Chapter 4 From Stem to Cup

A liquid that thins when stirred

A solution of a long-chain polysaccharide does not flow like water. At rest the chains are tangled; when the liquid is stirred or swallowed, the chains line up with the flow and the liquid becomes thinner. Liquids that behave this way are called shear-thinning or pseudoplastic, and many food thickeners, including glucomannans, behave this way above a certain concentration (Morris et al. 1981).

The simplest description is the power law of Ostwald and de Waele:

$\tau = K\,\dot{\gamma}^{\,n}, \qquad \eta_{\text{app}} = \frac{\tau}{\dot{\gamma}} = K\,\dot{\gamma}^{\,n-1},$

where $\tau$ is the shear stress, $\dot{\gamma}$ the shear rate, $K$ the consistency index and $n$ the flow index. For water $n = 1$ ; for a shear-thinning liquid $n < 1$ , and the apparent viscosity $\eta_{\text{app}}$ falls as the shear rate rises (Steffe 1996).

Calculation

Fitting $K$ and $n$ to a flow curve by a straight line on logarithmic axes, then apparent viscosity at two shear rates, three concentrations and two temperatures. The “measurements” are simulated; the scaling with concentration ( $K \propto c^{3.3}$ , typical of random-coil polysaccharides above the overlap concentration) and with temperature (Arrhenius, 20 kJ/mol) are assumptions.

import math, random

# 1. Fitting the power law τ = K·γ̇ⁿ to a flow curve. The "measurements" here are simulated
#    (K = 0.80 Pa·sⁿ, n = 0.55, 3 % noise), to show the method; real values must be measured.
random.seed(7)
rates = [1, 2, 5, 10, 20, 50, 100, 200]
stress = [0.80 * g ** 0.55 * random.gauss(1, 0.03) for g in rates]
x = [math.log(g) for g in rates]
y = [math.log(s) for s in stress]
mx, my = sum(x) / len(x), sum(y) / len(y)
n = sum((a - mx) * (b - my) for a, b in zip(x, y)) / sum((a - mx) ** 2 for a in x)
K = math.exp(my - n * mx)
print(f"fitted K = {K:.2f} Pa·sⁿ, n = {n:.2f} (n < 1: shear-thinning)")

# 2. Apparent viscosity η = K·γ̇ⁿ⁻¹, with K scaling as c^3.3 above the overlap concentration
#    (typical of random-coil polysaccharides; Morris et al. 1981) and an Arrhenius temperature
#    dependence (activation energy 20 kJ/mol assumed).
def eta(c, rate, t_c, K1=0.80, n1=0.55, Ea=20e3):
    Kc = K1 * (c / 1.0) ** 3.3 * math.exp(Ea / 8.314 * (1 / (t_c + 273.15) - 1 / 293.15))
    nc = max(0.3, n1 - 0.15 * math.log(c))          # more concentrated, more shear-thinning
    return Kc * rate ** (nc - 1)

print("\napparent viscosity, mPa·s (water at 20 °C ≈ 1 mPa·s)")
print("polysaccharide   20 °C at 10 / 50 s⁻¹     45 °C at 10 / 50 s⁻¹")
for c in (0.25, 0.5, 1.0):
    print(f"   {c:4.2f} %        {1000 * eta(c, 10, 20):6.0f} / {1000 * eta(c, 50, 20):5.0f}"
          f"          {1000 * eta(c, 10, 45):6.0f} / {1000 * eta(c, 50, 45):5.0f}")
# fitted K = 0.79 Pa·sⁿ, n = 0.55 (n < 1: shear-thinning)
#
# apparent viscosity, mPa·s (water at 20 °C ≈ 1 mPa·s)
# polysaccharide   20 °C at 10 / 50 s⁻¹     45 °C at 10 / 50 s⁻¹
#    0.25 %             5 /     3               2 /     2
#    0.50 %            37 /    21              19 /    11
#    1.00 %           284 /   138             149 /    72

Apparent viscosity against shear rate for the assumed solutions at 20 °C (solid) and 45 °C (dashed). A shear rate of about 50 s⁻¹ is often taken to represent the mouth.

The steep rise with concentration matters most. Doubling the concentration raises the viscosity nearly eightfold, so a cup made from the same stem can be watery or syrupy depending on how much water is added and how much polysaccharide comes out. Warming thins the liquid too, by about half between 20 and 45 °C under the assumed activation energy.

Note

No published flow curves for a fresh D. officinale decoction were found while writing this book. The values of $K$ and $n$ above are placeholders that show the method; the first measurements on real decoctions, with a rotational rheometer, would replace them.

