Mixing mechanism of solid powders is generally classified into three stages as follows: (1) convective mixing, (2) diffusive mixing and (3) shear mixing.
In the convective mixing, we assumed a simple model to make use of matrix method, and derived Eq. (5). In the case of diffusive mixing, we derived Eq. (11) by solving the equation of diffusion.
In the shear mixing, which plays an especially important role in the mixing of wetted powders, we assumed that the size reduction of gathered mass of wetted powders greatly affected the variance of the mixture.
Then we also assumed that the relation between Eqs. (12) and (13) represented the relation between σ² and N_p, and Eq. (14), the size reduction rate of gathered mass of wetted powders, and got the results as shown by Eqs. (17) and (20). From these four equations, we supposed that the theoretical curve for mixing was composed of two straight lines on semilog section paper (Fig. 10).
To make sure the propriety of these results, we conducted some experiments with a finger-prong type mixer, using wetted PVC-powders, and got results as shown in the figures of this report.

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In our former report we discussed the relation between water content and material temperature at the decreasing drying rate period under the constant drying condition. The relations among the gas temperature, t, material temperature, t_m, and water content, F, under the unsteady drying condition-in a dryer of continuous counter current or parallel current-were studied, too.
For drying granular and powdered materials, the high temperature gas (400700°C) is frequently used. In such a case, as in the case of drying a material containing organic solvents, the sensible heat needed for heating the evaporated vapor from the evaporating temperature to the temperature of the main gas stream (the so-called Ackermann effect), cannot be overlooked.
In this paper, the relations among t, t_m and F shall be discussed, taking into consideration the presence of this effect in the decreasing drying rate period.
I. Under the steady drying condition:
The heat at the surface of the material, q_nd, (Fig. 1) may be calculated by solving the differential equation, Eq. (11).
q_nd=h(t-t_m)b/(e^b-1) (15)
b=R_dC_p/h
The decreasing drying rate, R_d, is shown by Eq. (20).
R_d=W₀(-dw)/A₀dθ=R_c(F/F_c)=(h/C_p)(lnD)(F/F_c) (20)
The heat transferred from the main gas stream to the boundary film, q_td, (Fig. 1) is represented by:
q_td=h(t-t_m)be^b/(e^b-1) (17)
The heat, q_nd, causes the drying and the rise of the temperature of the material.
q_nd=h(t-t_m)b/(e^b-1)=(W₀/A₀)(-dw/dθ)r_m+(W₀/A₀)(c+c_ww)(dt_m/dθ) (19)
From Eqs. (19) and (20),
(dt_m/dw)={r_m-C_p(t-t_m)/(D^F/Fc-1)}/(c+c_ww) (21)
Eq. (21) shows the relation between t_m and w in the decreasing drying rate period. This equation can be solved by the numerical method. When the sensible heat of water at critical water content (c_ww_c) is small as compared with the specific heat of the dried material (c>c_ww_c), and r_m_??_r_w, Eq. (21) can be solved analytically:
(t-t_m)=r_wF_c/cln, D^∞Σ_k=11/n-k(D^F/Fc-1/D^F/Fc)^k
+(D/D-1)ⁿ(D^F/Fc-1/D^F/Fc)ⁿ{(t-t_w)-r_wF_c/clnD)^∞Σ_k=1(D/D-1)^k} (23)
n=(C_pF_c)/(clnD), D=C_p(t-t_w)+r_w}/r_w
Under the ordinary drying condition, the terms below the third one may be discarded.
II. Under the unsteady drying condition:
The heat balance in the differential small area of a continuous counter or parallel current dryer is given by:
±GC_Hdt=q_tdAdθ (25)
+ count. cur., - para. cur.
From Eqs. (20)', (17) and (25)

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The overall gas-side capacity coefficients (K_Ga) in the towers packed with 1''-, 1/2''-, 3/8''-Raschig rings and 1''-, 1/2''-Berl saddles, respectively, were measured by means of the absorption of ammonia by water. The gas-side capacity coefficient (k_Ga) was calculated by subtracting the resistance of liquid phase from K_Ga, using the equations the authors reported previously. K_Ga and k_Ga were correlated with liquid and gas rates by the exponents figured in Table 2, which were in agreement with the values obtained from the previous experiments.
Assuming that the effective surface area (a) was proportional to the wetted surface area (a_ω) as described in the authors' previous reports, k_G was derived by dividing k_Ga by a_ω. It was clarified that k_G derived in this way was completely independent of the liquid rates. From the nature of k_G, this independence of k_G of L appeared to be most reasonable.
The relation of k_G with other operational variables, especially with G, was expressed by Eqs. (8) and (9) for Raschig ring and Berl saddle, respectively.
Allowing some discrepancies between them, these relations were summarized into the following single equation for both Raschig rings and Berl saddles:
(k_GRT/a_tD_G)=0.014(G/a_tμ_G)^0.8(ρ_G²g/μ_G²a_t³)^0.2(μ_G/ρ_GD_G)^1/3
By the similar procedure, another single equation was obtained as follows, representing the liquid-side mass transfer coefficient:
k_L(ρ_L/μ_Lg)^1/3=0.02(L/a_tμ_L)^1/2(μ_L/ρ_LD_L)^-1/2

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