Compact and Thermosensitive Nature-inspired Micropump

Liquid transportation without employing a bulky power source, often observed in nature, has been an essential prerequisite for smart applications of microfluidic devices. In this report, a leaf-inspired micropump (LIM) which is composed of thermo-responsive stomata-inspired membrane (SIM) and mesophyll-inspired agarose cryogel (MAC) is proposed. The LIM provides a durable flow rate of 30 μl/h · cm2 for more than 30 h at room temperature without external mechanical power source. By adapting a thermo-responsive polymer, the LIM can smartly adjust the delivery rate of a therapeutic liquid in response to temperature changes. In addition, as the LIM is compact, portable, and easily integrated into any liquid, it might be utilized as an essential component in advanced hand-held drug delivery devices.


Theoretical estimation of the evaporation rate of the SIM
Evaporation occurs on the surface of the hydrophilic SIM with a contact angle of 71.1° ± 6.3° and on the exposed area of the MAC through the slit pores of the SIM when the LIM is exposed to a temperature lower than LCST. The pores of the SIM open as the material shrinks and the surface becomes hydrophobic with a contact angle of 90.1° ± 1.1° when the LIM is heated at a temperature higher than LCST. Evaporation also occurs at the hydrophobic SIM and the exposed area of the hydrophilic MAC through the open pores of the SIM.
The evaporation rate can be expressed as follows: where T is the absolute temperature of vapor, ( ) is the function of the contact angle of water vapor, [1,2] and S is the area of the evaporative surface. The wettability of the evaporative surface, which is changed by temperature variation, determines the value of ( ) . The deformability of the SIM determines the area of the evaporative surface. Therefore, the total evaporation rate on the SIM surface exhibits combined changes with respect to T, ( ), and S as temperature changes. For instance, the evaporation rate can be estimated as The evaporation rate on the surface of the SIM can be expressed as follows: eq 2), [3] where D is the diffusivity of vapor at ambient temperature, a is the radius of the bounding circle,

Effect of temperature on evaporation rate
From (eq.2), by assuming that all other factors are constant, the evaporation rate is exponentially increased as temperature increases.

Effect of relative humidity on evaporation rate
From (eq.2), by assuming that all other factors are constant, the evaporation rate is linearly decreased as relative humidity is decreased, where = −2 * .

Thermo-controlled pumping procedure of the micropump
The pumping rate of the pump is affected by the combined effect of water evaporation and swelling/deswelling features of the material composing the SIM. Therefore, we divided the evaporation of water in the SIM and the pumping of water from reservoir into four stages based on the variation and duration of temperature. ii. T > 33℃ (2 nd stage) When the temperature is higher than LCST, the pumping rate has a relationship with evaporation rate and water extrusion from the SIM as below.
where t is the duration time during which the temperature is higher than 33℃, and is the water extrusion rate from the SIM. Following the relations explained in supporting information 1.1, evaporation rate, , is the function of temperature T. As the water extruded from the SIM is absorbed at the MAC, increases with reducing ∆ between the MAC and the water reservoir. When the total evaporation from the pump exceeds the water extrusion from the SIM, the flow rate of the pump is smaller than the evaporation rate.
iii. T > 33℃, (3 rd stage) 13 When the temperature is maintained higher than 33℃, all of the absorbed water from THE SIM evaporates. Thus, the pumping rate and the evaporation rate become almost the same once again as iv. T < 33℃ (4 th stage) When the temperature is decreased lower than 33℃, the pumping rate has a following relationship for the evaporation rate and water absorption by the SIM.
where t is the duration time during which the temperature is lower than 33℃, and is the water absorption rate of the SIM. As temperature decreases lower than LCST, the SIM becomes to have hydrophilic feature and absorbs water. Therefore, the pumping flow rate of water is the sum of the evaporation flow rate and the water absorption rate of the SIM.