# Kinetics of Spreading over Porous Substrates

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Spreading over Thin Porous Substrates

#### 2.1. Newtonian Liquids: Complete Wetting

^{*}) i.e., Δ<<h

^{*}. The drop is considered to have a low slope and the influence of gravity is assumed to be negligible. i.e., the only forces acting are capillary ones.

#### 2.2. Non-Newtonian Liquids: Complete and Partial Wetting Case

## 3. Spreading over Thick Porous Substrates

_{max}, and the radius of the wetted region on the surface, l/l

_{max}, behave differentially during the spreading process. The wetted volume inside the porous substrate was unknown, however, to make possible a comparison if this volume was modelled as spherical cup of contact angle ψ (inside the porous substrates). However, the relative dynamic contact angle, θ/θ

_{max}and the effective contact angle within the porous substrates, ψ/ψ

_{max}, show also a universal behaviour [35].

## 4. Spreading of Surfactant Solutions over Porous Substrates

- Stage one: Drop base expands until a maximum value of drop base is reached and the contact angle rapidly decrease throughout this stage to the value of static advancing contact angle, θ
_{ad}. - Stage two: Radius of the drop base remains constant and the contact angle decreases linearly with time until hydrodynamic receding contact angle is reached. Note, in the case the static receding contact angle is equal to zero and the observed receding contact angle can be determined by hydrodynamic reasons only, like in the case of complete wetting.
- Stage three: The drop base shrinks and the contact angle remain constant until the complete disappearance of the drop.

## 5. Spreading over Sponges

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Schematics of three stages of spreading/imbibition of droplet over porous substrate in the case of partial wetting: L

_{ad}is the maximum radius of droplet base, θ

_{ad}is the static advancing contact angle, t

_{ad}is the time when θ

_{ad}is reached, θ

_{r}is the static receding contact angle, t

_{r}is the time when θ

_{r}is reached and t* is the time when spreading/imbibition is finished completely. [35].

**Figure 2.**Schematics of two stages of spreading/imbibition of droplet over porous substrates in the case of complete wetting: L

_{m}is the maximum radius of droplet base, t

_{m}is the time when L

_{m}is reached, θ

_{m}is the contact angle at the moment t

_{m}, t* is the time when complete imbibition is finished and θ

_{f}is the final contact angle at t*. The contact angle θ

_{f}is completely determined by hydrodynamic reasons and has nothing to do with the static receding contact angle, because there is no contact angle hysteresis in the case of complete wetting [35].

**Figure 3.**Measured dependencies of radii of the drop base (L, mm) and radii of the wetted region inside the porous layer (l, mm) on time (t, s). All relevant values are given in [14].

**Figure 5.**Dimensionless radius of the blood droplet base in the case of spreading over silanized and untreated Whatman 903 paper [29].

**Figure 6.**Dimensionless dynamic contact angle of blood droplet in the case of spreading over silanized and untreated Whatman 903 paper [35].

**Figure 7.**Dimensionless radius of the blood droplet base in the case of spreading over nitrocellulose membrane. In the case of 0.2 μm pores of nitrocellulose membrane only stage 1 and 2 are present [38].

**Figure 8.**Dimensionless radius of contact angle in the case of spreading of blood droplets over nitrocellulose membrane. In the case of 0.2 μm membrane pores there is no stage 3, it is a continuation of stage 2. The contact angle remained almost constant value after stage 1 [38].

**Figure 9.**Contact angle (

**a**) and droplet base diameter dimensionless (

**b**) profiles for different percentage (%) concentrations of surfactants on dry audio sponge.

**Figure 10.**Contact angle (

**a**) and droplet base diameter dimensionless (

**b**) profiles for different percentage (%) concentrations of surfactants on dry dish sponge.

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Johnson, P.; Trybala, A.; Starov, V. Kinetics of Spreading over Porous Substrates. *Colloids Interfaces* **2019**, *3*, 38.
https://doi.org/10.3390/colloids3010038

**AMA Style**

Johnson P, Trybala A, Starov V. Kinetics of Spreading over Porous Substrates. *Colloids and Interfaces*. 2019; 3(1):38.
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**Chicago/Turabian Style**

Johnson, Phillip, Anna Trybala, and Victor Starov. 2019. "Kinetics of Spreading over Porous Substrates" *Colloids and Interfaces* 3, no. 1: 38.
https://doi.org/10.3390/colloids3010038