The flow of a thin Newtonian fluid layer on a porous inclined plane is considered. Applying the long-wave theory, a nonlinear evolution equation for the thickness of the film is obtained. It is assumed that the flow through the porous medium is governed by Darcy’s law. The critical conditions for the onset of instability of a fluid layer flowing down an inclined porous wall, when the characteristic length scale of the pore space is much smaller than the depth of the fluid layer above, are obtained. The results of the linear stability analysis reveal that the film flow system on a porous inclined plane is more unstable than that on a rigid inclined plane and that increasing the permeability of the porous medium enhances the destabilizing effect. A weakly nonlinear stability analysis by the method of multiple scales shows that there is a range of wave numbers with a supercritical bifurcation, and a range of larger wave numbers with a subcritical bifurcation. Numerical solution of the evolution equation in a periodic domain indicates the existence of permanent finite-amplitude waves of different kinds in the supercritical stable region. The long-time waveforms are either time-independent waves of permanent form that propagate or time-dependent modes that oscillate slightly in the amplitude. The presence of the porous substrate promotes this oscillatory behavior. The results show that the shape and amplitude of the waves are influenced by the permeability of the porous medium.
The axisymmetric motion of a fluid caused by an unsteady stretching surface that has relevance in extrusion process and bioengineering has been investigated. It has been shown that if the unsteady stretching velocity is prescribed by rb/(1−αt), then the problem admits a similarity solution which gives much insight to the character of solutions. The asymptotic and numerical solutions are obtained and they could be used in the testing of computer codes or analytical models of more realistic engineering systems. The results are governed by a nondimensional unsteady parameter S and it has been observed that no similarity solutions exist for S > 4.
The linear stability characteristics of pressure-driven miscible two-fluid flow with same density and varying viscosities in a channel with velocity slip at the wall are examined. A prominent feature of the instability is that only a band of wave numbers is unstable whatever the Reynolds number is, whereas shorter wavelengths and smaller wave numbers are observed to be stable. The stability characteristics are different from both the limiting cases of interface dominated flows and continuously stratified flows in a channel with velocity slip at the wall. The flow system is destabilizing when a more viscous fluid occupies the region closer to the wall with slip. For this configuration a new mode of instability, namely the overlap mode, appears for high mass diffusivity of the two fluids. This mode arises due to the overlap of critical layer of dominant instability with the mixed layer of varying viscosity. The critical layer contains a location in the flow domain at which the base flow velocity equals the phase speed of the most unstable disturbance. Such a mode also occurs in the corresponding flow in a rigid channel, but absent in either of the above limiting cases of flow in a channel with slip. The flow is unstable at low Reynolds numbers for a wide range of wave numbers for low mass diffusivity, mimicking the interfacial instability of the immiscible flows. A configuration with less viscous fluid adjacent to the wall is more stable at moderate miscibility and this is also in contrast with the result for the limiting case of interface dominated flows in a channel with slip, where the above configuration is more unstable. It is possible to achieve stabilization or destabilization of miscible two-fluid flow in a channel with wall slip by appropriately choosing the viscosity of the fluid layer adjacent to the wall. In addition, the velocity slip at the wall has a dual role in the stability of flow system and the trend is influenced by the location of the mixed layer, the location of more viscous fluid and the mass diffusivity of the two fluids. It is well known that creating a viscosity contrast in a particular way in a rigid channel delays the occurrence of turbulence in a rigid channel. The results of the present study show that the flow system can be either stabilized or destabilized by designing the walls of the channel as hydrophobic surfaces, modeled by velocity slip at the walls. The study provides another effective strategy to control the flow system. C 2014 AIP Publishing LLC. [http://dx
Wound dressing material based on nano-biotechnological intervention by caging plumbagin on silver nanoparticle (PCSN) as a multi-site cross-linking agent of collagen scaffolds with potent anti-microbial and wound healing activity.
The influence of honey on biochemical and biophysical parameters of wounds was assessed by making an excision wound by cutting away a 4 cm2 (2 cm x 2 cm) full-thickness patch of skin from the shaven back of rats under ether anaesthesia. One milliliter of pure, commercial, unboiled honey was applied topically (Group II), or administered orally (Group III) or intraperitoneally (Group IV). The control rats were left untreated (Group I). The rate of healing was assessed by estimation of some biochemical parameters like DNA, total protein, total collagen, hexosamine and uronic acid contents of the granulation tissues formed different times after wound creation. All the biochemical parameters increased in honey-treated animals when compared with the control values. The increases were very significant with oral and intraperitoneal treatment when compared with those with the topical. Biophysical parameters like tensile strength, stress-strain behavior, rate of contraction, and period of epithelialization were also studied. There was an approximately 21% increase in tensile strength in Group II rats, whereas the increase was more in Group III (34.5%) and Group IV (52%) rats. The stress-strain behavior also followed the same trend. A significant increase in the rate of contraction was observed equally in all three honey-treated groups when their values were compared to the control. Among the three experimental groups, the intraperitoneal treatment decreased the period of epithelialization more significantly (37%) than the oral (22%) and topical (15%) treatments. The decrease in the period of epithelialization showed that the time taken by the wounds to heal was less with systemic treatment than with no treatment (control).
The tear film on the front of the eye is critical to proper eyesight; in many mathematical models of the tear film, the tear film is assumed to be on a flat substrate. We re-examine this assumption by studying the effect of a substrate which is representative of the human cornea. We study the flow of a thin fluid film on a prolate spheroid which is a good approximation to the shape of the human cornea. Two lubrication models for the dynamics of the film are studied in prolate spheroidal coordinates which are appropriate for this situation. One is a self-consistent leading-order hyperbolic partial differential equation (PDE) valid for relatively large substrate curvature; the other retains the next higher-order terms resulting in a fourth-order parabolic PDE for the film dynamics. The former is studied for both Newtonian and Ellis (shear thinning) fluids; for typical tear film parameter values, the shear thinning is too small to be significant in this model. For larger shear thinning, we find a significant effect on finite-time singularities. The second model is studied for a Newtonian fluid and allows for a meniscus at one end of the domain. We do not find a strong effect on the thinning rate at the center of the cornea. We conclude that the corneal shape does not have a significant effect on the thinning rate of the tear film for typical conditions.
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