Mathematical modeling of pulp washing on rotary drums and their numerical solution for various adsorption isotherms
The mechanism of the displacement washing of the bed of pulp fibers is mathematically modeled by the basic material balance equation. Linear as well as non-linear adsorption isotherms are used to describe the relationship between the concentration of the solute in the liquor and concentration of the solute on the fibers. In the present study, the numerical solutions are obtained of pulp washing model with different adsorption isotherms. For the numerical solution “pdepe” solver in MATLAB is applied on the axial domain of the system of partial differential equations. Numerical results thus obtained are compared with earlier workers analytically and numerically. The comparison shows that results are in good agreement with both analytically as well as numerically and also show the suitability of the isotherm coupling with the washing model. The technique used in the present investigation is simple, elegant and convenient for solving two point boundary value problems with varying range of parameters.
A cake-washing model with an overall cation transfer in kraft pulp washing
Abstract Cake washing of freely mobile ions was described by an advection–dispersion equation combined with the Donnan equilibrium and an overall ion transfer model between the external liquid phase and the fiber phase of kraft pulp. The ion exchange rate coefficients between the phases were determined from the earlier published leaching test results for an oxygen delignified Scandinavian hardwood kraft pulp. The time constant of the first order process model was about 19 s for calcium and manganese and about 6 s for sodium and magnesium. The calculated results for various elements during the acid displacement were compared with the published displacement experiments. Calculated concentrations and pH profiles in wash effluent and cake were shown. Moreover, changes in pH values and redistribution of ions between the external phase and the fiber phase in the cake during the acid displacement were also demonstrated.
Experimental study on bond behavior between high-strength grout and deformed steel bars
Abstract Engineers use high-strength grout to connect precast concrete members for its low shrinkage and good fluidity. This paper designed 87 central pull-out specimens using the control variable method to investigate the influence of factors on the rebar-grout bond property such as compressive strength, steel grade, bar diameter, transverse stirrups, and bond length. The test result showed that improving grout compressive strength (85.8 MPa–122.7 MPa) cannot improve the bond strength, which was different from the previous conclusions of concrete pull-out tests. Simplified formulas were presented for calculating the characteristic values of bond strength, residual strength, peak slip, and relative slip of load-holding platform based on parameter analysis. Then, a constitutive model was proposed to predict the full-range bond stress-slip curve of high-strength grout and steel bar specimens from bearing to failure. Finally, FEA models were established to evaluate the applicability and accuracy of the constitutive model.