## 2 Materials and Methods
The design of the experimental stand was based on the principle of geometric similarity (1):  
\[\frac{D_{w1}}{D_{w2}}=\frac{d_{DS1}}{d_{DS2}}=C, \tag{1}\]  
where \(D_{w1}\) is the diameter of a real wellbore, mm; \(d_{DS1}\) is the diameter of the real string, mm; \(D_{w2}\)--diameter of the experimental \"wellbore\", mm; \(d_{DS2}\) is the diameter of the experimental string, mm; and \(C\) is the coefficient of proportionality or \"constant of geometric similarity\". \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Unit** & **Value** \\ \hline \multicolumn{3}{c}{**Geometric Characteristics**} \\ \hline Stand base size & mm & 2700 \(\times\) 300 \\ Borehole diameter & mm & 74 \\ Pipe diameter & mm & 40 \\ The length of the “well” (equal to the length of the pipe) & mm & 2000 \\ Zenith angle of the “well” & degree & 0 \(\div\) 90 \\ sieve 1—cell & mm & 0.5 \(\times\) 0.5 \\ Sieve cleaning unit: & sieve 2—cell & mm & 1.0 \(\times\) 1.0 \\ sieve 3—cell & mm & 2.0 \(\times\) 2.0 \\ \hline \multicolumn{3}{c}{**Characteristics of Equipment and Measuring Devices**} \\ \hline Rotation per minute (drive) & rpm & 0–600 \\ Maximum pump performance & L/min & 258 \\ Tachometer laser (range) & rpm & 2.5–99,999 \\ Ultrasonic Doppler flow meter (range) & m/s & 0.03–12.2 \\ Scales electronic (range) & g & 5–40,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main technical characteristics of the experimental stand. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Unit** & **Value** \\ \hline Experiment series No. & - & 1 & 2 \\ \hline \(Q\)—consumption of BR & \(\times 10^{-3}\) m\({}^{3}\)/s (L/min) & 1.25 (75); 1.45 (87); 1.67 (100) & 0.83 (50); 1.05 (63); 1.25 (75) \\ \hline \(n\)—rotation frequency & s\({}^{-1}\) (rpm) & 0.83 (50); 1.67 (100); 2.50 (150) & 0.83 (50); 1.67 (100); 2.50 (150) \\ \hline \(Li\)—number of half-waves p & pcs & 0; 1; 3 & 0; 1; 3 \\ \hline \(\alpha\)—zenith angle & degree & 35; 55; 70 & 35; 55; 70 \\ \hline Rheological model of mud & - & DF No. 1—Newtonian model & DF No. 2—Pseudo-plastic model \\ \hline \(\rho\)—density & kg/m\({}^{3}\) & 1001 & 1035 \\ \hline PV (\(\eta\))—viscosity & mPa\(\cdot\)s & 0.941 (\(\eta\)) & 40.283 (PV) \\ \hline YP—yield point & Pa & - & 16.92 \\ \hline T—temperature & \({}^{\circ}\)C & 23 & 23 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The input parameters of the experiments. \[\frac{D_{w1}}{D_{w2}}=\frac{215.9}{74}=2.92;\ \frac{d_{DS1}}{d_{DS2}}=\frac{114.3}{40}=2.86;C \cong 2.89\approx 3\]  
\(DS\) deflection (wave amplitude) in the experimental stand (2) is represented as:  
\[f=\frac{(D_{w2}-d_{DS2})}{2} \tag{2}\]  
\[f=\frac{(74-40)}{2}=17\ \text{mm}\]  
In order to determine the effect of buckling on the destruction of mud plugs and well cleaning of cuttings particles, it was necessary to obtain an artificial buckling of the DS. At this stage of research, it was decided to abandon the creation of a system for smooth artificial regulation of the number of half-waves strings in favor of a simplified discrete system, due to the lack of knowledge of this drilling area and the need to test the hypothesis put forward. The half-waves strings were obtained by heating the pipes and subsequent irreversible bending deformation, while maintaining the diameter along the entire length. Thus, the pipes with 1 st and 3 rd half-waves were obtained, equal to the length of the well.