How much is in a cup, and how fast it comes out

Calculation

The polysaccharide available from 12 g of fresh stem, and its release over time at three temperatures, using first-order kinetics with an Arrhenius rate. The rate constant and activation energy are illustrative.

import math

# 1. How much polysaccharide is in a cup? Assumed: fresh stems 80 % water; polysaccharide
#    30 % of dry matter (the Chinese Pharmacopoeia requires at least 25 % in the dried herb).
fresh_g, water_frac, poly_dry = 12.0, 0.80, 0.30
poly_g = fresh_g * (1 - water_frac) * poly_dry
for cup_ml in (150, 250):
    print(f"{fresh_g:.0f} g fresh stem in {cup_ml} mL: up to {poly_g:.2f} g polysaccharide, "
          f"{100 * poly_g / cup_ml:.2f} % if all of it dissolved")

# 2. How fast does it come out? First-order release, X = 1 − exp(−k·t), with the rate rising
#    with temperature (Arrhenius). Illustrative: k = 0.10 per minute at 100 °C, Ea = 40 kJ/mol.
def released(t_min, temp_c, k100=0.10, Ea=40e3):
    k = k100 * math.exp(-Ea / 8.314 * (1 / (temp_c + 273.15) - 1 / 373.15))
    return 1 - math.exp(-k * t_min)

print("\nshare released from crushed stem")
print("minutes    60 °C    80 °C   100 °C")
for t in (5, 10, 20, 40):
    print(f"  {t:3d}     {100 * released(t, 60):5.0f} %  {100 * released(t, 80):5.0f} %  "
          f"{100 * released(t, 100):5.0f} %")
# 12 g fresh stem in 150 mL: up to 0.72 g polysaccharide, 0.48 % if all of it dissolved
# 12 g fresh stem in 250 mL: up to 0.72 g polysaccharide, 0.29 % if all of it dissolved
#
# share released from crushed stem
# minutes    60 °C    80 °C   100 °C
#     5        10 %     21 %     39 %
#    10        19 %     38 %     63 %
#    20        35 %     62 %     86 %
#    40        57 %     85 %     98 %

Under these assumptions a cup contains a few tenths of a gram of polysaccharide, at a concentration of about 0.3–0.5 % if all of it dissolves. Heat speeds release several-fold: at 100 °C most comes out within 20 minutes, at 60 °C barely a third. Crushing or pressing the stem first helps, because it breaks the tissue and shortens the distance the chains must travel.

Why boil soon after pressing?

The proposal behind this chapter was that a freshly pressed juice should be boiled at once, for three reasons: to stop the plant’s own enzymes from cutting the polysaccharide chains, to break open the cell walls, and to let the long chains dissolve and spread into a thick network. The second and third reasons follow from the calculations above. The first is plausible, since pressing mixes cell contents that the living tissue keeps apart and heat inactivates most plant enzymes, but no study measuring polysaccharide breakdown in fresh D. officinale juice left unheated was found. Heat has a cost as well: long boiling can break the chains themselves and lower the viscosity. How long to heat, and at what temperature, is therefore an open question that the measurements suggested above could settle.

Hypothesis · not established

Not established. Fresh D. officinale juice left at room temperature for two hours before heating has a lower polysaccharide molecular weight and a lower apparent viscosity at 50 s⁻¹ than juice heated to 95 °C within ten minutes of pressing. The hypothesis predicts a fall of at least 20 % in viscosity in the delayed samples, prevented by immediate heating. If delayed and immediate samples do not differ by 20 % or more, the hypothesis is refuted.

References

Morris, E. R., A. N. Cutler, S. B. Ross-Murphy, D. A. Rees, and J. Price. 1981. “Concentration and Shear Rate Dependence of Viscosity in Random Coil Polysaccharide Solutions.” Carbohydrate Polymers 1 (1): 5–21.

Steffe, James F. 1996. Rheological Methods in Food Process Engineering. 2nd ed. Freeman Press.

Fan, Y. (2026). Ecological Cultivation, Stress-Induced Polysaccharide Synthesis and Fresh-Extract Rheology of Dendrobium officinale: CAM Photosynthesis, VPD Water Control, Growth-Differentiation Balance and Nocturnal Core-Body-Temperature Regulation [铁皮石斛的生态栽培、逆境多糖合成与鲜汁流变学] (Version 1.0.0). 5D Library. https://doi.org/10.5281/zenodo.23729740 · Licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0).