This work presents results of finite element analysis of isothermal incompressible creeping viscoelastic flows with the tensor-logarithmic formulation of the Leonov model especially for the planar geometry with singular comers in the domain. In the case of 4:1 contraction flow, for all 5 meshes we have obtained solutions over the Deborah number of 100, even though there exists slight decrease of convergence limit as the mesh becomes finer. From this analysis, singular behavior of the comer vortex has been clearly seen and proper interpolation of variables in terms of the logarithmic transformation is demonstrated. Solutions of 4:1:4 contraction/expansion flow are also presented, where there exists 2 singular comers. 5 different types spatial resolutions are also employed, in which convergent solutions are obtained over the Deborah number of 10. Although the convergence limit is rather low in comparison with the result of the contraction flow, the results presented herein seem to be the only numerical outcome available for this flow type. As the flow rate increases, the upstream vortex increases, but the downstream vortex decreases in their size. In addition, peculiar deflection of the streamlines near the exit comer has been found. When the spatial resolution is fine enough and the Deborah number is high, small lip vortex just before the exit comer has been observed. It seems to occur due to abrupt expansion of the elastic liquid through the constriction exit that accompanies sudden relaxation of elastic deformation.

The new tube model with variable diameter (Marrucci and Ianniruberto, 2004), recently introduced to interpret new elongational data of polymer melts, is here extended to encompass arbitrary flows, specifically shear flows. The predicted results compare well with existing data of entangled polymer melts. Challenges still remain when the comparison is extended to recent elongational data on entangled solutions by Sridhar.

Background: Reduced deformability of red blood cells (RBCs) may play an important role on the pathogenesis of chronic vascular complications of diabetes mellitus. However, available techniques for measuring RBC deformability often require washing process after each measurement, which is not optimal for day­to-day clinical use at point of care. The objectives of the present study are to develop a device and to delineate the correlation of impaired RBC deformability with diabetic nephropathy. Methods: We developed a disposable ektacytometry to measure RBC deformability, which adopted a laser diffraction technique and slit rheometry. The essential features of this design are its simplicity (ease of operation and no moving parts) and a disposable element which is in contact with the blood sample. We studied adult diabetic patients divided into three groups according to diabetic complications. Group I comprised 57 diabetic patients with normal renal function. Group II comprised 26 diabetic patients with chronic renal failure (CRF). Group III consisted of 30 diabetic subjects with end-stage renal disease (ESRD) on hemo-dialysis. According to the renal function for the diabetic groups, matched non-diabetic groups were served as control. Results: We found substantially impaired red blood cell deformability in those with normal renal function (group I) compared to non-diabetic control (P = 0.0005). As renal function decreases, an increased impairment in RBC deformability was found. Diabetic patients with chronic renal failure (group II) when compared to non-diabetic controls (CRF) had an apparently greater impairment in RBC deformability (P = 0.07). The non-diabetic cohort (CRF), on the other hand, manifested significant impairment in red blood cell deformability compared to healthy: control (P = 0.0001). Conclusions: The newly developed slit ektacytometer can measure the RBC deformability with ease and accuracy. In addition, progressive impairment in cell deformability is associated with renal function loss in all patients regardless of the presence or absence of diabetes. In diabetic patients, early impairment in RBC deformability appears in patients with normal renal function.

Coalescence process of binary immiscible fluid mixtures having bimodal size distributions, prepared by mixing two pre-sheared samples at different shear rates, ${\gamma}_{pre1}\;and\;{\gamma}_{pre2}$, under shear flow at a final shear rate, ${\gamma}_f$, are examined by transient shear stress measurements and microscopic observations in comparison with the results for simply pre-sheared samples having narrow size distributions (unimodal distribution samples). Component fluids are a silicone oil (PDMS) and a hydrocarbon-formaldehyde resin (Genelite) and their viscosities are 14.1 and 21.0 $pa{\cdot}sec$ at room temperature $(ca.\;20^{\circ}C)$, respectively. The weight ratio of PDMS: Genelite was 7:3. Three cases, $({\gamma}_{pre1}=7.2sec^{-1},\;{\gamma}_{pre2}=12.0sec^{-1}\;and\;{\gamma}_f=2.4sec^{-1}),\;({\gamma}_{pre1}=0.8sec^{-1},\;{\gamma}_{pre2}=4.0sec^{-1}\;and\;{\gamma}_f=2.4sec^{-1}),\;and\;({\gamma}_{pre1}=7.2sec^{-1},\;{\gamma}_{pre2}=12.0^sec^{-1}\;and\;{\gamma}_f=7.2sec^{-1})$ the first case, transient shear stress did not show any significant difference but domains larger than the initial state are observed at short times. In the latter cases, there exist undershoot of shear stress, reflecting existence of deformed large domains, which is confirmed by the direct observation. It is concluded that coalescence between large and small domains more frequently occur than coalescence between the domains with similar size in the bimodal distribution samples.

In this work we show the results of our most recent Direct Numerical Simulations (DNS) of turbulent viscoelastic channel flow using spectral spatial approximations and a stabilizing artificial diffusion in the viscoelastic constitutive model. The Finite-Elasticity Non-Linear Elastic Dumbbell model with the Peterlin approximation (FENE-P) is used to represent the effect of polymer molecules in solution, The corresponding rheological parameters are chosen so that to get closer to the conditions corresponding to maximum drag reduction: A high extensibility parameter (60) and a moderate solvent viscosity ratio (0.8) are used with two different friction Weissenberg numbers (50 and 100). We then first find that the corresponding achieved drag reduction, in the range of friction Reynolds numbers used in this work (180-590), is insensitive to the Reynolds number (in accordance to previous work). The obtained drag reduction is at the level of $49\%\;and\;63\%$, for the friction Weissenberg numbers 50 and 100, respectively. The largest value is substantially higher than any of our previous simulations, performed at more moderate levels of viscoelasticity (i.e. higher viscosity ratio and smaller extensibility parameter values). Therefore, the maximum extensional viscosity exhibited by the modeled system and the friction Weissenberg number can still be considered as the dominant factors determining the levels of drag reduction. These can reach high values, even for of dilute polymer solution (the system modeled by the FENE-P model), provided the flow viscoelasticity is high, corresponding to a high polymer molecular weight (which translates to a high extensibility parameter) and a high friction Weissenberg number. Based on that and the changes observed in the turbulent structure and in the most prevalent statistics, as presented in this work, we can still rationalize for an increasing extensional resistance-based drag reduction mechanism as the most prevalent mechanism for drag reduction, the same one evidenced in our previous work: As the polymer elasticity increases, so does the resistance offered to extensional deformation. That, in turn, changes the structure of the most energy-containing turbulent eddies (they become wider, more well correlated, and weaker in intensity) so that they become less efficient in transferring momentum, thus leading to drag reduction. Such a continuum, rheology-based, mechanism has first been proposed in the early 70s independently by Metzner and Lamley and is to be contrasted against any molecularly based explanations.