Osmosis-Based Pressure Generation: Dynamics and Application

<div><p>This paper describes osmotically-driven pressure generation in a membrane-bound compartment while taking into account volume expansion, solute dilution, surface area to volume ratio, membrane hydraulic permeability, and changes in osmotic gradient, bulk modulus, and degree of membrane fouling. The emphasis lies on the dynamics of pressure generation; these dynamics have not previously been described in detail. Experimental results are compared to and supported by numerical simulations, which we make accessible as an open source tool. This approach reveals unintuitive results about the quantitative dependence of the speed of pressure generation on the relevant and interdependent parameters that will be encountered in most osmotically-driven pressure generators. For instance, restricting the volume expansion of a compartment allows it to generate its first 5 kPa of pressure seven times faster than without a restraint. In addition, this dynamics study shows that plants are near-ideal osmotic pressure generators, as they are composed of many small compartments with large surface area to volume ratios and strong cell wall reinforcements. Finally, we demonstrate two applications of an osmosis-based pressure generator: actuation of a soft robot and continuous volume delivery over long periods of time. Both applications do not need an external power source but rather take advantage of the energy released upon watering the pressure generators.</p></div

Dynamics of osmotically-driven pressure generation and comparison of the model based on Equation 4 with experimental data.

<p>A. Time-dependent pressure generation as a function of PEG-4000 concentration inside the dialysis cassette. B. Time-dependent pressure generation as a function of various mechanical constraints of the volume inside the dialysis cassette. C. Pressure generation dynamics as a function of various initial surface area to volume ratios. The dashed orange curve represents an initial <i>A/V</i> ratio taken from extensor cells of the plant <i>Phaseolus coccineus</i>.<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Mayer1" target="_blank">[24]</a> D. Pressure generation dynamics as a function of various <i>L_p,0</i> values.</p

Dynamics of pressure generation as a function of various parameters. Each row represents one experiment.

<p>Dynamics of pressure generation as a function of various parameters. Each row represents one experiment.</p

Bioinspired application of an osmotic pressure generator for actuation of a soft robot.

<p><b>A</b>. Design concept of a previously described elastomeric soft robot whose arms curve and can grip objects in response to pressurization of parallel channels with boundaries of differing thickness. Adapted from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Ilievski1" target="_blank">[17]</a>. <b>B</b>. Guard cells in their open and closed states. Thick interior walls make guard cells curl when osmotically pressurized, opening stomata. Adapted from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Hill1" target="_blank">[28]</a>. <b>C</b>. Actuation of the soft robotic gripper used in this work in response to watering an attached osmotic pressure generator. The extent of deflection is shown after 1, 2, and 3 hours. <b>D</b>. System pressure and deflection angle (as defined in C) of the gripper as a function of time.</p

Dynamics of pressure buildup and release in plant extensor cells as calculated withEquation 4 and parameters based on literature values.

<p>The <i>L_p,0</i> value used in the calculations was 3.6×10⁻¹⁴ m Pa⁻¹ s⁻¹ <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Moshelion1" target="_blank">[25]</a>, the cell volume was 3.23×10⁻¹³ m³, the surface area was 2.02×10⁻⁸ (both estimated from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Mayer1" target="_blank">[24]</a>), and <i>V_in(P_in)</i> was <i>V_in = </i>(3.23×10⁻¹³)exp[1.06×10⁻⁶ <i>P_in</i>+0.047 ln(<i>P_in</i>)] (developed from literature bulk elastic modulus values<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Mayer1" target="_blank">[24]</a> and the definition of bulk elastic modulus<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Zimmermann1" target="_blank">[27]</a>). In these calculations <i>ΔΠ</i> followed the van't Hoff relation and <i>f</i> was assumed to be zero. A. Pressure buildup upon sudden introduction of an osmotic gradient with an initial <i>ΔΠ</i> of 1 MPa <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Eliassi1" target="_blank">[23]</a> B. Pressure release upon sudden disappearance of an osmotic gradient. Initial <i>P_in</i> was 1 MPa. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Eliassi1" target="_blank">[23]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0091350#pone.0091350-Mayer1" target="_blank">[24]</a> The difference between the maximum pressure from the pressurization curve and the starting pressure from the depressurization curve can be accounted for by the fact that our model assumes no significant biochemical regulation of osmotic pressure during this fast pressurization. As a consequence, the influx of water leads to a decrease in <i>ΔΠ</i>.</p