scholarly journals Chaotic Mixing in a Free Helix Extruder using a New Solution to the Biharmonic Equation

AIChE Journal ◽  
2022 ◽  
Author(s):  
Gregory A. Campbell ◽  
Ross Taylor ◽  
Mark D. Wetzel ◽  
Shaji Chempath ◽  
Sirisha Bomma ◽  
...  
Keyword(s):  
Biharmonic Equation ◽  
Chaotic Mixing

scholarly journals Chaotic Mixing in a Free Helix Extruder using a New Solution to the Biharmonic Equation

2021 ◽  
Author(s):  
Gregory Campbell ◽  
Ross Taylor ◽  
Mark Wetzel ◽  
Sirisha Bomma ◽  
Shaji Chempath ◽  
...  
Keyword(s):  
Flow Field ◽  
Time Distribution ◽  
Residence Time Distribution ◽  
Biharmonic Equation ◽  
Cross Flow ◽  
Chaotic Mixing ◽  
Screw Extruder ◽  
Chaotic Flow ◽  
Single Screw ◽  
Single Screw Extruder

A recently published approach for modeling the cross flow in an extruder channel using a new solution to the biharmonic equation is utilized in a study of chaotic mixing in a free helix single screw extruder. This novel extruder was designed and constructed with the screw flight, also referred to as the helix, detached from the screw core. Each of the screw elements could be rotated independently to obtain chaotic motion in the screw channel. Using the new extruder, experimental evidence for the increased mixing of a dye, for both a Dirac and droplet input, with a chaotic flow field relative to the traditional residence time distribution is presented. These experimental results are compared using the new biharmonic equation-based model. Because of the ability to periodically rotate only the flight/helix, the chaotic mixing results are minimally confounded by the existence of Moffat eddies.

Chaotic mixing and heat transfer in time-periodic 3-D Stokes flows

2002 ◽  
Author(s):  
Antonio Jose Silveiro Rodrigo ◽  
Jose Paulo Barbosa Mota ◽  
Esteban Saatdjian
Keyword(s):  
Heat Transfer ◽  
Chaotic Mixing ◽  
Stokes Flows ◽  
Time Periodic

scholarly journals Scalar Signatures of Chaotic Mixing in Porous Media

2021 ◽  
Vol 126 (3) ◽  
Author(s):  
J. Heyman ◽  
D. R. Lester ◽  
T. Le Borgne
Keyword(s):  
Porous Media ◽  
Chaotic Mixing

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

Chaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microfluidic device

2016 ◽  
Vol 5 (1) ◽  
pp. 1-8
Author(s):  
Yasser Aboelkassem
Keyword(s):  
Mathematical Modeling ◽  
Stream Function ◽  
Microfluidic Device ◽  
Fourier Expansion ◽  
Expansion Method ◽  
Small Oscillation ◽  
Chaotic Mixing ◽  
Mixing Efficiency ◽  
Induced Flow ◽  
Mixing Patterns

AbstractChaotic mixing by oscillating a Stokeslet in a circular Hele-Shaw microffluidic device is presented in this article. Mathematical modeling for the induced flow motions by moving a Stokeslet along the x-axis is derived using Fourier expansion method. The solution is formulated in terms of the velocity stream function. The model is then used to explore different stirring dynamics as function of the Stokeslet parameters. For instance, the effects of using various oscillation amplitudes and force strengths are investigated. Mixing patterns using Poincaré maps are obtained numerically and have been used to characterize the mixing efficiency. Results have shown that, for a given Stokeslet’s strength, efficient mixing can be obtained when small oscillation amplitudes are used. The present mixing platform is expected to be useful for many of biomicrofluidic applications.

Construction of dipole type singular solutions for a biharmonic equation with critical Sobolev exponent

2002 ◽  
Vol 2 (4) ◽  
Author(s):  
Sarni Baraket
Keyword(s):  
Fourth Order ◽  
Weak Solutions ◽  
Biharmonic Equation ◽  
Critical Sobolev Exponent ◽  
Singular Solutions ◽  
Invariant Equation ◽  
Conformally Invariant ◽  
Sobolev Exponent

AbstractIn this paper, we construct positive weak solutions of a fourth order conformally invariant equation on S

A Meshless Local Petrov-Garlerkin Method for Solving the Biharmonic Equation

2014 ◽  
Vol 931-932 ◽  
pp. 1488-1494
Author(s):  
Supanut Kaewumpai ◽  
Suwon Tangmanee ◽  
Anirut Luadsong
Keyword(s):  
Relative Error ◽  
Biharmonic Equation ◽  
Interpolation Method ◽  
Step Function ◽  
Special Treatment ◽  
Maximum Relative Error ◽  
Heaviside Step Function ◽  
Treatment Techniques ◽  
Point Interpolation Method ◽  
Point Interpolation

A meshless local Petrov-Galerkin method (MLPG) using Heaviside step function as a test function for solving the biharmonic equation with subjected to boundary of the second kind is presented in this paper. Nodal shape function is constructed by the radial point interpolation method (RPIM) which holds the Kroneckers delta property. Two-field variables local weak forms are used in order to decompose the biharmonic equation into a couple of Poisson equations as well as impose straightforward boundary of the second kind, and no special treatment techniques are required. Selected engineering numerical examples using conventional nodal arrangement as well as polynomial basis choices are considered to demonstrate the applicability, the easiness, and the accuracy of the proposed method. This robust method gives quite accurate numerical results, implementing by maximum relative error and root mean square relative error.

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