Peter Gospodinov

Stability loss and sensitivity in hollow fiber drawing

Stability of hollow fiber drawing is studied, based on the quasi‐one‐dimensional equations of thin film dynamics. It is shown that the model isothermal drawing process is unstable when the draw ratio E (that of output to input velocities) exceeds the critical value E*=20.22 when the viscosity force is dominating. Under stable regimes with E<E*, the response of the as‐drawn fiber to external perturbations is studied (the sensitivity problem). In unstable situations with E≳E*, onset of the so‐called draw resonance regime with self‐sustained oscillations is predicted by using numerical simulation. The effects of the inertia, gravity, surface tension, and gas pressure differential are considered.

Diffusion of sulfate ions into cement stone regarding simultaneous chemical reactions and resulting effects

This study presents a model of sulfate ion diffusion into cement stone, in particular the simultaneous chemical reactions and resulting effects (filling of material voids with chemical products and hampering of ion motion within the specimen). The diffusion development is followed by the solution of the diffusion equation, introducing a specific relation for the diffusion coefficient and considering appropriate initial and boundary conditions. The change of the material structure is theoretically and experimentally assessed. A possibility for studying diffusion in multiply connected areas (i.e., in real materials that contain inclusions, inert filler, and reinforcement) is outlined. Good agreement between theory and experiment is obtained.

Monte Carlo simulation and Navier–Stokes finite difference calculation of unsteady-state rarefied gas flows

A comparative analysis of two approaches (molecular and continuum) for three one-dimensional unsteady-state rarefied gas flows with small Knudsen number is presented. Numerical results have been obtained by using Direct Simulation Monte Carlo (DSMC) method for the molecular and a finite difference method for the continuum approaches, respectively.

The effect of liquid push out of the material capillaries under sulfate ion diffusion in cement composites

Abstract The paper treats complex phenomena that accompany the diffusion of sulfate ions into cement paste or systems. The ion distribution within the material was studied by designing a specific diffusion model. The model accounts for two phenomena: capillary filling with products of the chemical reactions and the subsequent liquid push out of the capillary. The approach allows to quantify the concentration of free ions having penetrated the cement stone and that of chemically reacted ions, and to assess the liquid push out. Experimental data are also presented.

Newtonian glass fiber drawing: Chaotic variation of the cross-sectional radius

A model of Newtonian glass fiber drawing at fixed temperature in the unsteady range (the draw ratio E>20.22) is considered. In this range under steady boundary conditions, as is well known, the draw resonance instability sets in, resulting in self-sustained oscillations. These oscillations lead to a periodic variation of the cross-sectional radius of the fiber. In the present work we consider the case where the spinline radius varies periodically. Such a variation may result from flow oscillations in the fiber forming channels in the direct-melt process, or from the variation of the preform cross-sectional radius in drawing of optical fibers. When this variation takes place in the range E>20.22, the self-sustained periodic oscillations of the draw resonance are replaced by quasiperiodic and periodic (mode-locked) subharmonic or (under the appropriate conditions) chaotic oscillations (strange attractors). The routes to chaos found in the present work include (1) smooth period doubling bifurcation of (any) mode-locked periodic solution, (2) abrupt explosions of quasiperiodic solutions. The predicted chaotic variation of the spinline radius at the winding mandrel may result in a similar variation of the cross-sectional radius of the solidified fibers.

Stationary Cylindrical Couette Flow at Different Temperature of Cylinders: the Local Knudsen Number Effect

The stationary Couette gas flow between rotating inner cylinder and stationary outer one is studied using DSMC method and numerical solution of a continual model. Different cases were studied by varying the temperature of the stationary cylinder and the Knudsen number. The continuum model results are obtained by setting a local value of Knudsen number in the corresponding first order slip boundary conditions. The comparison results showed that the slip boundary conditions with local Knudsen number included improves the accuracy of the continual model.

Cylindrical Couette Flow of Rarefied Gas: Comparison between Navier‐Stokes and DSMC Computations

The cylindrical Couette flow of a rarefied gas is studied in the case of two cylinders rotating with different velocities. Velocity, density and temperature profiles are investigated by the Direct Monte Carlo Simulation method and a numerical solution of the Navier‐Stokes equations for compressible flow is found. We have obtained numerical results for gas velocity and temperature at the walls for different values of rotation velocities of the cylinders. The gas lags or outstrips in comparison with the walls or it has the elastic rigid body behavior. These results are important for applications in non‐planar microfluidic problems. The results obtained by both methods are in a good agreement at the smaller Knudsen number Kn = 0.02 and differs notably at the larger Kn = 0.1.

Modeling of Cylindrical Couette Flow of Rarefied Gas. The Case of Rotating Outer Cylinder

The cylindrical Couette flow of a rarefied gas is studied in the case when the outer cylinder is rotating while the inner cylinder is at rest. Velocity, density and temperature profiles are investigated by a Direct Monte Carlo Simulation method and a numerical solution of the Navier‐Stokes equations for compressible flow is found. The results obtained by both methods are: in an excellent agreement at a small Knudsen number Kn = 0.02; in a satisfactory agreement at Kn = 0.1 and they vastly differs each other at a moderate Kn = 0.5. The comparison shows that the continuum approach can be used successfully for calculations of non‐planar isothermal rarefied gas flows at small Knudsen numbers Kn<0.1. These results are important for applications in non‐planar microfluidic problems.