We study higher local integrability of a weak solution to the steady Stokes problem. We consider the case of a pressure- and shear-rate-dependent viscosity, i.e., the elliptic part of the Stokes problem is assumed to be nonlinear and it depends on p and on the symmetric part of a gradient of u, namely, it is represented by a stress tensor T (Du, p):= v(p, |D|2)D which satisfies r-growth condition with r \in (1, 2]. In order to get the main result, we use Calderón-Zygmund theory and the method which was presented for example in the paper Caffarelli, Peral (1998)., Václav Mácha., and Obsahuje seznam literatury
The influence of particle shape (aspect ratio) on the intrinsic viscosity is investigated, taking three Czech kaolin products (floated kaolins) as paradigmatic examples. An average aspect ratio is obtained for each kaolin from a comparison of particle size measurements using sedimentation and laser diffraction. The intrinsic viscosity is obtained by a multistep procedure: firstly, flow curves are recorded for each kaolin with the optimum deflocculant concentration, secondly, the (apparent) relative viscosities read off from the flow curves are plotted against the kaolin volume fraction and, thirdly, these data are fitted using the Krieger relation to obtain the intrinsic viscosity in the asymptotic dilute limit. It is shown that the data determined with the method proposed are within the Jeffery and Brenner bounds and that an average aspect ratio of about 20 (17-22) results in an intrinsic viscosity of about 10 (7-13), compared to 2.5 for spherical particles. Although currently th e measurement precision is not suffi cient to seriously assess the influence of Brownian motion, the method can principally be used to predict the intrinsic viscosity when the average aspect ratio of the system (and its particle size distribution) is known, and vice versa., Eva Gregorová, Willi Pabst and Jean-Baptiste Bouchet., and Obsahuje bibliografické odkazy
Isothermal and non-isothermal infiltration experiments with tracer breakthrough were carried out in the laboratory
on one intact column (18.9 cm in diameter, 25 cm in height) of sandy loam soil. For the isothermal experiment, the
temperature of the infiltrating water was 20°C to the initial temperature of the sample. For the two non-isothermal experiments
water temperature was set at 8°C and 6°C, while the initial temperature of the sample was 22°C. The experiments
were conducted under the same initial and boundary conditions. Pressure heads and temperatures were monitored in two
depths (8.8 and 15.3 cm) inside the soil sample. Two additional temperature sensors monitored the entering and leaving
temperatures of the water. Water drained freely through the perforated plate at the bottom of the sample by gravity and
outflow was measured using a tipping bucket flowmeter. The permeability of the sample calculated for steady state stages
of the experiment showed that the significant difference between water flow rates recorded during the two experiments
could not only be justified by temperature induced changes of the water viscosity and density. The observed data
points of the breakthrough curve were successfully fitted using the two-region physical non-equilibrium model. The results
of the breakthrough curves showed similar asymmetric shapes under isothermal and non-isothermal conditions.
Dependence of ATP hydrolysis kinetics by the chloroplast coupling factor (CF1) on medium viscosity was studied at varying temperatures. For samples with oxidized and reduced CF1 γ-subunit, this dependence was shown to be described by Cramers’ relationship k - (η/ηo)-n, where k is the reaction rate constant, η/ηo is the medium/water viscosity ratio, and 0 < n < 1. Transition of the γ-subunit from its reduced to oxidized state was accompanied by increasing n value, which is indicative of increasing friction losses between certain enzyme sections and the solution. The increased medium viscosity produced no effect on the reaction activation energy which appeared to be almost the same for the both enzyme states. The molecular mechanisms responsible for CF1 activity loss in viscous media are discussed., A.N. Malyan., and Obsahuje bibliografii