1. Origin of the Knudsen Effect

    The Knudsen Effect is named after Martin Hans Christian Knudsen (1871–1949), a Danish physicist who made pioneering contributions to the study of rare gas dynamics and molecular transport phenomena.In the early 20th century, Knudsen investigated how gas behavior changes when confined in narrow capillaries or pores, where the size of the channels is comparable to the mean free path of gas molecules.Through his experiments between 1909 and 1911, Knudsen discovered that:

       · When the pores or tubes are extremely small, gas molecules collide more frequently with the walls than with each other.

       · This changes gas flow and heat transfer behavior dramatically, deviating from classical continuum (Navier–Stokes) theory.

    These discoveries led to two famous phenomena bearing his name:

    Knudsen's findings laid the foundation for modern microfluidics, vacuum technology, and nanoporous material science — including aerogels.

2. What Is the Knudsen Effect?

    The Knudsen Effect refers to the phenomenon that occurs when the pore size of a material becomes comparable to or smaller than the mean free path of gas molecules.In such a situation, gas molecules collide more frequently with the pore walls than with each other, which significantly reduces the thermal conductivity of the gas phase inside the pores.

       · The mean free path (λ) is the average distance a gas molecule travels between two collisions.

       o For air at room temperature and atmospheric pressure, λ ≈ 70 nm.

3.  Knudsen Number (Kn)

    The strength of the Knudsen effect is represented by the Knudsen number, defined as: Kn=λ/r ,where:

       · λ = mean free path of gas molecules

       · r = pore radius

    Depending on the value of Kn, heat transfer behavior changes:

4. How It Works in Aerogels

    In silica aerogels, the pore sizes are typically 10–100 nm, which are comparable to or smaller than the mean free path of air molecules.
This means ( Kn>1 ), so the system is in the free molecular regime, where the Knudsen effect is very strong. As a result:

       · Gas molecules are trapped in nanopores and mostly collide with the solid silica walls, not with each other.

       · These wall collisions are mostly random reflections, transferring very little energy.

       · Therefore, the gas-phase thermal conductivity is greatly suppressed — often 1/10 or less of that of free air.

5. Components of Aerogel Thermal Conductivity

    The total thermal conductivity of aerogel (k_total) has three parts: k_total=k_solid+k_gas+k_radiation 

       · k_solid: heat conduction through the silica skeleton (very low due to its sparse structure)

       · k_gas: heat conduction through the air in pores (strongly reduced by the Knudsen effect)

       · k_radiation: heat transfer by thermal radiation (significant only at high temperature)

    The Knudsen effect mainly reduces (k_gas), which is why aerogels have extremely low total thermal conductivity (typically 0.012–0.018 W/m·K).

6. Summary

1. Structural Nature — Extremely Porous 3D Network with Ultra-high porosity (>90%)

    Silica aerogel typically has a porosity between 90% and 99.8%, meaning:

       · Only 1–10% of its volume is solid material;

       · The rest is air-filled voids.

    As a result:

       · The load-bearing cross-sectional area is extremely small;

       · Stress concentrates on the thin silica necks connecting nanoparticles;

       · Once one link breaks, a cascade collapse occurs through the network.

Analogy: It’s like a 3D scaffold made of glass needles — extremely light, but very easy to break.

 2. Chemical Bond Nature — Strong but Brittle Si–O–Si Bonds

    The silica skeleton is built from Si–O–Si covalent bonds, which are:

       · Strong (bond energy ≈ 450 kJ/mol), but

       · Directional and non-ductile — they cannot deform plastically like metallic bonds.

    Therefore, when external stress exceeds the critical point, the bonds fracture suddenly instead of yielding.

    In other words: Once a Si–O–Si chain is overstressed, it snaps instantly rather than absorbing energy by deformation.

3. Microstructural Fragility — Stress Concentration at Nanoscales

       · Primary particle size: 10–50 nm

       · Particles are linked by thin “neck-like” bridges

       · Each node has a low coordination number, so load transfer paths are few

    When force is applied:

       · Local bonds break first,

       · The network collapses locally,

       · Microcracks propagate into macroscopic fractures.

4. Drying Process Effects — Capillary Forces Create Microcracks

    During the sol–gel process, the drying stage can introduce residual damage:

       · In non-supercritical drying, capillary pressure can crush the delicate gel network;

       · Even in supercritical drying, minor shrinkage or microcracks may remain;

       · These become stress initiation sites under later mechanical loading.

 5. Macroscopic Mechanical Properties — Very Low Modulus and Fracture Toughness

    These values show: Silica aerogel’s fracture toughness is about 1/10 of glass and 1/1000 of metals,making it almost incapable of resisting bending, compression, or impact.

