A boundary element method for compound non-Newtonian drops

A boundary integral method for the simulation of the deformation of axisymmetric compound non-Newtonian drops suspended in a Newtonian fluid which is subjected to an axisymmetric flow eld is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term. The latter yields an extra integral over the domain of the non-Newtonian material in the boundary integral formulation. By transforming the integral representation for the velocity to cylindrical coordinates we can reduce the dimension of the computational problem. Apart from a numerical validation of the method we present simulation results for a drop consisting of an Oldroyd-B fluid and a viscoelastic material. Moreover, we extend the method to compound drops, which are composed of a viscous inner core encapsulated by a viscoelastic material. The simulation results for these drops are consistent with theoretical results from the literature. Moreover, it is shown that the method can be used to identify the dominant breakup mechanism of compound drops and its relation to the specic non-Newtonian character of the drops

A comparison of boundary element and finite element methods for modeling axisymmetric polymeric drop deformation

A modified boundary element method (BEM) and the DEVSS-G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start-up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd-B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation

A boundary integral method for two-dimensional (non)-Newtonian drops in slow viscous flow

A boundary integral method for the simulation of the time-dependent deformation of Newtonian or non-Newtonian drops suspended in a Newtonian fluid is developed. The boundary integral formulation for Stokes flow is used and the non-Newtonian stress is treated as a source term which yields an extra integral over the domain of the drop. The implementation of the boundary conditions is facilitated by rewriting the domain integral by means of the Gauss divergence theorem. To apply the divergence theorem smoothness assumptions are made concerning the non-Newtonian stress tensor. The correctness of these assumptions in actual simulations is checked with a numerical validation procedure. The method appears mathematically correct and the numerical algorithm is second order accurate. Besides this validation we present simulation results for a Newtonian drop and a drop consisting of an Oldroyd-B fluid. The results for Newtonian and non-Newtonian drops in two dimensions indicate that the steady state deformation is quite independent of the drop-fluid. The deformation process, however, appears to be strongly dependent on the drop-fluid. For the non-Newtonian drop a mechanical model is developed to describe the time-dependent deformation of the cylinder for small capillary numbers

Effects of reynolds number on physiological-type pulsatile flows in a pipe with ring-type constrictions

10.1002/(SICI)1097-0363(19990730)30:6<743International Journal for Numerical Methods in Fluids306743-761IJNF

Axisymmetric non-Newtonian drops treated with a boundary integral method

Defendants-appellants Officers Krzeminski and Lemons (the Officers ) appeal from a judgment for nominal damages and attorney\u27s fees entered in the United States District Court for the District of Connecticut (Eginton, J.) following a jury trial in a civil rights action predicated on an illegal search and seizure conducted in the home of plaintiffs-appellees. Responding to special interrogatories submitted by the court, the jury found that there had been a consent to the entry of the premises and that the seizure of certain objects within the premises was permissible under the doctrine of plain view and by consent. However, the jury, in further response to interrogatories, determined that a warrantless search within the premises was improper because it was neither a search incident to a lawful arrest nor one conducted with the consent of the proper party. The Officers contend on appeal that the jury should have been permitted to consider whether the search was permissible under the doctrine of plain view and therefore assert that the court denied the Officers a valid defense theory by failing to include the theory of plain view search in its special interrogatory and in its instruction. We hold that no error was committed by the district court in either the framing of its interrogatories or in its jury instruction because the doctrine of plain view does not validate searches conducted without a warrant. On cross-appeal, plaintiffs-cross-appellants ( the Ruggieros ) contend that the district court erred by failing to place on the Officers the burden of proving exceptions to the search warrant requirement. Instead, the judge gave the jury the customary charge with respect to the burden of proof in civil actions. We find that no error was committed by the district court in so instructing the jury, and that, in any 560*560 event, the burden of proving unreasonable search in an action brought under 42 U.S.C. § 1983 (1988) should be borne by those who urge unreasonableness