Note: / = [0.791n(Re)-1.64]"2 for all correlations
(4) The vapor pressures of volatile component, Pjm (Pa) and Ppm (Pa) which is often determined by the vapor-liquid equilibrium. The driving force of MD is vapor pressure difference across the membrane imposed by a temperature difference across the membrane, or by a vacuum or a sweeping gas. An important assumption adopted in modeling MD is that the kinetic effects at the vapor-liquid interface are negligible. In other words, the vapor and liquid are assumed to be in the equilibrium state at the temperature of the membrane surface and at the pressure within the membrane pores. According to this assumption, vapor-liquid equilibrium equations can be applied to determine the partial vapor pressures of each component at each side of the membrane. For pure solvent, the partial vapor pressure is equal to the saturation pressure. According to the famous Antoine equation,
where pj (Pa) is the saturation pressure, T (K) is the temperature, and a, b and c are substance constants and are readily available in the references [53-55], For water, a = 23.1964, h = 3816.44, c = -46.13.
By means of mathematical model, we can know the performance of DCMD and find out the main factors affecting the process. Some results are obtained based on a specified microporous flat sheet membrane with the characteristics; d = 0.5 /jm, sftS - 3000 m"1 and hm = 300W m"2-K'1. The heat transfer coefficient is calculated by the following correlation obtained from the experiment:
4.2.1. The effect of temperature
In DCMD, the driving force for mass transfer of a volatile component through the membrane is its vapor pressure difference caused by the corresponding temperature difference between the two sides of the membrane. In principle, mass flux through the membrane can be improved by either increasing the feed temperature or decreasing the permeate temperature. Fig. 15 shows the change of mass flux with feed temperature under constant permeate temperature. The influence of feed temperature is remarkable in DCMD, As shown in Fig. 15, mass flux increases with feed temperature in an exponential way, reflecting the exponential increase of vapor pressure with temperature for the volatile components.
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