Three mathematical models are developed for meniscus roll coating in which there is steady flow of a Newtonian fluid in the narrow gap, or nip, between two contrarotating rolls in the absence of body forces.The zero flux model predicts a constant pressure gradient within the central core and two eddies, each with an inner structure, in qualitative agreement with observation. The small flux model takes account of a small inlet flux and employs the lubrication approximation to represent fluid velocity as a combination of Couette and Poiseuille flows. Results show that the meniscus coating regime is characterized by small flow rates (λ [Lt ] 1) and a sub-ambient pressure field generated by capillary action at the upstream meniscus. Such flows are found to exist for small modified capillary number, Ca(R/H0)1/2 [lsim ] 0.15, where Ca and R/H0 represent capillary number and the radius to semi-gap ratio, respectively.A third model incorporates the full effects of curved menisci and nonlinear free surface boundary conditions. The presence of a dynamic contact line, adjacent to the web on the upper roll, requires the imposition of an apparent contact angle and slip length. Numerical solutions for the velocity and pressure fields over the entire domain are obtained using the finite element method. Results are in accord with experimental observations that the flow domain consists of two large eddies and fluid transfer jets or ‘snakes’. Furthermore, the numerical results show that the sub-structure of each large eddy consists of a separatrix with one saddle point, two sub-eddies with centres, and an outer recirculation.Finally finite element solutions in tandem with lubrication analysis establish the existence of three critical flow rates corresponding to a transformation of the pressure field, the emergence of a ‘secondary snake’ (another fluid transfer jet) and the disappearance of a primary snake.

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Experiments reported by Blake et al. [Phys. Fluids. 11, 1995(1999] suggest that the dynamic contact angle formed between the free surface of a liquid and a moving solid boundary at a fixed contact-line speed depends on the flow field/geometry near the moving contact line. The present paper examines quantitatively whether or not it is possible to attribute this effect to bending of the free surface due to hydrodynamic stresses acting upon it and hence interpret the results in terms of the so-called "apparent" contact angle. It is shown that this is not the case. Numerical analysis of the problem demonstrates that, at the spatial resolution reported in the experiments, the variations of the "apparent" contact angle (defined in two different ways) caused by variations in the flow field, at a fixed contact-line speed, are too small to account for the observed effect. The results clearly indicate that the actual (macroscopic) dynamic contact angle, i.e. the one used in fluid mechanics as a boundary condition for the equation determining the free surface shape, must be regarded as dependent not only on the contact-line speed but also on the flow field/geometry in the vicinity of the moving contact line.

Knowledge of the mechanical behavior of spinal dura mater is important for a number of applications including the experimental and computational modeling of physiological phenomena and spinal cord trauma. However, mechanical characterization of dura mater is relatively sparse and is further compounded by the use of the tangent modulus as the sole measure of stiffness. This study aims to provide a more complete description of the mechanical properties of spinal dura mater, including the effect of strain rate. Bovine dura mater was tested under uniaxial tension in both the longitudinal and the circumferential directions at three different strain rates; 0.01, 0.1, and 1.0 s(-1). An Ogden model was fitted to the resulting stress-stretch data. The morphology of the dura mater was assessed using Sirius red and H&E staining. No significant effect of the strain rate was found for the Ogden model parameters. Longitudinal specimens were significantly stronger and more deformable than circumferential samples, probably due to the structural arrangement of the collagen fibers. At low strains, however, the circumferential specimens were stiffer than the longitudinal ones. The findings of this study will allow more complete representations of the spinal dura mater to be developed.