6. Methods to Improve Toughness

    Researchers and manufacturers are developing several strengthening strategies:

    (1)Fiber Reinforcement

       · Introduce glass, aramid, or polymer fibers;

       · Create aerogel blankets or composite panels;

       · Greatly improves flexural and compressive strength.

    (2)Organic–Inorganic Hybridization

       · Graft flexible polymer chains (e.g., PDMS, PVA, PMMA) onto silica skeletons;

       · Increases elasticity and crack resistance.

    (3) Nanostructure Optimization

       · Control particle size, neck thickness, and pore size distribution;

       · Build hierarchical porous networks to enhance energy absorption.

1. Core Physics: Capillary Pressure (Laplace Pressure)
     · During drying, liquid–gas interfaces form menisci inside nanopores, exerting negative capillary pressure on the fragile skeleton:

P=2γcos⁡θrP = \frac{2 \gamma \cos \theta}{r}
    · γ\gamma: surface tension of solvent
    · θ\theta: contact angle (for hydrophilic surfaces, θ≈0∘\theta \approx 0^\circ, cos⁡θ≈1\cos \theta \approx 1)
    · rr: pore radius (smaller pore → higher stress)
    · Magnitude example (hydrophilic case):
       o Ethanol: γ≈0.022 N/m,r=10 nm⇒P≈4.4 MPa\gamma \approx 0.022\ \text{N/m}, r=10\ \text{nm} \Rightarrow P \approx 4.4\ \text{MPa}
       o Water: γ≈0.072 N/m,r=10 nm⇒P≈14.4 MPa\gamma \approx 0.072\ \text{N/m}, r=10\ \text{nm} \Rightarrow P \approx 14.4\ \text{MPa}

    Such stress is far above the yield strength of the “wet” silica skeleton, leading to elastic–plastic deformation, pore collapse, shrinkage, densification, or even cracking.

2. Structural & Chemical Factors
    · Smaller pores / narrow distribution → stronger capillary stress.
    · Insufficient neck growth (weak skeleton) due to poor aging → prone to irreversible plastic shrinkage.
    · Surface state: hydrophilic Si–OH surfaces (low θ\theta) → high stress; hydrophobic surfaces (high θ\theta) reduce stress.
    · Solvent: high γ\gamma (e.g., water) increases stress.
    · Sample geometry: thick monoliths develop drying gradients → cracks; thin films/felts are less prone.
    · Pre-shrinkage (syneresis) during gelation/aging can set the stage for further collapse.

Summary: Shrinkage mainly comes from capillary pressure; small pores, hydrophilic surfaces, high-γ\gamma solvents, weak skeletons, and thick parts all worsen it.

1. How is the pore structure of aerogel formed?

    Aerogels are typically produced using the sol–gel process, and their pore structure develops through three main steps:

    (1)Sol Formation

        a. A precursor (e.g., tetraethyl orthosilicate, TEOS) undergoes hydrolysis and condensation reactions in solution.

        b. This generates a large number of uniformly dispersed silica nanoparticles.

    (2) Gelation

        a. As condensation continues, these nanoparticles connect via chemical or hydrogen bonds, forming a 3D interconnected network.

        b. The pores are still filled with solvent (alcohols or water) — this is called a "wet gel."

    (3) Drying

        a. The critical step is to remove the solvent without collapsing the fragile network.

        b. Simple evaporation causes capillary forces and collapse.

        c. Therefore, supercritical drying or surface modification + controlled drying is used to replace liquid with gas while retaining the network.

        d. The result is a solid with a nanostructured porous network (pore size ~10–100 nm, porosity 80–99%).

    In summary: the aerogel's pore structure is formed by a nanoparticle network from sol–gel chemistry, preserved by a special drying process.

2. If we use 3D printing to create a similar porous structure, is it also an aerogel?

    Strictly speaking, no.

    (1) Essential difference

        a. Aerogel pores are naturally self-assembled at the nanoscale via chemical reactions.

        b. Most 3D printing technologies today can only fabricate pores at the microscale or larger, not true nanostructures.

        c. The printed object would be a porous scaffold, but not classified as an aerogel.

    (2) Definition issue

        a. The widely accepted definition of aerogel is: a material derived from a sol–gel process, dried to preserve its nanostructured porous network.

        b. If a material does not come from this process, even if it looks similar, it usually isn't considered an aerogel.

3. Interesting frontier

    · If future 3D printing technologies can build structures with nanoscale precision, high porosity, and ultralow density, then we might achieve “aerogel-like” materials.

    · Some researchers are already combining 3D printing inks with sol–gel precursors to print wet gels and then dry them into true 3D-printed aerogels.

