MATERIALE PLASTICE ♦ 51♦ No. 3 ♦ 2014 http://www.revmaterialeplastice.ro 225 Stopper Effects in Network Type Polymers VIOREL-PUIU PAUN 1 *, VALENTIN NEDEFF 2 , DAN SCURTU 3 , GABRIEL LAZAR 2 , VLAD GHIZDOVAT 4 , MARICEL AGOP 5 , LAURA-GHEUCA SOLOVASTRU 6 *, RADU FLORIN POPA 7 1 Politehnica University of Bucharest, Faculty of Applied Sciences, Physics Department, Bucharest 060042, Romania 2 ”Vasile Alecsandri” University of Bacau, Faculty of Engineering, 157 Marasesti Str., 600115 Bacau, România 3 “Gheorghe Asachi” Technical University, Fluid Mechanics Department,, 59A D. Mangeron Rd., 700050, Iasi, Romania “Alexandru Ioan Cuza” University of Iaºi, Faculty of Physics,11 Carol I Blv, 700506, Iasi, Romania 5 “Gheorghe Asachi” Technical University, Physics Department, 59A D. Mangeron Rd., 700050, Iasi, Romania 6 University of Medicine and Pharmacy “Gr. T. Popa”, Department of Dermatology, 16 University Str., 700115,Romania 7 University of Medicine and Pharmacy “Gr. T. Popa”, Surgery Department, 16 University Str., 700115, Iaºi, Romania The specific parameters describing the flows of Bingham type rheological fluids through a circular pipe, under the action of a pressure gradient in the direction of the movement are established, using the Non- Standard Scale Relativity Theory approach. In such context, an analytical solution and a numerical application (for KELTAN 4200 — an etilene-co-propilene copolymer) are obtained. The friction effort has two components, one of specific fluid gliding, the other of shearing, depending on transverse speed gradient. In the central area of the fluid movements a particles agglomeration (fluid stopper) occurs, defined by a constantly moving structure. Keywords: rheology, friction effort, polymers, fluid stopper, speed A great variety of materials is categorized as complex fluids: polymers (elastomers, thermoplastics, and composites) [1], colloidal fluids, biological fluids (DNA - who creates cells by means of a simple but very elegant language and it is responsible for the remarkable way in which individual cells organize into complex systems like organs and these organs form even more complex systems like organisms -, proteins, cells, dispersions of biopolymers and cells, human blood), foams, suspensions, emulsions, gels, micelar and liquid-crystal phases, molten materials, etc. Therefore, fluids with non-linear viscous behaviours, as well as viscoelastic materials are complex [2-3]. Particle dynamics in complex fluids is highly nonlinear. For example, the formation of amorphous solids (glasses, granular or colloids) do not comply with the physical mechanism explaining solids crystallization. So, in amorphous solids, either lowering the temperature or increasing the density, the dynamic process achieves a level where the system cannot totally relax and therefore becomes rigid. This phenomenon is known as glass transition (when the temperature lowers) or jamming transition (when density increases) [4,5]. Also, the stress of a viscoelastic fluid, unlike the Newtonian fluid, depends not only on the actually stress applied, but on the one applied during previous deformation of the fluid [6]. In order to develop new theoretical models we must admit that the complex fluids systems that display chaotic behaviour are recognized to acquire self-similarity (space- time structures seem to appear) in association with strong fluctuations at all possible space-time scales [1-3]. Then, for temporal scales that are large with respect to the inverse of the highest Lyapunov exponent, the deterministic trajectories are replaced by a collection of potential trajectories and the concept of definite positions by that of probability density [7,8]. Since the non-differentiability appears as a universal property of the complex fluids systems, it is necessary to construct a non-differentiable physics. In such conjecture, * email: paun@physics.pub.ro; laura_solovastru@gmail.ro by considering that the complexity of the interactions processes is replaced by non-differentiability, it is no longer necessary to use the whole classical “arsenal” of quantities from the standard physics (differentiable physics). This topic was developed in the Scale Relativity Theory (SRT) [7,8] and in the non-standard Scale Relativity Theory (NSRT) [9-23]. In the framework of SRT or NSRT we assume that the movements of complex fluids entities take place on continuous but non-differentiable curves (fractal curves) so that all physical phenomena involved in the dynamics depend not only on the space-time coordinates but also on the space-time scales resolution. From such a perspective, the physical quantities that describe the dynamics of complex fluids may be considered fractal functions [7,8,]. Unlike the classical case previously studied [24], the entities of the complex fluids may be reduced to and identified with their own trajectories, so that the complex fluids will behave as a special interaction-less “fluid” by means of its geodesics in a non-differentiable (fractal) space (Schrödinger or hydrodynamic forms). In the present paper, we propose the NSRT approach to analyze the complex fluids dynamics. Particularly, we determine the parameters that characterize the Bingham type fluid flows, through a horizontal pipe with circular section. The study contains an analytical solution and a numerical application, using the Navier-Stokes type equations, from the NSRT approach, in cylindrical coordinates and the friction effort for a Bingham type fluid. Our numerical mathematical model differs than other models used to describe the Bingham fluids [25,26]. Experimental part The polidispersed heterogeneous mixtures that have fluid continuous phase can also have a discontinuous phase given by solid or fluid particles with different properties, such as density, granulometry and shape. The