2.2.2. Design and fabrication of microchannels
From the permeation coefficient determined in Section 2.2.2 and the
designated dialysis residence time, the specific surface area of the
dialysis membrane—the channel area with respect to the channel
volume—was determined. As shown in Fig. 2, a microchannel is assumed
to have a dialysis membrane sandwiched between a feed-side channel and a
permeation side channel, and GdnHCl permeates from the feed side to the
permeation side through the dialysis membrane. When GdnHCl solution was
supplied with the concentrations c f0 [mol/L]
and c p0 [mol/L] and flow ratesv f [m3/s] andv p [m3/s] from the inlet of
the feed-side channel and the permeation side channel, the following
equation can be derived for the mass balance of GdnHCl, assuming thatv f and v p are constant
throughout the flow channel:
\begin{equation}
\text{\ \ }\frac{v_{p}+v_{f}}{v_{p}\cdot v_{f}}\cdot\frac{P\cdot WZ}{L}=\ln\frac{c_{f0}-c_{pZ}}{c_{fZ}-c_{p0}},\ (3)\nonumber \\
\end{equation}where W [m] and Z [m] represent the width and
length of the microchannel, and c fZ [mol/L]
and c pZ [mol/L] are the concentrations of
GdnHCl at the feed side and permeation side outlets, respectively. The
following formula can be established for the mass balance of the inlet
and outlet:
\begin{equation}
\text{\ \ }\left(c_{fZ}-c_{f0}\right)\cdot v_{f}+\left(c_{pZ}-c_{p0}\right)\cdot v_{p}=0\ (4)\nonumber \\
\end{equation}At the flow channel design stage, assuming that a sufficient permeate
flow rate is applied (v p>> v f), eq. (3) can be
simplified to eq. (5).
\begin{equation}
\text{\ \ }\frac{1}{v_{f}}\cdot\frac{P\cdot WZ}{L}=\ln\frac{c_{f0}-c_{pZ}}{c_{fZ}-c_{p0}}\ \ (5)\nonumber \\
\end{equation}When using the channel height on the feed side d [m] and the
residence time τ [s], the channel volume is WZd =v f·τ , and eq. (5) becomes
\begin{equation}
\text{\ \ }\frac{\tau}{d}\cdot\frac{P}{L}=\ln\frac{c_{f0}-c_{pZ}}{c_{fZ}-c_{p0}}\text{\ \ }\left(6\right).\nonumber \\
\end{equation}In this study, the standard residence time, τ , of the
microchannel was set to 20 minutes, much shorter than the residence time
of conventional dialysis processes, which usually take several days, and
longer than the time required for the folding of the model enzyme, CA,
which is around 10 minutes (Ikai et al., 1978). Within this residence
time, the channel height d (= WZd /WZ ) required to
reduce the GdnHCl concentration from c f0 = 5 M
for protein unfolding to c fZ = 0.5 M required for
refolding (Cleland & Wang, 1992; Wetlaufer & Xie, 1995) was determined
to be 500 μm, using eqs. (4) and (6).
The channel length was determined by setting a feed volume flow ratev f = 0.05 mL/min and a channel width of 5 mm, to
be 40 cm. Using these values, serpentine type microchannels were
fabricated (Figure 3). A GdnHCl solution with or without CA was fed into
the feed-side inlet, and pure water or folding buffer was fed from the
permeation side inlet. As the permeate side channel, poly (methyl
methacrylate) (PMMA), which has strength, transparency, and chemical
resistance, was used. As the feed-side channel for introducing proteins,
poly (dimethylpolysiloxane) (PDMS), which has transparency, low damage,
and low adsorptivity to protein, was used. The PDMS flow path was
prepared by first fabricating a machined PMMA (convex) mold, into which
PDMS prepolymer mixture (Sylgard 184) was poured, and an incubator
LTI-601SD (EYELA, Tokyo, Japan) was used for curing the PDMS for one
hour at 60 °C (Briones et al., 2006).