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FENE Model
In polymer physics, the finite extensible nonlinear elastic (FENE) model, also called the FENE dumbbell model, represents the dynamics of a long-chained polymer. It simplifies the chain of monomers by connecting a sequence of beads with nonlinear springs. Its direct extension the FENE-P model, is more commonly used in computational fluid dynamics to simulate turbulent flow. The P stands for the last name of physicist Anton Peterlin, who developed an important approximation of the model in 1966. The FENE-P model was introduced by Robert Byron Bird ''et al.'' in the 1980s. In 1991 the FENE-MP model (PM for modified Peterlin) was introduced and in 1988 the FENE-CR was introduced by M.D. Chilcott and J.M. Rallison. Formulation The spring force in the FENE model is given Warner's spring force, as :\textbf_i=k\frac, where R_i = , \textbf_i, , ''k'' is the spring constant and Lmax the upper limit for the length extension. Total stretching force on ''i-''th bead can be written ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer Physics
Polymer physics is the field of physics that studies polymers, their fluctuations, mechanical properties, as well as the kinetics of reactions involving degradation of polymers and polymerisation of monomers.P. Flory, ''Principles of Polymer Chemistry'', Cornell University Press, 1953. .Pierre Gilles De Gennes, ''Scaling Concepts in Polymer Physics'' CORNELL UNIVERSITY PRESS Ithaca and London, 1979M. Doi and S. F. Edwards, ''The Theory of Polymer Dynamics'' Oxford University Inc NY, 1986 While it focuses on the perspective of condensed matter physics, polymer physics was originally a branch of statistical physics. Polymer physics and polymer chemistry are also related to the field of polymer science, which is considered to be the applicative part of polymers. Polymers are large molecules and thus are very complicated for solving using a deterministic method. Yet, statistical approaches can yield results and are often pertinent, since large polymers (i.e., polymers with many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polymer
A polymer () is a chemical substance, substance or material that consists of very large molecules, or macromolecules, that are constituted by many repeat unit, repeating subunits derived from one or more species of monomers. Due to their broad spectrum of properties, both synthetic and natural polymers play essential and ubiquitous roles in everyday life. Polymers range from familiar synthetic plastics such as polystyrene to natural biopolymers such as DNA and proteins that are fundamental to biological structure and function. Polymers, both natural and synthetic, are created via polymerization of many small molecules, known as monomers. Their consequently large molecular mass, relative to small molecule compound (chemistry), compounds, produces unique physical property, physical properties including toughness, high rubber elasticity, elasticity, viscoelasticity, and a tendency to form Amorphous solid, amorphous and crystallization of polymers, semicrystalline structures rath ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monomers
A monomer ( ; ''wikt:mono-, mono-'', "one" + ''wikt:-mer, -mer'', "part") is a molecule that can chemical reaction, react together with other monomer molecules to form a larger polymer chain or two- or three-dimensional network in a process called polymerization. Classification Chemistry classifies monomers by type, and two broad classes based on the type of polymer they form. By type: * natural vs synthetic, e.g. glycine vs caprolactam, respectively * polar vs nonpolar, e.g. vinyl acetate vs ethylene, respectively * cyclic vs linear, e.g. ethylene oxide vs ethylene glycol, respectively By type of polymer they form: * those that participate in condensation polymerization * those that participate in addition polymerization Differing stoichiometry causes each class to create its respective form of polymer. : The polymerization of one kind of monomer gives a polymer#Monomers and repeat units, homopolymer. Many polymers are copolymers, meaning that they are derived from two diff ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Fluid Dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid dynamics, fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by Boundary value problem#Boundary value conditions, boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulence, turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed Closed-form solution, analytical or Empirical research, empirical analysis of a particular problem can be used for compa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anton Peterlin (physicist)
Anton Peterlin () (25 September 1908 – 24 March 1993) was a Slovenian physicist. Life and career Peterlin was born in Ljubljana, Slovenia. After receiving his D. Sc. in physics from Humboldt University of Berlin in Berlin, Germany in 1938, Peterlin accepted in 1939 the chair as a professor of physics at the University of Ljubljana, where he remained for 22 years. Besides his pedagogical duties, he accepted in 1947 the position of the founding director of the Jožef Stefan Institute in Ljubljana. In 1960, Peterlin left his home country. In order to be able to continue his theoretical research on macromolecules he accepted the position of a full professor and head of the Institute of Physics at the Technical University of Munich, Germany. Only a year later he relocated to North Carolina where he was entrusted with the directorship of the newly founded Camille Dreyfus Laboratory at the Research Triangle Institute, which was almost entirely devoted to basic research on polymers. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Byron Bird
Robert Byron Bird (February 5, 1924 – November 13, 2020) was an American chemical engineer and professor emeritus in the department of chemical engineering at the University of Wisconsin-Madison. He was known for his research in transport phenomena of non-Newtonian fluids, including fluid dynamics of polymers, polymer kinetic theory, and rheology. He, along with Warren E. Stewart and Edwin N. Lightfoot, was an author of the classic textbook Transport Phenomena. Bird was a recipient of the National Medal of Science in 1987. Childhood and education Robert Byron Bird was born on February 5, 1924, in Bryan, Texas. His father, Byron Bird, was a professor of civil engineering at Texas A&M University. In his, Bird recounts he obtain his elementary and junior high education in Fort Dodge, Iowa, and thereafter he attending Central High school in Washington D. C. Bird attended University of Maryland from 1941 to 1943, where he was initiated into the Alpha Rho chapter of Alpha Chi Si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hooke's Law
In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring by some distance () scales linearly with respect to that distance—that is, where is a constant factor characteristic of the spring (i.e., its stiffness), and is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ("as the extension, so the force" or "the extension is proportional to the force"). Hooke states in the 1678 work that he was aware of the law since 1660. Hooke's equation holds (to some extent) in many other situations where an elastic body is deformed, such as wind blowing on a tall building, and a musician plucking a string of a guitar. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean. Hooke's law is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brillouin And Langevin Functions
The Brillouin and Langevin functions are a pair of special functions that appear when studying an idealized paramagnetic material in statistical mechanics. These functions are named after French physicists Paul Langevin and Léon Brillouin who contributed to the microscopic understanding of magnetic properties of matter. The Langevin function is derived using statistical mechanics, and describes how magnetic dipoles are aligned by an applied field. The Brillouin function was developed later to give an explanation that considers quantum physics. The Langevin function could then be a seen as a special case of the more general Brillouin function if the quantum number J would be infinite (J \to \infty ). Brillouin function for paramagnetism The Brillouin function arises when studying magnetization of an ideal paramagnetism, paramagnet. In particular, it describes the dependency of the magnetization M on the applied magnetic field B, defined by the following equation: The function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
