Authors' Reply to Comments

Abstract

494number Dt/L~2 and the ~dimensionless number kt/Lã re important; only in case of which has to be proved experimentally, it is allowed to reduce our equation 4 to equation 9 as proposed by the authors in their paper.3. As a value for D, the authors use the numerical value of the molecular diffusion coefl5cient-which, in our opinion, is valid only for relatively free mobility of the molecules but does not apply to the restricted mobility in the yarns. We therefore would propose a diffusion coefficient related to the structure of the textile, so that in which td is the porosity of the fabric, based on the fractional volume of voids in the yarn around the fibers. Eventually, the effective diffusion constant may also be expressed as a function of the tortuosity of the textile structure.We hope that our critical comments, may support and stimulate the discussion on the interesting field of diffusion, mass transfer, and Huid How in and around textile structures. I Our model was developed to investigate certain aspects of domestic laundry. During domestic laundry, a load of textile articles is contacted with a certain volume of water, which may be agitated or soaked. During this operation, two important variables are the textile porosity and the mass of the load or the clothto-liquor ratio. In a laboratory washing machine, mechanical agitation is induced by an oscillating paddle. Our model proposes that the flow of water from the agitated bath penetrates the porous load only to a certain distance, giving rise to stagnant regions. When the mechanical agitation increases, the flow of water increases'between the textile articles and also through the yarps-i.e. around the fibers. This physical model has been tested by rinsing an aqueous solution of KCI from six pieces of textile in one liter of water in a 2-1 tergotometer.Van der Linden and Groot Wassink basically raise two questions: 1 ) How do we see the contribution of convection or flow in our model?2) Can the bulk diffusion coefficient describe the motion of KCI ions in the immobile water in the stagnant region.In our model, the contribution of convection is characterized by the term MH, the amount of salt located in the convective region of the porous load. This term can be calculated from the rinsing rate of salt solution from the textile pieces (Fig. 3) and is given in Table I in our paper. For cotton pieces, Table I shows that, as the agitator Reynolds number increases by a factor of 2.5, the ratio MH Mo-' for a constant Mo increases by a factor of 4.2. This is an indication that the convective region increases significantly due to the increased flow of water around the fibers and between the textile pieces. The time scales of the convective (-2s) and the diffusional (--10s) removal may also be estimated from Figure 3, using the initial and the subsequent removal rates. Under the agitation conditions of Figure 3, the initial removal time agrees with the mixing time of the bath, indicating a comparable magnitude of the water velocity in the bath and in the convecti...