The flow with solid-liquid two-phase media inside centrifugal pumps is very complicated and the relevant method for the hydraulic design is still immature so far. There exist two main problems in the operation of the two-phase flow pumps, i.e., low overall efficiency and severe abrasion. In this study, the three-dimensional, steady, incompressible, and turbulent solid-liquid two-phase flows in a low-specific-speed centrifugal pump are numerically simulated and analyzed by using a computational fluid dynamics (CFD) code based on the mixture model of the two-phase flow and the RNG k-ɛ two-equation turbulence model, in which the influences of rotation and curvature are fully taken into account. The coupling between impeller and volute is implemented by means of the frozen rotor method. The simulation results predicted indicate that the solid phase properties in two-phase flow, especially the concentration, the particle diameter and the density, have strong effects on the hydraulic performance of the pump. Both the pump head and the efficiency are reduced with increasing particle diameter or concentration. However, the effect of particle density on the performance is relatively minor. An obvious jet-wake flow structure is presented near the volute tongue and becomes more remarkable with increasing solid phase concentration. The suction side of the blade is subject to much more severe abrasion than the pressure side. The obtained results preliminarily reveal the characteristics of solid-liquid two-phase flow in the centrifugal pump, and are helpful for improvement and empirical correction in the hydraulic design of centrifugal pumps.

In recent years, new concepts in textile dyeing technology have been investigated which aim to decrease the use of chemicals and the emission of water. In this work, dyeing of cotton textiles with reactive dyes has been investigated in a silicone non-aqueous dyeing system. Compared with conventional aqueous dyeing, almost 100% of reactive dyes can be adsorbed on cotton textiles without using any salts in non-aqueous dyeing systems, and the fixation of dye is also higher (80%~90% for non-aqueous dyeing vs. 40%~50% for traditional dyeing). The pseudo-second-order kinetic model can best describe the adsorption and equilibrium of reactive dyes in the non-aqueous dyeing systems as well as in the traditional water dyeing system. In the non-aqueous dyeing systems, the adsorption equilibrium of reactive dyes can be reached quickly. Particularly in the siloxane non-aqueous dyeing system, the adsorption equilibrium time of reactive dye is only 5–10 min at 25 °C, whereas more time is needed at 60 °C in the water dyeing system. The surface tension of non-aqueous media influences the adsorption rate of dye. The lower the surface tension, the faster the adsorption rate of reactive dye, and the higher the final uptake of dye. As a result, non-aqueous dyeing technology provides an innovative approach to increase dye uptake under a low dyeing temperature, in addition to making large water savings.

The main goal of this article is to study the diffusion mechanism of aqueous solutions and the swelling of cellulosic fibers in the silicone non-aqueous dyeing system via fluorescent labeling. Due to non-polar media only adsorbing on the surface of fiber, cellulosic fiber could not swell as a result of the non-polar media. However, because water molecules can diffuse into the non-crystalline region of the fiber, cellulosic fiber could swell by water which was dispersed or emulsified in a non-aqueous dyeing system. To study the diffusion mechanism of an aqueous solution in the siloxane non-aqueous dyeing system, siloxane non-aqueous media was first diffused to the cellulosic fiber because of its lower surface tension. The resulting aqueous solution took more time to diffuse the surface of the cellulosic fiber, because water molecules must penetrate the siloxane non-aqueous media film. Compared with the fluorescent intensity of the fiber surface, the siloxane film could be re-transferred to the dye bath under the emulsification of the surfactant and the mechanical force. Therefore, a longer diffusion time of the aqueous solution ensured the dyeing feasibility for cellulosic fiber in the non-aqueous dyeing system.

Silicone reverse dyeing technology provides an important means of saving water and salts-free in the textile dyeing industry. The interactions between dyes and surfactants may influence the hydrolysis of dye during dyeing. In this investigation, the effect of ethylene oxide content in nonionic surfactant on the hydrolytic reaction of reactive dye was firstly investigated in a siloxane reverse emulsion dyeing system. Compared with no surfactants, the hydrolytic reaction of vinyl sulfone reactive dye was a slowdown when some nonionic surfactants were used during dyeing. Usually, the hydrophobic groups in nonionic surfactants were dodecyl chains but their polar head groups were different. The hydrolytic reaction of vinyl sulfone dye showed that the longer of EO (ethylene oxide) chains, the faster the hydrolytic reaction of vinyl sulfone dye. From the absorption spectrum of dye, it could be concluded that more of dyes would be solubilized into the formed micelles, and dye-surfactant complexes were adhered to the surface of micelles if the molecular structure of surfactant had a shorter EO chains. Furthermore, the intramolecular or intermolecular hydrogen bond could be formed between dye and surfactant, which would further influence the hydrolytic reaction of vinyl sulfone dye. However, the solubility of surfactant in siloxane non-aqueous media would decrease with the increase of EO chains. Meanwhile, the dispersion of dye was enhanced as well as the hydrolytic reaction of dye. From this investigation, some surfactant can be used to improve the fixation of reactive dye during dyeing. Furthermore, washing times after dyeing and the ecological problems can be decreased.

The Navier-Stokes equation can be written in a form of Poisson equation. For laminar flow in a channel (plane Poiseuille flow), the Navier-Stokes equation has a non-zero source term (∇²u(x, y, z) = F_x (x, y, z, t) and a non-zero solution within the domain. For transitional flow, the velocity profile is distorted, and an inflection point or kink appears on the velocity profile, at a sufficiently high Reynolds number and large disturbance. In the vicinity of the inflection point or kink on the distorted velocity profile, we can always find a point where ∇²u(x, y, z) = 0. At this point, the Poisson equation is singular, due to the zero source term, and has no solution at this point due to singularity. It is concluded that there exists no smooth orphysically reasonable solutions of the Navier-Stokes equation for transitional flow and turbulence in the global domain due to singularity.