Determination of Partial Propagation Velocity and Partial Isentropic Compressibility Coefficient in Water-Ethanol System

Abstract

This study introduces an innovative approach to the layered model, emphasizing the physical-chemical characterization of miscible liquid systems through ultrasonic techniques, with a specific focus on the water-ethanol system used in pharmaceutical formulations. Traditional characterization methods, while effective, face challenges due to the complex nature of solutions, such as the need for large pressure variations and strict temperature control. The proposed approach integrates partial molar volumes and partial propagation velocity functions into the layered model, enabling a nuanced understanding of miscibility and interactions. Ultrasonic techniques are used to calculate the isentropic compressibility coefficient for each component of the mixture as well as the total value using an additive mixing rule. Unlike conventional methods, this technique uses tabulated and experimental data to estimate the propagation velocity in the mixture, leading to a more precise computation of the isentropic compressibility coefficient. The results indicate a significant improvement in predicting the behavior of the water-ethanol system compared to the classical layered model. The methodology demonstrates the potential to provide new physicochemical insights that can be applied to other miscible systems beyond water-ethanol. This research has implications for improving the efficiency and accuracy of liquid medication formulations in the pharmaceutical industry.

Keywords: layered models; partial properties; propagation velocity; water–ethanol.

Figure 1

(a) Schematic diagram of pulse-echo and transmission techniques used to measure the propagation velocity of the mixture, (b) layered model considering the substances of the mixture as if they were separated in layers, taking into account the new approaching variables in the miscible case (top) and the conventional variables used in the nonmiscible system (bottom).

Figure 2

Scheme of experimental ($c_m$) and tabulated data ($V_m$, ${\overline{V}}_a$ and ${\overline{V}}_b$) input to calculate $c_{a\left(x_a\right)}$ and $c_{b\left(x_a\right)}$, which are used to determine $K_{sa}$ and $K_{sb}$. These coefficients are used to estimate the total $K_s$, which is compared to the conventionally calculated value.

Figure 3

(a) Piezoceramic probe, (b) setup scheme.

Figure 4

Water–ethanol molar volume properties at 20 °C [1].

Figure 5

Response pattern at 20 °C and $x_w=0$.

Figure 6

Experimental propagation velocity: new and conventional layers approach comparison at 20 °C.

Figure 7

Water and ethanol propagation velocity functions at 20 °C.

Figure 8

$K_{sW}$ and $K_{sE}$ functions in the water–ethanol solution at 20 °C.

Figure 9

Total $K_s$ comparison to the solution water–ethanol at 20 °C, $de{v}_{max}=22\%$ ($x_W=0.65$).