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Poro-elasto-capillary wicking of cellulose sponges

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Science Advances  30 Mar 2018:
Vol. 4, no. 3, eaao7051
DOI: 10.1126/sciadv.aao7051
  • Fig. 1 Capillary rise in cellulose sponges.

    (A) Optical images for wicking of water (main panel) and turpentine (inset) in the initially dry sponge. The sponge swells when contacting water or aqueous liquids (movie S1). From left to right, t = 0, 1, 10, 100, 1000 s. Scale bar, 10 mm. (B) Experimentally measured rise height of water (black symbols) and turpentine (red symbols) versus time. In the early stages (filled symbols), the rise height grows like t1/2 (gray line) for both the liquids. In the late stages (open symbols), the rise height of water follows the t1/5 rule (black line), whereas that of turpentine behaves like t1/4 (red line). (C) The power law of the height changes when the rise height h reaches Jurin’s height of macropores: hJ = γ/(ρgR), so the transition occurs at h/hJ ~ 1. The symbols for different liquids are listed in table S1. All the experimental data for the rise height are the average of three measurements, with the error bars smaller than the size of symbols.

  • Fig. 2 Microscopic images of the cellulose sponge.

    SEM images of macropores (A), micropores (B), and cross section of the sheets (C). Scale bars, 300 μm (A) and 10 μm (B and C). (D) Merging of micropores due to hygroscopic expansion of the cellulose sheet, as imaged by ESEM. The pores start to grow when the relative humidity (RH) exceeds 90%, and they coalesce with their neighbors. Scale bar, 10 μm. (E) Schematic illustration of micropore expansion and coalescence. The micropores grow from r0 to r1 in radius (pore expansion) and then merge to form large micropores of radius r (coalescence).

  • Fig. 3 The difference of wicking behavior between early and late stages.

    (A) Optical image of a sponge wetted by water. At small h, or in the early stages, the macro voids are completely filled with liquid. However, at large h, or in the late stages, they are only partially filled with liquid. A white curved line indicates the deformation of sponge due to the constraint of the dry upper part (section S1). The blue and red boxes show macro voids completely and partially filled with liquid, respectively. Scale bar, 10 mm. (B) Schematic of liquid-filling behavior in the late stages. Macro voids are not completely filled with liquid due to gravitational effects, whereas micropores are fully occupied with liquid. The radius of curvature δ of the meniscus in the macro void is determined by the balance between gravitational and capillary forces: δ ~ γ/(ρgh). (C) Schematic of a macro void of radius R in a microporous sheet in the early stages. Both macro and micro voids are completely filled with liquid. (D) Simplified model of the sponge whose wetting behavior is mathematically analyzed. Black box shows the liquid path near the wetting front. The liquid permeates into micropores from the wet corner of macropores.

  • Fig. 4 Wicking dynamics in different stages.

    (A) Experimentally measured rise height versus time in the early stages. (B) The early-stage data are collapsed onto a single line when plotted according to our scaling law h ~ [γRt/(ζμ)]1/2. The law holds for both the aqueous and nonaqueous liquids. (C) Two collapsed lines for aqueous (black line) and nonaqueous liquids (red line). (D) Experimentally measured rise height of aqueous liquids versus time in the late stages. (E) The late-stage data are collapsed onto a single line when plotted against our scaling law h ~ (Bt)1/5. (F) The experimental results appear to collapse onto a single line but disobey the t1/4 rule (Eq. 1). The symbols for different liquids are listed in table S1.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/3/eaao7051/DC1

    section S1. Effects of isotropic volumetric expansion on liquid rise height

    section S2. Correlation between hygroscopic strain and pore coalescence

    section S3. Recovery of microporous structure of cellulose sponges

    section S4. The volume fraction of aqueous liquid in a cellulose sheet

    section S5. Effects of water concentration on hygroscopic strain

    section S6. Mechanical properties of cellulose sponges

    section S7. Capillary rise in pre-swollen sponges

    section S8. Scaling laws of water rise within bread made from starch

    fig. S1. The measurement data of the cellulose sponge structure.

    fig. S2. Macroscopic experiments for pore coalescence.

    fig. S3. Numerical analysis of porous sheet deformation.

    fig. S4. Moisture flux into cellulose sheet in ESEM chamber.

    fig. S5. Microporous structure of cellulose sponges after cycles of wetting and drying with water.

    fig. S6. Analysis of the cellulose sheets.

    fig. S7. Hygroscopic strain of saturated sponge for different water contents in aqueous glycerin and ethylene glycol.

    fig. S8. Shear modulus of dry and wet cellulose sponge.

    fig. S9. Capillary rise height of water versus time in an initially dry sponge (black) and pre-swollen sponge (red).

    fig. S10. Capillary rise in porous bread.

    table S1. List of liquid properties and symbols.

    movie S1. Wicking and swelling in the cellulose sponge.

    movie S2. The merging of micropores in the cellulose sheets.

    References (3638)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Effects of isotropic volumetric expansion on liquid rise height
    • section S2. Correlation between hygroscopic strain and pore coalescence
    • section S3. Recovery of microporous structure of cellulose sponges
    • section S4. The volume fraction of aqueous liquid in a cellulose sheet
    • section S5. Effects of water concentration on hygroscopic strain
    • section S6. Mechanical properties of cellulose sponges
    • section S7. Capillary rise in pre-swollen sponges
    • section S8. Scaling laws of water rise within bread made from starch
    • fig. S1. The measurement data of the cellulose sponge structure.
    • fig. S2. Macroscopic experiments for pore coalescence.
    • fig. S3. Numerical analysis of porous sheet deformation.
    • fig. S4. Moisture flux into cellulose sheet in ESEM chamber.
    • fig. S5. Microporous structure of cellulose sponges after cycles of wetting and drying with water.
    • fig. S6. Analysis of the cellulose sheets.
    • fig. S7. Hygroscopic strain of saturated sponge for different water contents in aqueous glycerin and ethylene glycol.
    • fig. S8. Shear modulus of dry and wet cellulose sponge.
    • fig. S9. Capillary rise height of water versus time in an initially dry sponge (black) and pre-swollen sponge (red).
    • fig. S10. Capillary rise in porous bread.
    • table S1. List of liquid properties and symbols.
    • Legends for movies S1 and S2
    • References (36–38)

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    Other Supplementary Material for this manuscript includes the following:

    • movie S1 (.mov format). Wicking and swelling in the cellulose sponge.
    • movie S2 (.mov format). The merging of micropores in the cellulose sheets.

    Files in this Data Supplement:

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