Chapter 13, Physical Separation Processes Video Solutions, Fundamentals of Food Process Engineering

Problem 1

Based on data for apple juice filtration in Table 13.2, calculate the filtration area of a rotary filter that must be used to filter $4000 \mathrm{~L} / \mathrm{h}$ of juice having a suspended solids content of $50 \mathrm{~kg} / \mathrm{m}^3$. Assume $\mathrm{k}$ is proportional to solids content. The medium resistance increases with increasing pre-coat thickness. A 10-cm-thick precoat is usually used on rotary filters. Assume the medium resistance is proportional to the precoat thickness. The rotational speed of the filter is $2 \mathrm{rev} / \mathrm{min}$ and the diameter is $2.5 \mathrm{~m}$. A filtration cycle on a rotary filter is the time of immersion of the drum in the slurry and in this particular system, $45 \%$ of the total circumference is immersed at any given time.

Kratika Bhadauria

Numerade Educator

01:56

Problem 2

The following data were obtained in a laboratory filtration of apple juice using a mixture of rice hulls and perlite as the filter aid. The filtrate had a viscosity of 2.0 centipose. The suspended solids in the juice is $5 \mathrm{~g} / \mathrm{L}$, and rice hulls and perlite were added each at the same concentration as the suspended solids. The filter has an area of $34 \mathrm{~cm}^3$. Calculate:
(a) The specific cake resistance and the medium resistance.
(b) The optimum filtration time per cycle and the average volume of filtrate per unit area per hour at the optimum cycle time.
$$
\begin{array}{lccc}
\hline \text { Time }(\mathrm{s}) & \text { Volume }(\mathrm{mL}) & \text { Time }(\mathrm{s}) & \text { Volume }(\mathrm{mL}) \\
\hline 100 & 40 & 400 & 83 \\
200 & 60 & 500 & 91 \\
300 & 73 & & \\
\hline
\end{array}
$$

Kratika Bhadauria

Numerade Educator

02:26

Problem 3

The following data were reported by Slack [Process Biochem. 17(4):7, 1982] on flux rates at different solids content during ultrafiltration of milk. Test if the flux vs. solids content follow that might be predicted by the theory on polarization concentration. What might be the reasons for the deviation? All flow rates are the same and the same membrane was used in the series of tests.
$$
\begin{array}{lc}
\hline \begin{array}{l}
\text { Mean solids } \\
\text { Content }(\%)
\end{array} & \begin{array}{c}
\text { Flux } \\
\left(L /\left(m^2 \cong h\right)\right)
\end{array} \\
\hline 12.3 & 28.9 \\
13.6 & 25.5 \\
14.9 & 22.1 \\
24.1 & 23.8 \\
\hline
\end{array}
$$

Chai Santi

Numerade Educator

04:14

Problem 4

The following analysis has been reported for retentate and permeate in ultrafiltration of skim milk. Retentate: $0.15 \%$ fat, $16.7 \%$ protein, $4.3 \%$ lactose, $22.9 \%$ total solids. Permeate: $0 \%$ fat, $0 \%$ protein, $4.6 \%$ lactose, $5.2 \%$ total solids.
(a) Calculate the rejection factor for lactose by the membrane used in this process.
(b) If the membrane flux in this process follows the data in Problem 3, calculate the lactose content of skim milk which was subjected to a diafiltration process where the original milk containing $8.8 \%$ total solids, $4.5 \%$ lactose, $3.3 \%$ protein and $0.03 \%$ fat was concentrated to $17 \%$ total solids, diluted back to $10 \%$ total solids and re-concentrated by UF to $20 \%$ total solids.

Harshita Goel

Numerade Educator

02:46

Problem 5

Calculate the average particle diameter and total particle surface area assuming spherical particles, per kg solids, for a powder which has a bulk density of $870 \mathrm{~kg} / \mathrm{m}^3$ and which has the following particle size distribution:
$$
\begin{array}{llc}
\hline+14, & -10 \text { mesh } & 10 \% \\
+18, & -14 \text { mesh } & 14.6 \% \\
+25, & -18 \text { mesh } & 22.3 \% \\
+35, & -45 \text { mesh } & 30.2 \% \\
+60, & -45 \text { mesh } & 22.9 \% \\
\hline
\end{array}
$$

Supratim Pal

Numerade Educator