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Using indentation to characterize the poroelasticity of gels

Yuhang Hu's picture

When an indenter is pressed into a gel to a fixed depth, the solvent in the gel migrates, and the force on the indenter relaxes. Within the theory of poroelasticity, the force relaxation curves for indenters of several types are obtained in a simple form, enabling indentation to be used with ease as a method for determining the elastic constants and permeability of the gel. The method is demonstrated with a conical indenter on an alginate hydrogel.


Lianhua Ma's picture

Dear Yuhang,

I am reading your  interesting paper.  As stated in your paper, combining  indentation and analytical formula  is surely an effective approach to characterize material parameters of gels.

1. I have a question regarding poroelastic relaxation and viscoelastic relaxation of gels. As you pointed out ,
"our indentation experiment shows that the relaxation behavior of the covalently crosslinked alginate hydrogel cannot be explained by viscoelasticity, but is consistent with poroelasticity",

Could you explain this in more detail? I am not familar with viscoelasticity, in Fig.4(b), F/h^2 has the dimension of stress, and the  relationship between F/h^2  and  t represents apparent relaxation behaviour, why can't this relaxation curve be explained by viscoelasticity? just because the viscoelastic relaxation time depends on the size of h?

2. Could you recommend some papers regarding the poroelastic relaxation time(which is quadratic in the radius of the contact)?

3. The FE simulation is also performed to simulate the indentation in this paper, Can we obtain the poroelastic properties of gels only by FE simulation?

Thank you

Yuhang Hu's picture

Hi Lianhua,


It is really one of the key points in this paper that indentation can be an effective way to differentiate viscoelasticity and poroelasticity. Time dependent behavior of gels can be due to the viscous relaxation of polymer network or the diffusion of solvent molecules in it. Viscous time is size independent while diffusive time scales with length square. In this indentation problem, h is the only length scale. So if the indentation depth is large, diffusive time can be much much larger than viscous relaxation time. In this case, if our observation time is long enough, we will mainly observe diffusive effect.


You are right at the point that the relaxation behavior can also be induced by viscoelasticity. But under mm length scale (as shown in my experiment), poroelasticity prevails. If we scale down the indentation depth to micrometer or nanometer, it is highly possible that we can observe both viscoelastic and poroelastic effects. I am also willing to capture it in my future work.


You can take the following references for your information:

C. Y. Hui, Y. Y. Lin, F. C. Chuang, K. R. Shull, and W. C. Ling, J. Polymer Sci B: Polymer Phys. 43, 359 (2006).

M. Galli and M. L. Oyen, CMES 48, 241 (2009).






Li Han's picture

Yuhang, nice work! Just my two cents. Maybe it is worthwhile to compare the diffusivity derived from your indentation measurement with a direct fluorescence measurement just to see how accurate the method is. Meanwhile, any idea why the numerical simulation seems to deviate more and more from your experimental data with time?

Again, congratulations. 


Li Han

Yuhang Hu's picture

Hi Li Han,

 Thank you for your valuable comment.

Indeed more experiments need to be done to further validate this method.

Comparison with fluorescence measurement is a good approach.

Alginate gel is self-degradable.

Its further relaxation may be due to it.

In another upcoming work, I will show much better result on PDMS gels.


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