Aerogels achieve bulk porosities ranging between 90% and 99% alongside low volumetric mass densities due to drying techniques that remove interstitial pore solvents without inducing skeletal shrinkage or structural collapse. During standard ambient pressure drying (APD), the formation of curved solid-liquid-gas interfaces produces menisci within the pores. According to the Young-Laplace equation, surface tension within nanometer-scale pores generates capillary pressures reaching hundreds of megapascals. This force crushes delicate inorganic or polymeric solid skeletons, reducing the structure to a dense xerogel.

Supercritical Carbon Dioxide ($text{sCO}_2$) drying resolves this structural breakdown by taking advantage of fluid properties above the thermodynamic critical point of carbon dioxide ($T_c = 31.1^circtext{C}$, $P_c = 7.38text{ MPa}$), where the liquid-gas phase boundary vanishes. When surface tension drops to zero, capillary pressure is eliminated, allowing solvent extraction without mechanical stress, thereby preserving the original three-dimensional wet gel network.

From thermodynamic and mass-transport perspectives, $text{sCO}_2$ extraction represents a multi-physics coupled domain involving molecular diffusion, convective mass transfer, and phase behavior within confined geometry. During the initial displacement phase, liquid-phase $text{sCO}_2$ under pressure diffuses into the pore network to mix with the trapped organic solvent (typically ethanol or acetone). Under these condition, $text{sCO}_2$ combines gas-like diffusion coefficients and low dynamic viscosities with liquid-like solvent capacity, penetrating deep within pores measuring only a few nanometers across.

Mass transport kinetics inside these nanopores are governed by Knudsen diffusion mechanisms. As the concentration of dissolved $text{sCO}_2$ inside the pore space reaches saturation, the fluid converts into a single-phase supercritical binary mixture. During the subsequent depressurization step, the fluid returns to a gaseous state and vents from the vessel. If depressurization rates exceed critical thresholds, localized fluid expansion creates internal pressure gradients that exceed the tensile strength of the solid aerogel skeleton, causing fracturing or irreversible volumetric swelling. Precise regulation of thermal fields, pressure decay rates, and phase transition dynamics during supercritical processing dictates the physical preservation of aerogel micro-topologies.