Spatial instability of a viscous liquid sheet

In the present study, the spatial instability for a two‐dimensional viscous liquid sheet, which is thinning with time, has been analysed. The study includes the derivation of a spatial dispersion equation, numerical solutions for the growth rate of sinuous disturbances, and parameter sensitivity studies. For a given wave number, the growth rate of the disturbance is essentially a function of Weber number, Reynolds number, and gas/liquid density ratio. The analysis indicates that the cut‐off wave number of the disturbance becomes larger with an increase in Weber number or gas/liquid density ratio. Thus, the liquid sheet should produce finer drops. When the Reynolds number decreases, the higher viscosity has a greater damping effect on shorter waves than longer waves. This could explain that only large drops and ligaments were observed in past measurements for the disintegration of a very viscous sheet. The spatial instability results of the present study were also compared with the temporal theory. The importance of spatial analysis was found and demonstrated for the cases of low Weber numbers. The temporal theory underestimates growth rates when the Weber number is less than 100. The discrepancy between the two theories increases as the Weber number further decreases. Copyright © 2005 John Wiley & Sons, Ltd.     

Efficient Solution of the Complex Quadratic Tridiagonal System for C2 PH Quintic Splines

The construction of C ² Pythagorean-hodograph (PH) quintic spline curves that interpolate a sequence of points p ₀,...,p _N and satisfy prescribed end conditions incurs a tridiagonal system of N quadratic equations in N complex unknowns. Albrecht and Farouki [1] invoke the homotopy method to compute all 2 ^N+k solutions to this system, among which there is a unique good PH spline that is free of undesired loops and extreme curvature variations (k{–1,0,+1} depends on the adopted end conditions). However, the homotopy method becomes prohibitively expensive when N10, and efficient methods to construct the good spline only are desirable. The use of iterative solution methods is described herein, with starting approximations derived from ordinary C ² cubic splines. The system Jacobian satisfies a global Lipschitz condition in C ^N , yielding a simple closed-form expression of the Kantorovich condition for convergence of Newton–Raphson iterations, that can be evaluated with O(N ²) cost. These methods are also generalized to the case of non-uniform knots.     

Elasto-plastic analysis of influences of bond deformability on the mechanical behavior of fiber networks

Micromechanical modeling of three-dimensional (3D) fiber networks is performed by reducing the web structure to fiber segments and fiber–fiber bonds to explore the influence of fiber–fiber bond deformability on fiber network’s elasto-plasticity. The fiber segment between every two adjacent bonds is described by a Timoshenko beam element, while fiber–fiber bonds are taken as a different two-node element due to the extremely large height-to-span ratio. This overcomes the rigid-bond assumption employed by most previous network models, providing the feasibility to build the relationship between bonding condition and global mechanical properties, resulting in a 3D network structure and able to accommodate curled fibers. Both fibers and bonds are assumed to be elasto-plastic and described by the bilinear kinematic hardening model. Deformation of the network with load increasing is simulated by the Newton–Raphson method. Numerical tensile tests show reasonable results and agree qualitatively with experiments. The influence of bond deformability on the mechanical behavior of the network is discussed in detail.