lattice resolution.

Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions

The dynamics of macroscopically homogeneous sheared suspensions of neutrally buoyant, non-Brownian spheres is investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics. We show that the complex dynamics of sheared suspensions can be characterized as a chaotic motion in phase space and determine the dependence of the largest Lyapunov exponent on the volume fraction ϕ. We also offer evidence that the chaotic motion is responsible for the loss of memory in the evolution of the system and demonstrate this loss of correlation in phase space. The loss of memory at the microscopic level of individual particles is also shown in terms of the autocorrelation functions for the two transverse velocity components. Moreover, a negative correlation in the transverse particle velocities is seen to exist at the lower concentrations, an effect which we explain on the basis of the dynamics of two isolated spheres undergoing simple shear. In addition, we calculate the probability distribution function of the transverse velocity fluctuations and observe, with increasing ϕ, a transition from exponential to Gaussian distributions. The simulations include a non-hydrodynamic repulsive interaction between the spheres which qualitatively models the effects of surface roughness and other irreversible effects, such as residual Brownian displacements, that become particularly important whenever pairs of spheres are nearly touching. We investigate, for very dilute suspensions, the effects of such a non-hydrodynamic interparticle force on the scaling of the particle tracer diffusion coefficients D y and D z , respectively, along and normal to the plane of shear, and show that, when this force is very short-ranged, both are proportional to ϕ 2 as ϕ → 0. In contrast, when the range of the non-hydrodynamic interaction is increased, we observe a crossover in the dependence of D y on ϕ, from ϕ 2 to ϕ as ϕ → 0. We also estimate that a similar crossover exists for D z but at a value of ϕ one order of magnitude lower than that which we were able to reach in our simulations.

Adaptation to oxygen deprivation in cultures of human pluripotent stem cells, endothelial progenitor cells, and umbilical vein endothelial cells

Hypoxia plays an important role in vascular development through hypoxia-inducible factor-1alpha (HIF-1alpha) accumulation and downstream pathway activation. We sought to explore the in vitro response of cultures of human embryonic stem cells (hESCs), induced pluripotent stem cells (iPSCs), human endothelial progenitor cells (hEPCs), and human umbilical cord vein endothelial cells (HUVECs) to normoxic and hypoxic oxygen tensions. We first measured dissolved oxygen (DO) in the media of adherent cultures in atmospheric (21% O(2)), physiological (5% O(2)), and hypoxic oxygen conditions (1% O(2)). In cultures of both hEPCs and HUVECs, lower oxygen consumption was observed when cultured in 1% O(2). At each oxygen tension, feeder-free cultured hESCs and iPSCs were found to consume comparable amounts of oxygen. Transport analysis revealed that the oxygen uptake rate (OUR) of hESCs and iPSCs decreased distinctly as DO availability decreased, whereas the OUR of all cell types was found to be low when cultured in 1% O(2), demonstrating cell adaptation to lower oxygen tensions by limiting oxygen consumption. Next, we examined HIF-1alpha accumulation and the expression of target genes, including VEGF and angiopoietins (ANGPT; angiogenic response), GLUT-1 (glucose transport), BNIP3, and BNIP3L (autophagy and apoptosis). Accumulations of HIF-1alpha were detected in all four cell lines cultured in 1% O(2). Corresponding upregulation of VEGF, ANGPT2, and GLUT-1 was observed in response to HIF-1alpha accumulation, whereas upregulation of ANGPT1 was detected only in hESCs and iPSCs. Upregulation of BNIP3 and BNIP3L was detected in all cells after 24-h culture in hypoxic conditions, whereas apoptosis was not detectable using flow cytometry analysis, suggesting that BNIP3 and BNIP3L can lead to cell autophagy rather than apoptosis. These results demonstrate adaptation of all cell types to hypoxia but different cellular responses, suggesting that continuous measurements and control over oxygen environments will enable us to guide cellular responses.

Flow channeling in a single fracture induced by shear displacement

The effect on the transport properties of fractures of a relative shear displacement

Directional locking and deterministic separation in periodic arrays

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Transport in rough self-affine fractures

of rough walls with complementary self-affine surfaces has been studied experimentally and numerically. The shear displacement

Tracer dispersion in two-dimensional rough fractures.

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Design and development of microbioreactors for long-term cell culture in controlled oxygen microenvironments.

induces an anisotropy of the aperture field with a correlation length scaling as

Anomalous diffusion with absorption: Exact time-dependent solutions

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Gravity Driven Deterministic Lateral Displacement for Particle Separation in Microfluidic Devices

and significantly larger in the direction perpendicular to