 
Conclusion

    · Aerogel pore structures are formed by sol–gel chemistry + special drying methods.

    · Simply 3D printing a porous structure ≠ aerogel; it would be called a porous material.

    · But if 3D printing is combined with sol–gel methods, then 3D-printed aerogels are possible.

1. Fundamental Differences

    Silica Aerogel

        · Preparation: Produced by the sol–gel process followed by supercritical drying.

        · Structure: A three-dimensional, continuous nanoporous network with porosity as high as 80–99%.

        · Properties:

        o Extremely low density (0.003–0.2 g/cm³)

        o Very high surface area (500–1200 m²/g)

        o Ultra-low thermal conductivity (as low as 0.012–0.016 W/m·K)

        o High optical transparency (up to >80% visible light transmittance)

    Fumed Silica (Pyrogenic Silica)

        · Preparation: Produced mainly by hydrolysis of silicon tetrachloride (SiCl₄) in a hydrogen-oxygen flame (chemical vapor process).

        · Structure: Amorphous nanoparticles (7–40 nm), loosely aggregated, not forming a continuous porous network.

        · Properties:

        o White, lightweight powder

        o High surface area (200–400 m²/g)

        o Strong rheological and thickening effects

        o High adsorption capacity

2. Application Differences

    Silica Aerogel

        · Building & Construction: Super-thin insulation for walls, roofs, curtain walls, and retrofitting of historical buildings

        · Energy & Batteries: Thermal management and fire protection for lithium-ion batteries and energy storage systems

        · Petrochemical/Industrial: High-temperature pipeline and equipment insulation

        · Aerospace: Spacecraft thermal insulation (famously used by NASA for Mars missions)

        · Optics & Acoustics: Transparent insulating glass, sound-absorbing and wave-absorbing materials

        · Environmental: Oil-spill sorbents, air-filtration materials

    Fumed Silica

        · Rubber/Plastics: Reinforcing filler to improve strength and wear resistance (especially in silicone rubber)

        · Coatings/Inks: Thickener, anti-settling agent, rheology modifier

        · Adhesives/Sealants: Improves flow control and stability

        · Pharma/Food: Anti-caking agent, excipient, carrier

        · Cosmetics: Enhances texture, spreadability, and stabilit

3. Summary
    Nature
        · Aerogel → A nanoporous 3D solid network (lightweight, super-insulating)

        · Fumed Silica → A nanoparticle powder (rheology modifier, reinforcing agent)

    Applications

        · Aerogel → High-performance insulation, optics, aerospace, specialty uses (high-value functional material)

        · Fumed Silica → Commodity additive across many industries (cost-effective, broad usage)

    You can think of fumed silica as a nano-powder “additive” to tune system performance, while silica aerogel is a nano-sponge “structural material” with unique functional properties.

1. Drying Methods of Aerogels and Their Differences

    Drying is the most critical step in aerogel fabrication. The goal is to remove solvents while preserving the 3D nanoporous network. Main methods include:
    （1）Ambient Pressure Drying (APD)
        · Low cost, but large shrinkage and uneven pore distribution result in degraded performance.
    （2）Freeze Drying (FD)
        · Removes solvent by sublimating ice; however, large pores or collapse may occur.
    （3）Supercritical CO₂ Drying (CO₂-SCD)
        · Mild conditions, decent pore retention, but requires multiple solvent exchanges and pore uniformity is limited.
    （4）Supercritical Ethanol Drying (EtOH-SCD)
        · Directly dries under ethanol supercritical conditions, eliminating capillary stress.
        · Produces the most uniform nanopore distribution, high porosity, large surface area, and excellent thermal stability.
        · Silica aerogels remain intact even at 500–1000℃.

    In summary: Aerogels prepared by EtOH-SCD have the most uniform nanoporous structure and best thermal stability, making them the top choice for high-end applications.

2.  IBIH is a global leader in using ethanol supercritical drying technology to mass-produce high-quality aerogels.
     IBIH employs advanced EtOH-SCD technology with proprietary large-scale horizontal drying equipment.
     Achieved industrial-scale production from lab to tens of thousands of metric square metres, with full intellectual property rights.
    Performance Highlights:
        · Porosity up to 85–99% with narrow pore size distribution.
        · Thermal conductivity as low as 0.016 W/(m·K).
        · Structural stability maintained at 500–1000℃
        · Visible light transmittance >80%, suitable for translucent  insulation.
        · Excellent compressive resilience and long service life.

Overall Evaluation:
    IBIH’s EtOH-SCD silica aerogels combine ultralow thermal conductivity, exceptional thermal stability, and optical transparency, representing the global top level. They are especially suited for high-end applications in energy-efficient buildings, new energy batteries, and aerospace.