## 3 Results
### Pseudobinary MGS/RDA Films with Fixed MGS Amount  
In this set of experiments, a fixed amount of MGS was spread at the air-water surface of the Langmuir trough and RDA was added on top of it. Therefore, the supplementation of RDA resulted in an increased amount of total lipid at the air-water surface. This experimental regime emulates the _in vivo_ clinical administration of RDA, where the formulation will be delivered to a fixed amount of TFLL thus resulting in raised total lipid concentration at the ocular surface. The delivery of RDA represented via the number of oil phase (OP) molecules resulted (Figure 4) in (i) an increase in \(\pi\) achieved at the completion of the surface films compression and (ii) an overall shift of the \(\pi\)(A)-isotherms to higher \(\pi\) values. These effects are standard responses for surface layers when supplemented with extra surfactant quantities [13]. Brewster angle microscopy showed (Figure 5) that the delivery of RDA to MGS films resulted in overall thickening (raised brightness of the BAM images) of the films and disappearance of the monolayer regions in the layers upon supplementation with RDA at \(\leq\)50% of the film area. Figure 4: Surface pressure (\(\pi\))/area (A) isotherms of MGS/RDA pseudobinary films. Here MGS content is kept constant and the total lipid amount is increased by supplementation with RDA. This regime is similar to the effect of RDA delivery via eyedrops at the ocular surface (see main text or details). The supplementation with RDA is performed via droplets of the ophthalmic nanoemulsion and the pharmaceutical amount is quantified by the amount of molecules oil phase (OP) delivered to the MGS layer. It is thought that the stability of TFLL (and of the TF as a whole) at consecutive blinks is influenced by the lipid layer viscoelasticity [1; 2; 6; 22]. Hereof, the dilatational rheology of the films was examined via the step deformation technique allowing us to calculate the transient elasticity modulus \(\mathrm{E_{d}(t)}\) from the surface pressure relaxation transients:  
\[\mathrm{E_{d}(t)}=-\mathrm{A_{o}(d\pi(t)/dA)} \tag{2}\]  
where Ao is the initial film area and \(\Delta\)A is the area change. Figure 6 summarizes the dependences of the transient elasticity modulus on time which were analyzed via the Kohlrausch-Williams-Watts (KWW) equation (Equation (3)). \[\mathrm{E_{d}(t)}=\mathrm{E.~{}exp}\left(-(t/\gamma)^{\beta}\right)+\mathrm{E_{ EQ}} \tag{3}\]  
Figure 5: Thickening of MGS films supplied with RDA (brightness of the images is attenuated to ensure visibility) visualized with Brewster angle microscopy images (500 \(\mathrm{\SIUnitSymbolMicro m}\)\(\times\) 300 \(\mathrm{\SIUnitSymbolMicro m}\)). The amount of RDA delivered to the MGS film is quantified via the amount of molecules oil phase (OP) supplemented by the formulation. Figure 6: (**a**) Stress relaxation transients of MGS films supplied with extra amounts of RDA (quantified via the micrograms OP delivered by the formulation). (**b**) Stress relaxation transient fitted with Kohlrausch–Williams–Watts (KWW) equation (Equation (3)). For microscopically heterogeneous systems the fractional exponent \(\beta\leq 1\) (so-called stretched exponential) is a material characteristic that decreases further away from unity with increasing (i) the strength of interaction amongst the units and/or (ii) the film heterogeneity (i.e., augmented amount of interacting arrays) [23]. Physical interpretation of the values of \(\beta\) is provided by the spatial rearrangement model [24; 25]: 3/4--self-avoiding walks in 2D; 3/5--self-avoiding walks in 3D; 1/2--self-avoiding walks in 4D, Brownian motion, diffusion-limited growth/segregation; 1/3--anomalous diffusion on percolating clusters, growth of ensemble of clusters--Ostwald ripening, spinodal decomposition. Values of \(\beta\geq 1\) (compressed exponential) are also found in the \"jammed\" state of the soft matter where no fast relaxation channel exists [23].